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Impact of Different Developmental Instars on Locusta migratoria Jumping Performance

Impact of Different Developmental Instars on Locusta migratoria Jumping Performance Hindawi Applied Bionics and Biomechanics Volume 2020, Article ID 2797486, 11 pages https://doi.org/10.1155/2020/2797486 Research Article Impact of Different Developmental Instars on Locusta migratoria Jumping Performance 1 2,3 2 4 1 Xiaojuan Mo , Donato Romano , Mario Milazzo, Giovanni Benelli, Wenjie Ge , 2,3,5 and Cesare Stefanini School of Mechanical Engineering, Northwestern Polytechnical University, 710072 Xi’an, China The BioRobotics Institute, Sant’Anna School of Advanced Studies, 56025 Pisa, Italy Department of Excellence in Robotics & A.I., Sant’Anna School of Advanced Studies, Pisa 56127, Italy Department of Agriculture, Food, and Environment, University of Pisa, 56124 Pisa, Italy Healthcare Engineering Innovation Center (HEIC), Khalifa University, Abu Dhabi, UAE Correspondence should be addressed to Donato Romano; donato.romano@santannapisa.it and Wenjie Ge; gwj@nwpu.edu.cn Received 28 April 2019; Revised 18 September 2019; Accepted 6 January 2020; Published 26 March 2020 Academic Editor: Mohammad Rahimi-Gorji Copyright © 2020 Xiaojuan Mo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Ontogenetic locomotion research focuses on the evolution of locomotion behavior in different developmental stages of a species. Unlike vertebrates, ontogenetic locomotion in invertebrates is poorly investigated. Locusts represent an outstanding biological model to study this issue. They are hemimetabolous insects and have similar aspects and behaviors in different instars. This research is aimed at studying the jumping performance of Locusta migratoria over different developmental instars. Jumps of third instar, fourth instar, and adult L. migratoria were recorded through a high-speed camera. Data were analyzed to develop a simplified biomechanical model of the insect: the elastic joint of locust hind legs was simplified as a torsional spring located at the femur-tibiae joint as a semilunar process and based on an energetic approach involving both locomotion and geometrical data. Asimplified mathematical model evaluated the performances of each tested jump. Results showed that longer hind leg length, higher elastic parameter, and longer takeoff time synergistically contribute to a greater velocity and energy storing/releasing in adult locusts, if compared to young instars; at the same time, they compensate possible decreases of the acceleration due to the mass increase. This finding also gives insights for advanced bioinspired jumping robot design. 1. Introduction Allometric changes such as longer limbs, greater muscu- lar force, greater contractile velocities, and muscular Humans develop locomotion ability at the age of around one mechanical advantages can be easily observed in most juve- year [1]. On the contrary, a wide number of animals get their nile vertebrates, improving their locomotion and boosting locomotion ability after being born [2]. This fact can be survival rates [2, 7–14]. However, although there is a wide related to the prolonged parental care performed by humans number of researches focused on the ontogenetic locomotion compared to other animal species, in which juvenile individ- ability in vertebrate animals [1, 7, 15–23], only a few studies uals often face the same survival pressure as adult ones. In are focused on invertebrate animals [2, 24–31], and most of addition, it is well known that those juveniles are exposed them are focused on the jumping ability of locusts. to higher rates of mortality because of their smaller sizes The jumping performance of different developmental and because of the hostile environment [3–6]. instars in various locust species have been largely investigated [2, 27–29]. The allometric growth of the metathoracic leg, the Ontogenetic locomotion research aims at answering two questions: (i) How do locomotion performances vary over increase in the mass of the femoral muscle relative to body different developmental stages? (ii) How may particular mass, and the lengthening of the semilunar processes con- components of the locomotion system change during growth? tribute to the augmentation of jumping performance from 2 Applied Bionics and Biomechanics Table 1: Weight and linear dimension parameters characterizing the tested third instars, fourth instars and adults of Locusta migratoria. Stage Weight (g) Body (mm) Femur (mm) Tibiae (mm) Tarsus (mm) Samples Third instar 0:24 ± 0:06 19:83 ± 1:58 10:58 ± 1:12 9:58 ± 0:94 3:90 ± 0:46 35 0:32 ± 0:09 23:56 ± 2:02 11:24 ± 0:93 10:21 ± 0:81 4:23 ± 0:54 Fourth instar 17 1:65 ± 0:36 44:61 ± 3:71 20:06 ± 1:69 18:72 ± 1:51 6:79 ± 0:91 Adult 29 mean exponent of 1.15 across ontogeny and was otherwise nymphs to adults [28]. The lengthening and thickening of the semilunar processes and the relative increase in the cross- unaffected by ambient temperature in the range of 15-35 C sectional area of the extensor apodeme [27] work together [39]. The energy stored by L. migratoria adults increases to make up a stiffer spring system in the adult hind leg. In disproportionately from fifth instars and is greater over Schistocerca gregaria Forskål, this helps the hind legs of characterizing jumps of young instars, supporting results adults to store twofold energy, developing a higher takeoff achieved on S. gregaria [29]. velocity, i.e., >2.5 m/s, which is necessary to initiate flight in A few researches focused on ontogenetic locomotion adults [27, 30]. development in invertebrates, and they specifically investi- The development and deposition of resilin in the energy gated the ontogenetic jumping performance of locusts [28, storage component for locust jumping has been investigated 29, 32, 34, 39–45]. However, little has been reported about by Burrows [32]. The thickness of the semilunar process and the configurations of hind legs during the takeoff phase in extensor resilin of newly molted instars and adults is initially locusts of different instars and their potential effect on the thinner, then it increases because of resilin deposition after jumping performances. Based on this, the present study each molting, showing a general growing trend ontogeneti- aimed to investigate if and how different hind leg configura- cally, while prior to a molt, the extensor resilin shows a tions during the takeoff can affect the jumping performances declining trend. The jumping ability and performance of in various developmental instars (i.e., third instar, fourth locusts at different life stages are consistent with the changes instar and adult). The geometrical parameters of L. migra- that occur during each molting cycle, which affect the energy toria individuals were combined with experimental data to store [32]. The energy stored during the deformation of the set up a simplified mathematical model to assess the jumping semilunar process, composites of hard cuticle and the performance of the tested locusts, and to explain the energy rubber-like protein resilin, is around 50% of the jumping shift from L. migratoria nymphs to adults [2, 7, 27]. energy needed. In addition, it has been demonstrated that layered resilin/cuticle composites all share a similar distribu- 2. Materials and Methods tion in the five nymphal stages and in adults in locusts [33]. This structure may be ubiquitous in jumping insects and play 2.1. Experimental Setup and Material Preparation. A set of 29 an important role in energy storing for jumping, in addition L. migratoria adults, 17 fourth instars, and 35 third instars, to the energy stored in the muscles. was reared in different cylindrical transparent plastic boxes The adults of the American locust, Schistocerca ameri- (50 cm in diameter and 70 cm in length) with a 16 : 8 (L : D) cana Drury, develop high-power, low-endurance jumps, h photoperiod at 25 ± 1 C, 40 ± 5% RH. Temperature and while the juveniles perform less-power, high-endurance RH conditions were the same during experiments. The health jumps [34], which is different from vertebrates [7, 15, 22, of each locust was constantly checked during the whole 35]. This can be explained by the fact that juvenile locusts period assuring proper diet composed of wheat, fresh vegeta- use repeated jumping acts to escape from a wide number of bles, and water ad libitum [44, 46, 47]. The experiments were their predators, with special reference to invertebrate ones carried out by using healthy locusts with no injuries (e.g., no (e.g., spiders and mantis) [29]. Besides, adults have to achieve damaged legs, wings, or antennae). The tested locusts were a powerful jump to initiate flight in order to escape from fas- used at least 24 h after molting, to reduce the potential influ- ter predators, such as frogs, lizards, and birds, moving away ence of soft newborn cuticles and small muscle mass on their with powerful flapping and gliding [29, 36–38]. The trade- locomotion and jumping performance [32, 39, 48]. off between jumping power and endurance is consistent with All the locusts were weighed to 0.01 g with a scale. The the ontogeny of life-history behaviors. However, juvenile dimensions of the main features (i.e., femur, tibiae, and tarsus locusts also use hopping as a model of locomotion exhibiting length) were measured to the nearest 0.01 mm using a caliper. adifference between predator escape jumps and normal loco- Table 1 reports the results as mean value ± SD before testing motion jumps [29, 34]. In this framework, the effects of the their jumping performances. various instars on jumping performances of the African A white-colored solid jumping platform was positioned desert locust S. gregaria were investigated with an ontoge- inside a foam box (70 × 35 × 30 cm). The jumping platform netic growth model [29]. Results show that force, accelera- was lit with four LED illuminators (RODER SRL, Oglianico tion, takeoff velocity, and kinetic energy, except power TO, Italy) which emit red light (420 lm each at k = 628 nm) output, varied as an exponential function of body mass. to match the maximum absorption frequency of the camera Furthermore, a study on the effect of body mass and tem- [49–53]. The jumping behavior of each locust was stimu- perature on the jumping performance of L. migratoria lated by teasing the rear of its body with a transparent plastic indicates that jump energy scaled with body mass with a bar (2 mm diameter), to elicit the maximum “escape jumps.” Applied Bionics and Biomechanics 3 The tracking paths were carefully checked to ensure that Femur the tracking path corresponded to the raw image sequences [49]. Tracked center pixels of each video were converted into 3 distances measured in millimeters with a scale ratio based on Body Tibiae the graph paper and imported into the MATLAB software (MATLAB and Statistics Toolbox Release 2012b, The Math- Works, Inc., Natick, Massachusetts, United States). x 2.3. Statistical Analysis. The influence of life stage on the con- Ground sidered parameters, i.e., the time intervals of different phases (cocking time, takeoff time, and release time), takeoff angle, Figure 1: Simplified mechanical model of a L. migratoria. legs’ configuration over time, velocities at T , T , and K 3 4 values (elastic parameters of tested jumps), and dimension The jumps of each locust were recorded for 5 times inter- parameters were analyzed separately using a general linear spersed by 10 minutes to allow the locusts to have a total model with the following structure: y = βX + ε, where y is recovery between jumps [43, 44]. Tested locusts jump from the vector of the observations with normal distribution (i.e., a prepared platform, and the body of locust body axis during takeoff time, velocity at T , or takeoff angle), β is the inci- the jumps is theoretically perpendicular to the axis of the 3 dence matrix linking the observations to fixed effects, X is camera. Jumps deviating more than 15 with respect to the the vector of fixed effects (i.e., locust developmental instars), perpendicular plane to the axis of the camera lens were and ε is the vector of the random residual effects. ANCOVA excluded to limit the difference between the actual and per- (analysis of covariance) was used to analyze the effect of life ceived takeoff angle [39]. A Hotshot 512 sc high-speed cam- stage on the jumping performance while considering body era (NAC Image Technology, Simi Valley, CA, USA) was weight as a covariate, due to the fact that the difference of used to record 2000 fps videos of the jumping tasks and store body weight is inevitable and the effect of body weight on sequential 7600 images with a resolution of 512 × 512 pixels the jumping performance should be elicited from the effect directly into its internal memory. All the samples were ana- of life stage. A threshold P value of 0.05 was set to test the sig- lyzed via the ProAnalyst Suite (Xcitex, Cambridge, MA, nificance of differences between means. Post-hoc letters USA) to track the locust centroid trajectory for each jump. obtained by Tukey’s HSD test separated averages. 2.2. Model Description. A simplified mechanical model of a L. 3. Results migratoria locust is depicted in Figure 1. The body, the femur, and the tibiae are outlined as three rigid bars. The x A set of 81 jump videos of different locusts (29 adults, 17 axis coincides with the ground, and θ is the angle between fourth instars, and 35 third instars) was analyzed with the the body and the x axis: when the distance of the body line abovementioned methods. The results for all the parameters to the x axis increases positively, the value of θ is positive; are illustrated within the following subsections. otherwise, the value is negative. θ is the angle between the femur and body: when the femur line is upon the body line, 3.1. Time Intervals and Takeoff Angles of Tested Locusts. The the value of θ is positive; otherwise, the value is negative. cocking time (F =2:4780 ; P =0:0906, Figure 2(a)) and 2,80 θ is the angle between the femur and the tibiae. θ is the 3 4 takeoff time (F =2:7304 ; P =0:0715, Figure 2(b)) charac- 2,80 angle between the tibiae and the x axis. Both the values of terizing third instars, fourth instars, and adults of L. migra- θ and θ are strictly positive due to the structure of locust 3 4 toria locusts showed no significant differences, while the hind legs. release time ( F =6:2732 ; P <0:05, Figure 2(c)) showed 2,80 The cocking time was defined as the time interval needed significant differences among third instar, fourth instar, and for a L. migratoria individual to prepare to jump, from con- adult locusts. The release time of third instar locusts was sig- tracting the hind legs backward (T ) to being ready to jump nificantly longer than adult and fourth instar locusts (T ). The takeoff time is the time interval from the first (Figure 2(c)). The trajectory of the body center during the observed movement of the hind leg (T ) to the detection of takeoff phase of L. migratoria was close to a straight line, hind legs losing contact with the ground ðT Þ. The release and takeoff angle was defined as the slope angle of the body time is the time interval from the moment in which the hind center trajectory of the tested locusts during takeoff [54, legs lose contact with ground ðT Þ to the moment when the 55]. Considering the takeoff angle, no significant differences hind legs stop moving and are kept in a fixed position relative were detected in third instar, fourth instar, and adult locusts to body ðT Þ. ðF =0:8065 ; P =0:4502Þ . 2,80 Images of the jumping at T , T , T , and T , respectively, 1 2 3 4 θ and θ were significantly affected by the insect were carefully picked out from sequential images to evaluate 1 2 instars at T . Both θ (F =3:1813 ; P <0:05, the geometrical and temporal parameters (i.e., θ , θ , θ , θ , 2 1 2,80 1 2 3 4 Figure S1b, in supplementary materials attached) and θ cocking time, takeoff time, and release time) via Microsoft (F =3:5052 ; P <0:05)of adult locusts were significantly Office Visio. The centroid of each locust was tracked during 2,80 smaller than fourth instar locusts. θ (F =7:5272 ; P <0:05, each jump by considering it positioned between the base of 3 2,80 the middle and hind legs and bilaterally symmetrical from Figure S1c) of fourth instar locusts at T was significantly the vertical view [54]. higher than that of third instar locusts. θ 3 4 Applied Bionics and Biomechanics 400 30 Third instar Fourth instar Adult Third instar Fourth instar Adult (a) (b) AB Third instar Fourth instar Adult Third instar Fourth instar Adult (c) (d) Figure 2: Mean cocking time (a), takeoff time (b), release time (c), and takeoff angles (d) of third instar, fourth instar, and adult L. migratoria. Different letters above each column indicate significant differences (P <0:05). Whiskers represent standard errors. (F =3:8030 ; P <0:05) of third instar locusts at T was (F =4:3591 ; P <0:05) and more than twice those of 2,80 4 2,80 significantly smaller than fourth instar ones. θ adults (3.3%) and fourth instars (2.19%) (Table 2). (F =5:8588 ; P <0:05)and θ (F =4:6958 ; P <0:05, The elasticity of the hind legs is simplified as a torsional 2,80 4 2,80 spring (torsional stiffness: K) at femur-tibiae joints [56], the Figure S1d) of fourth instar locusts were significantly smaller displacement in the vertical direction at T and T are h than third instar ones at T . Based on the established 3 4 3 and h , the mass of locust is m, and the gravitational acceler- simplified model in Figure 1, mean configurations of tested adult fourth instar and third instar locusts at T , T , T ,and T ation is g, equals to 9.81 m/s . The velocity of the mass center 1 2 3 4 at T was set as 0 m/s, and the velocity of the mass center is v are plotted (Figures S2a, S2b, and S2c in supplementary 2 3 materials) using the mean dimension parameters (Table 1), and v at T and T , respectively. The values of θ at T , T , 4 3 4 3 2 3 and T are θ , θ , and θ , respectively. θ was considered center position tracking results, and mean angle data (Figure S1). 4 32 33 34 34 to be the free position of the torsional spring. Based on energy conservation, the following formulas were used: 3.2. Velocities at T and T and Elastic Element Parameter of 3 4 Tested Locusts. The velocity at T (F =9:8738 ; P <0:05) 3 2,80 E = mgh +0:5mv , 3 3 3 and T (F =10:5871 ; P <0:0001) were significantly 4 2,80 ð1Þ E = mgh +0:5mv , affected by the tested L. migratoria instar. The velocity at 4 4 4 T and T of third instar individuals was significantly 3 4 smaller when compared to that of adults and fourth instars 2 2 ð2Þ mgh + mv =0:5KðÞ θ − θ −ðÞ θ − θ : (Figures 3(a) and 3(b)). For the third instar, fourth instar, 3 3 32 34 33 34 and adult locusts, the mean velocities at T were bigger than the mean velocities at T . The velocity decrease percentage The energy of locusts at T and T were defined in Equa- 3 4 from T to T of third instars (7.7%) is significantly higher tion (1) individually, and the corresponding values were 3 4 Time (ms) Time (ms) Angle (°) Time (ms) Applied Bionics and Biomechanics 5 3 3 2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 0 0 Third instar Fourth instar Adult Third instar Fourth instar Adult (a) (b) 2.5 1.5 –1 0.5 –2 0 12 3 4 Third instar Fourth instar Adult 2 2 2 0.5[(𝜃 −𝜃 ) −(𝜃 −𝜃 ) ] [rad ] 32 34 33 34 Adult Fourth instar Third instar (c) (d) Figure 3: Mean velocities of third instar, fourth instar, and adult L. migratoria at T (a) and T (b). (c) Mean K value calculated based on 3 4 Equation (2) of all tested third instar, fourth instar, and adult locusts separately. Different letters above each bar indicate significant differences (P <0:05). Whiskers represent standard errors. (d) The relationship between the jump energy of locusts after takeoff phase at 2 2 T moment and 0:5½ðθ − θ Þ − ðθ − θ Þ  of all tested third instar, fourth instar, and adult locusts’ jumps. 3 32 34 33 34 Table 2: Mean velocity and energy of tested L. migratoria at T and T moments. 3 4 Type Weight (g) E mJ E mJ v (m/s) v (m/s) v − v /v ðÞ ðÞ ðÞ 3 4 3 4 3 4 3 Third instar 0:24 ± 0:06 0:27 ± 0:15 0:24 ± 0:15 1:43 ± 0:42 1:32 ± 0:43 7.7% 0:32 ± 0:09 0:55 ± 0:24 0:55 ± 0:27 1:82 ± 0:25 1:78 ± 0:32 Fourth instar 2.19% Adult 1:65 ± 0:36 3:89 ± 2:21 3:71 ± 2:38 2:12 ± 0:65 2:05 ± 0:69 3.30% listed in Table 2. Based on Equation (2), elastic param- 3.3. Hind Leg Length of Tested Locusts. The tibiae length of eter K values of all tested jumps were calculated with hind legs was significantly affected by L. migratoria instar known kinematic data and angle data. Elastic parameter (F =24:4218 ; P <0:001). The tibiae length of adults was 2,80 K was significantly affected by the insect instars significantly longer than that of fourth and third instars (F =5:2980 ; P <0:05), and K of tested adult locust (Figure S3a, in supplementary materials attached). The 2,80 jumps was significantly higher than that of fourth instar femur length of hind legs was significantly affected by L. and third instar locust jumps (Figures 3(c) and 3(d)). migratoria instar (F =18:3199 ; P <0:001). This femur 2,80 Velocity (m/s) K (Nmm/rad) Energy (mJ) Velocity (m/s) 6 Applied Bionics and Biomechanics 1 7 0 3 –1 –2 0.5 1 1.5 2 –1 0 1 –1 0 1 10 10 10 10 10 10 Mass (g) Mass (g) Mass (g) Adult Adult Third instar Adult Third instar Fourth instar Fourth instar Fitted result Fourth instar Fitted result Third instar (a) (b) (c) Figure 4: (a) The allometric relationship between jump energy and body mass of all tested third instar, fourth instar, and adult locust jumps. 1:342±0:16 2 All tested jumps were included in the regression: E =1:8018m (R =0:8288). (b) The allometric relationship between mass-specific work (the ratio of jump energy divided by body mass) and body mass of all tested third instar, fourth instar, and adult locusts’ jumps. All 0:342±0:136 2 tested jumps were included in the regression: E =1:8018m (R =0:2388). (c) The allometric relationship between mass-specific work and body mass of all tested third instar, fourth instar, and adult locust jumps. The straight red, blue, and black lines are the average ratio of jumping energy divided by body mass of all tested third instar, fourth instar, and adult locusts individually. length of adults was significantly longer than that of fourth effect, small size jumpers, such as fourth and third instar and third instars (Figure S3b, in supplementary materials locusts, should reach similar (or slightly higher) takeoff attached). The ratio of tibiae length to femur length of velocities if compared to adult locusts. However, experimen- hind legs was not significantly affected by L. migratoria tal results disagree with both conclusions. Firstly, mass- instars (F =0:1378 ; P =0:8715). The relation between specific works showed an increasing trend during growing 2,80 mass and hind leg femur length and tibiae length of tested (Figures 4(b) and 4(c)). Secondly, even though adult locusts third instar, fourth instar, and adult locusts were included have bigger masses than younger instar ones (Table 2), adults 0:3144±0:0259 in the regression L =16:7880m ðR =0:8806Þ have significantly larger takeoff velocities (Figure 3(a)). These femur 0:3299±0:0241 and L =15:5597m ðR =0:9033Þ individually apparent paradoxes showed that L. migratoria locusts at dif- tibiae (Figure S4a and Figure S4b, in supplementary materials ferent developmental instars cannot be expected to perform attached). as geometrically similar jumpers. The relation between mass and energy of all tested jumps 4. Discussion of third instar, fourth instar, and adult locusts (Figure 4(a)) 1:342±0:16 was included in the regression: E =1:8018m How locust morphology can vary to fit the mutable (R =0:8288). Similar regression values were concluded in mechanical demands of increasing body size and mass 1:14±0:09 2 two separate studies: E =1:91m (R =0:96) for L. has been investigated by specific scaling models or allom- 1:114 2 migratoria juveniles [39] and E =1:7906m (R =0:939) etries [27–29]. In our study, jumping performance related [29] for S. gregaria juveniles. In both published research, to some specific parameters (viz. tibiae length, body adult locusts’ jumps have greater kinetic energy than the weight, and main joint angles) of L. migratoria individuals value predicted using the regression that concluded using at different life stages were analyzed. Results showed that only juveniles; for example, S. gregaria adults produces the jumping performance of L. migratoria adults outper- around four times as much kinetic energy as the regression formed those of young instars, both in terms of absolute predicted for juveniles using adult body mass [29]. In our velocity (Figure 3(a)) and mass specific work (Figure 3(f)). experiment, the regression included tested jumps of both Suppose L. migratoria locusts at different developmental adult and instar locusts, because the regression using only instars follow a geometrically similar jump model [57], where 1:8018±0:4840 2 juveniles is E =3:5278m (R =0:5473) and the both skeletal and muscular properties obey the laws of geo- coefficient of determination R is 0.5473, which is relatively metric scaling—“muscle work”—which means the energy lower than that including both adult and instar locusts delivered during the push-off should scale at the same rate of mass and mass-specific works are independent of scale. (R =0:939). If we adopt the regression using only juveniles to predict the kinetic jumping energy of adults, the pre- Two conclusions should be obtained based on this model: (i) The specific energy (E /m) should be the same for all dicted jumping energy is greater than the real kinetic energy, which is different from previous published results. tested instars and adults of L. migratoria. (ii) Due to a size E (mJ) E /m (mJ/g) E /m (mJ/g) 3 Applied Bionics and Biomechanics 7 96 10.5 9.5 90 9 88 8.5 86 8 7.5 82 7 5 10 15 20 5 10 15 20 25 30 Age Age Male Male Female Female (a) (b) Figure 5: (a) The development curve of skelic index and age [69]. (b) The development curve of average velocity of 100 m sprint best record and age [70]. Considering the state of the art, the authors examined the spring rather than a rigid bending lever in S. gregaria [42]. scaling ofjumpingperformance inL. migratoria to understand The obvious deflection of tibiae during takeoff [60] can store whether there is a connection between functional and mor- at least 10% of the total kinetic energy of the jump [42]. The phological designs. Even though adult locusts have body effect of leg compliance on jumping performance is also masses bigger than fourth instar and third instar locusts investigated in jumping robots [61, 62], and results demon- (Table 2), adults have significantly higher velocity and energy strated that proper leg compliance can improve the perfor- after takeoff (Table 2). This result is comparable with existing mance of a jumping robot using the initially stored energy research focused on S. gregaria. Juvenile S. gregaria locusts in the compliant legs to be used. Based on this, the significant increase in tibiae length were considered meaningful to produce takeoff velocities of 0.9-1.2 m/s, while adult locusts show takeoff velocities around twice as high as that of juveniles improve jumping performances of adult locusts. (2.5 m/s) [29]. In addition, the kinetic energy of the jump in S. Secondly, the established mechanical model revealed gregaria have values that range from a low of 0.004 mJ in afirst- that locust adults have a significantly bigger K value if instar locust to as high as 15.99 mJ in an adult [29]. The greater compared to fourth instar and third instar individuals (Figure 3(c)). This seems directly connected with the better takeoff velocity in adult locusts and excellent jumping perfor- mance can be explained by different reasons. jumping performance characterizing adult locusts. A sharp Firstly, the lengths of the femur and tibiae show a signif- improvement of velocity and energy in adults is reported icant increase in L. migratoria individuals during its devel- to be a result of the combination of a bigger mean cross- opment, in a comparable manner to results previously sectional area of the femur muscle [28, 63, 64] coupled with the fact that a rather long life span gives adult locusts lon- achieved on S. gregaria [42]. Jump distance is demonstrated to be proportional to the distance through which the force ger time to stiffen their semilunar process and extensor acts [41, 58, 59], which is related directly to limb length. cuticle [27, 32, 40, 65, 66]. A stiffer spring system in adults Thus, the relatively longer legs (including the femur and tib- was also estimated by the abovementioned modeling, where iae) of older juveniles likely provide the approaches to propel the elasticity of the hind legs of locusts was supposed to be modeled as a torsional spring located at the femur-tibiae these animals farther and with greater jump energy [39]. In addition, the muscle mass in the femurs of adult locusts joint [56], neglecting other elastic contributions [67, 68]. shows a higher percentage of body mass compared to those The results showed that the stiffness of fourth instar and in young instar locust [27] and shows an aligned increase in third instar locusts are close, and rather smaller than that the angle of muscle pennation [28]; both lead to a greater of adults, differing by orders of magnitude. Finally, due to the viscoelasticity of muscular tissues, longer capacity for energy storage and greater jump velocity [28]. The importance of tibiae mechanical property has been takeoff times in adults L. migratoria decrease the energy con- investigated [29, 42], and the authors pointed out that the sumption during takeoff caused by internal dissipative forces. increase of tibiae length in S. gregaria during growth can help There is an interestingly similar phenomenon in locusts 2 2 locusts to adapt to the acceleration decrease caused by the and humans. The value of 0:5½ðθ − θ Þ − ðθ − θ Þ  in 32 34 33 34 increase of body mass [42] with an enlarged takeoff time in fourth instar locusts showed an increasing trend compared adults. James et al. also reported that the increased relative to third instar ones, while for adult locusts it showed a hind limb length and relative mass of jumping muscles decreasing trend (Figure 3(d)). This is very similar to the ensure the improvement of jumping performance [58]. In skelic index (standing height minus sitting height divided contrast, Katz and Gosline stressed that tibiae play an impor- by sitting height and multiplied by 100) development trend in human beings (Figure 5(a)); the skelic index has its tant role during the takeoff phase and work like a bending Skelic index Average velocity (m/s) 8 Applied Bionics and Biomechanics is compensated by peculiar morphological design and stiff- maximum value at around 15 years old and then decreases. Both the takeoff velocity of tested locusts (Figure 3(a)) and ness. Longer hind legs boost the acceleration time and com- average velocity of 100 m sprint best record (Figure 5(b)) pensate for the supposed acceleration decrease [29, 42]. A showed an increasing trend until becoming adults. The best bigger tibiae-to-femur ratio means a relatively longer tibiae, locomotion performance for both locusts and humans hap- supporting the prediction that the tibia works as a leaf spring pens in adults. It likely conveys that the locomotion perfor- and the deflection of tibiae can store a significant part of mance is a combined result of both geometrical parameters energy needed by each jump. The spring system of locust and material property. For adults, the best geometrical hind legs is composed by elastic cuticles and a semilunar pro- 2 2 cess. The thickness of the semilunar process and extensor parameters (0:5½ðθ − θ Þ − ðθ − θ Þ  for locusts and 32 34 33 34 skelic index for humans) and best material property (muscle resilin show a general increasing trend during development, occupation rate and elastic parameters) are achieved simulta- while decreasing during molting [32]. The stronger spring neously and result in the best locomotion performance. system in adult locusts is consistent with the calculation Interestingly, the percentage velocity difference from T results based on a simplified mathematical model proposed to T strongly increases as the body size decreases, from here. The stiffer spring system and bigger muscle occupation adults (3.3%) and fourth instar (2.19%) to third instar rate work together to improve the adult locust jumping per- locusts (7.7%) (Table 2). This phenomenon may be con- formance [32]. This study adds basic knowledge on the nected to the fact that smaller instars have a higher frontal jumping mechanisms in various developmental instars of L. area-to-body mass ratio compared to larger instars, which migratoria locusts considering a different leg configuration makes them more susceptible to the effects of aerodynamic as well as body mass, length of hind legs, velocity, and energy. drag [39, 71]. Another possible reason is the longer release We also proposed a simplified mathematical model to calcu- time in third instar locusts. The takeoff angles in all tested late the elastic features of each jump in young instars and locusts are similar, close to 45 , helping to maximize the adults of L. migratoria. jumping distance [39, 72, 73]. The ontogenetic jumping performance of locusts In agreement with the findings obtained studying S. reported here can inspire roboticists to select the most suit- americana [34], the compromise between power and endur- able instars as a model organism to design advanced jumping ance was noticed in the present research. Indeed, L. migra- robots. Firstly, jumping represents the only locomotion toria adults took a longer time than 10 minutes to be ready mode (e.g., early instar locusts) or can be coupled with flap- for the next jump. In several instances, after recording a pow- ping and gliding wings (e.g., adult locusts). Secondly, the erful jump in an adult locust, it was hard to record another mass (Table 1), the consumed energy (Table 2), and the elas- one, while the situation was different for fourth instar and tic parameter K (Figure 3(c)) increase around one order of third instar locusts. After a less powerful jump, it took less magnitude from third instar to adult locusts, which con- time before the next one was ready for another jump and they vinces us that size and weight are key parameters in jumping were willing to jump another time if stimulated again within robot design together with the elastic and actuation systems. a short time interval. Thirdly, it is important to consider geometrical parameters in Overall, we detected a longer takeoff time in adult locusts, robots’ design, due to the significant variation of geometrical if compared to young instars, although the velocity was param eters (e.g., joint angles, tibiae length and the ratio of higher and the release time shorter, probably to allow the tibiae length to femur length of hind legs) in locusts and their spread of wings to start the flight. Locusts can learn motor impact on jumping performance. actions at the level of the single ganglia [74]. Therefore, a lon- ger takeoff time, as well as a higher velocity and a shorter Data Availability release time, could be chieflyinfluenced by their increasing motor experience from young instar to adult. Furthermore, The excel data used to support the findings of this study are the specialization of leg control seems to be related to partic- available from the corresponding author upon request. ular neural circuits involved in sensory-motor mechanisms occurring within the prothoracic ganglion of these insects Conflicts of Interest [75, 76]. In addition, adults were found to be more efficient in storing energy in their hind legs and releasing it during The authors declare that there is no conflict of interest the jump. Indeed, K of tested adults’ jumps were significantly regarding the publication of this paper. higher compared to that of fourth and third instars: this could be related to a more efficient composite storage device, Acknowledgments consisting of a greater mass of soft resilin and a thicker hard cuticle in adult locomotor structures due to growth, contrib- The authors want to thank the BioRobotics Institute, San- uting to adults with enhanced performances during the t’Anna School of Advanced Studies and the China Scholar- jumping behavior [77–79]. Further research is still needed ship Council (CSC) for funding this research. This research to shed light on the abovementioned issue. was also supported by the National Key Research and Devel- In conclusion, velocity after takeoff and energy per jump opment Program of China under Grant 2017YFB1300101 are significantly higher in adult locusts over the fourth and and the EU H2020 Project “Submarine cultures perform third instars, while the body mass of adult locusts is a half long-term robotic exploration of unconventional environ- magnitude bigger than the fourth and third instar ones. This mental niches” (subCULTron) (640967FP7). Applied Bionics and Biomechanics 9 [9] J. Westerga and A. Gramsbergen, “The development of loco- Supplementary Materials motion in the rat,” Developmental Brain Research, vol. 57, Figure S1: (a) the mean values of θ , θ , θ , and θ of tested no. 2, pp. 163–174, 1990. 1 2 3 4 adult, fourth instar, and third instar locusts separately at T 1 [10] G. A. Cavagna, P. Franzetti, and T. Fuchimoto, “The mechan- (a), T (b), T (c), and T (d). 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Impact of Different Developmental Instars on Locusta migratoria Jumping Performance

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Hindawi Applied Bionics and Biomechanics Volume 2020, Article ID 2797486, 11 pages https://doi.org/10.1155/2020/2797486 Research Article Impact of Different Developmental Instars on Locusta migratoria Jumping Performance 1 2,3 2 4 1 Xiaojuan Mo , Donato Romano , Mario Milazzo, Giovanni Benelli, Wenjie Ge , 2,3,5 and Cesare Stefanini School of Mechanical Engineering, Northwestern Polytechnical University, 710072 Xi’an, China The BioRobotics Institute, Sant’Anna School of Advanced Studies, 56025 Pisa, Italy Department of Excellence in Robotics & A.I., Sant’Anna School of Advanced Studies, Pisa 56127, Italy Department of Agriculture, Food, and Environment, University of Pisa, 56124 Pisa, Italy Healthcare Engineering Innovation Center (HEIC), Khalifa University, Abu Dhabi, UAE Correspondence should be addressed to Donato Romano; donato.romano@santannapisa.it and Wenjie Ge; gwj@nwpu.edu.cn Received 28 April 2019; Revised 18 September 2019; Accepted 6 January 2020; Published 26 March 2020 Academic Editor: Mohammad Rahimi-Gorji Copyright © 2020 Xiaojuan Mo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Ontogenetic locomotion research focuses on the evolution of locomotion behavior in different developmental stages of a species. Unlike vertebrates, ontogenetic locomotion in invertebrates is poorly investigated. Locusts represent an outstanding biological model to study this issue. They are hemimetabolous insects and have similar aspects and behaviors in different instars. This research is aimed at studying the jumping performance of Locusta migratoria over different developmental instars. Jumps of third instar, fourth instar, and adult L. migratoria were recorded through a high-speed camera. Data were analyzed to develop a simplified biomechanical model of the insect: the elastic joint of locust hind legs was simplified as a torsional spring located at the femur-tibiae joint as a semilunar process and based on an energetic approach involving both locomotion and geometrical data. Asimplified mathematical model evaluated the performances of each tested jump. Results showed that longer hind leg length, higher elastic parameter, and longer takeoff time synergistically contribute to a greater velocity and energy storing/releasing in adult locusts, if compared to young instars; at the same time, they compensate possible decreases of the acceleration due to the mass increase. This finding also gives insights for advanced bioinspired jumping robot design. 1. Introduction Allometric changes such as longer limbs, greater muscu- lar force, greater contractile velocities, and muscular Humans develop locomotion ability at the age of around one mechanical advantages can be easily observed in most juve- year [1]. On the contrary, a wide number of animals get their nile vertebrates, improving their locomotion and boosting locomotion ability after being born [2]. This fact can be survival rates [2, 7–14]. However, although there is a wide related to the prolonged parental care performed by humans number of researches focused on the ontogenetic locomotion compared to other animal species, in which juvenile individ- ability in vertebrate animals [1, 7, 15–23], only a few studies uals often face the same survival pressure as adult ones. In are focused on invertebrate animals [2, 24–31], and most of addition, it is well known that those juveniles are exposed them are focused on the jumping ability of locusts. to higher rates of mortality because of their smaller sizes The jumping performance of different developmental and because of the hostile environment [3–6]. instars in various locust species have been largely investigated [2, 27–29]. The allometric growth of the metathoracic leg, the Ontogenetic locomotion research aims at answering two questions: (i) How do locomotion performances vary over increase in the mass of the femoral muscle relative to body different developmental stages? (ii) How may particular mass, and the lengthening of the semilunar processes con- components of the locomotion system change during growth? tribute to the augmentation of jumping performance from 2 Applied Bionics and Biomechanics Table 1: Weight and linear dimension parameters characterizing the tested third instars, fourth instars and adults of Locusta migratoria. Stage Weight (g) Body (mm) Femur (mm) Tibiae (mm) Tarsus (mm) Samples Third instar 0:24 ± 0:06 19:83 ± 1:58 10:58 ± 1:12 9:58 ± 0:94 3:90 ± 0:46 35 0:32 ± 0:09 23:56 ± 2:02 11:24 ± 0:93 10:21 ± 0:81 4:23 ± 0:54 Fourth instar 17 1:65 ± 0:36 44:61 ± 3:71 20:06 ± 1:69 18:72 ± 1:51 6:79 ± 0:91 Adult 29 mean exponent of 1.15 across ontogeny and was otherwise nymphs to adults [28]. The lengthening and thickening of the semilunar processes and the relative increase in the cross- unaffected by ambient temperature in the range of 15-35 C sectional area of the extensor apodeme [27] work together [39]. The energy stored by L. migratoria adults increases to make up a stiffer spring system in the adult hind leg. In disproportionately from fifth instars and is greater over Schistocerca gregaria Forskål, this helps the hind legs of characterizing jumps of young instars, supporting results adults to store twofold energy, developing a higher takeoff achieved on S. gregaria [29]. velocity, i.e., >2.5 m/s, which is necessary to initiate flight in A few researches focused on ontogenetic locomotion adults [27, 30]. development in invertebrates, and they specifically investi- The development and deposition of resilin in the energy gated the ontogenetic jumping performance of locusts [28, storage component for locust jumping has been investigated 29, 32, 34, 39–45]. However, little has been reported about by Burrows [32]. The thickness of the semilunar process and the configurations of hind legs during the takeoff phase in extensor resilin of newly molted instars and adults is initially locusts of different instars and their potential effect on the thinner, then it increases because of resilin deposition after jumping performances. Based on this, the present study each molting, showing a general growing trend ontogeneti- aimed to investigate if and how different hind leg configura- cally, while prior to a molt, the extensor resilin shows a tions during the takeoff can affect the jumping performances declining trend. The jumping ability and performance of in various developmental instars (i.e., third instar, fourth locusts at different life stages are consistent with the changes instar and adult). The geometrical parameters of L. migra- that occur during each molting cycle, which affect the energy toria individuals were combined with experimental data to store [32]. The energy stored during the deformation of the set up a simplified mathematical model to assess the jumping semilunar process, composites of hard cuticle and the performance of the tested locusts, and to explain the energy rubber-like protein resilin, is around 50% of the jumping shift from L. migratoria nymphs to adults [2, 7, 27]. energy needed. In addition, it has been demonstrated that layered resilin/cuticle composites all share a similar distribu- 2. Materials and Methods tion in the five nymphal stages and in adults in locusts [33]. This structure may be ubiquitous in jumping insects and play 2.1. Experimental Setup and Material Preparation. A set of 29 an important role in energy storing for jumping, in addition L. migratoria adults, 17 fourth instars, and 35 third instars, to the energy stored in the muscles. was reared in different cylindrical transparent plastic boxes The adults of the American locust, Schistocerca ameri- (50 cm in diameter and 70 cm in length) with a 16 : 8 (L : D) cana Drury, develop high-power, low-endurance jumps, h photoperiod at 25 ± 1 C, 40 ± 5% RH. Temperature and while the juveniles perform less-power, high-endurance RH conditions were the same during experiments. The health jumps [34], which is different from vertebrates [7, 15, 22, of each locust was constantly checked during the whole 35]. This can be explained by the fact that juvenile locusts period assuring proper diet composed of wheat, fresh vegeta- use repeated jumping acts to escape from a wide number of bles, and water ad libitum [44, 46, 47]. The experiments were their predators, with special reference to invertebrate ones carried out by using healthy locusts with no injuries (e.g., no (e.g., spiders and mantis) [29]. Besides, adults have to achieve damaged legs, wings, or antennae). The tested locusts were a powerful jump to initiate flight in order to escape from fas- used at least 24 h after molting, to reduce the potential influ- ter predators, such as frogs, lizards, and birds, moving away ence of soft newborn cuticles and small muscle mass on their with powerful flapping and gliding [29, 36–38]. The trade- locomotion and jumping performance [32, 39, 48]. off between jumping power and endurance is consistent with All the locusts were weighed to 0.01 g with a scale. The the ontogeny of life-history behaviors. However, juvenile dimensions of the main features (i.e., femur, tibiae, and tarsus locusts also use hopping as a model of locomotion exhibiting length) were measured to the nearest 0.01 mm using a caliper. adifference between predator escape jumps and normal loco- Table 1 reports the results as mean value ± SD before testing motion jumps [29, 34]. In this framework, the effects of the their jumping performances. various instars on jumping performances of the African A white-colored solid jumping platform was positioned desert locust S. gregaria were investigated with an ontoge- inside a foam box (70 × 35 × 30 cm). The jumping platform netic growth model [29]. Results show that force, accelera- was lit with four LED illuminators (RODER SRL, Oglianico tion, takeoff velocity, and kinetic energy, except power TO, Italy) which emit red light (420 lm each at k = 628 nm) output, varied as an exponential function of body mass. to match the maximum absorption frequency of the camera Furthermore, a study on the effect of body mass and tem- [49–53]. The jumping behavior of each locust was stimu- perature on the jumping performance of L. migratoria lated by teasing the rear of its body with a transparent plastic indicates that jump energy scaled with body mass with a bar (2 mm diameter), to elicit the maximum “escape jumps.” Applied Bionics and Biomechanics 3 The tracking paths were carefully checked to ensure that Femur the tracking path corresponded to the raw image sequences [49]. Tracked center pixels of each video were converted into 3 distances measured in millimeters with a scale ratio based on Body Tibiae the graph paper and imported into the MATLAB software (MATLAB and Statistics Toolbox Release 2012b, The Math- Works, Inc., Natick, Massachusetts, United States). x 2.3. Statistical Analysis. The influence of life stage on the con- Ground sidered parameters, i.e., the time intervals of different phases (cocking time, takeoff time, and release time), takeoff angle, Figure 1: Simplified mechanical model of a L. migratoria. legs’ configuration over time, velocities at T , T , and K 3 4 values (elastic parameters of tested jumps), and dimension The jumps of each locust were recorded for 5 times inter- parameters were analyzed separately using a general linear spersed by 10 minutes to allow the locusts to have a total model with the following structure: y = βX + ε, where y is recovery between jumps [43, 44]. Tested locusts jump from the vector of the observations with normal distribution (i.e., a prepared platform, and the body of locust body axis during takeoff time, velocity at T , or takeoff angle), β is the inci- the jumps is theoretically perpendicular to the axis of the 3 dence matrix linking the observations to fixed effects, X is camera. Jumps deviating more than 15 with respect to the the vector of fixed effects (i.e., locust developmental instars), perpendicular plane to the axis of the camera lens were and ε is the vector of the random residual effects. ANCOVA excluded to limit the difference between the actual and per- (analysis of covariance) was used to analyze the effect of life ceived takeoff angle [39]. A Hotshot 512 sc high-speed cam- stage on the jumping performance while considering body era (NAC Image Technology, Simi Valley, CA, USA) was weight as a covariate, due to the fact that the difference of used to record 2000 fps videos of the jumping tasks and store body weight is inevitable and the effect of body weight on sequential 7600 images with a resolution of 512 × 512 pixels the jumping performance should be elicited from the effect directly into its internal memory. All the samples were ana- of life stage. A threshold P value of 0.05 was set to test the sig- lyzed via the ProAnalyst Suite (Xcitex, Cambridge, MA, nificance of differences between means. Post-hoc letters USA) to track the locust centroid trajectory for each jump. obtained by Tukey’s HSD test separated averages. 2.2. Model Description. A simplified mechanical model of a L. 3. Results migratoria locust is depicted in Figure 1. The body, the femur, and the tibiae are outlined as three rigid bars. The x A set of 81 jump videos of different locusts (29 adults, 17 axis coincides with the ground, and θ is the angle between fourth instars, and 35 third instars) was analyzed with the the body and the x axis: when the distance of the body line abovementioned methods. The results for all the parameters to the x axis increases positively, the value of θ is positive; are illustrated within the following subsections. otherwise, the value is negative. θ is the angle between the femur and body: when the femur line is upon the body line, 3.1. Time Intervals and Takeoff Angles of Tested Locusts. The the value of θ is positive; otherwise, the value is negative. cocking time (F =2:4780 ; P =0:0906, Figure 2(a)) and 2,80 θ is the angle between the femur and the tibiae. θ is the 3 4 takeoff time (F =2:7304 ; P =0:0715, Figure 2(b)) charac- 2,80 angle between the tibiae and the x axis. Both the values of terizing third instars, fourth instars, and adults of L. migra- θ and θ are strictly positive due to the structure of locust 3 4 toria locusts showed no significant differences, while the hind legs. release time ( F =6:2732 ; P <0:05, Figure 2(c)) showed 2,80 The cocking time was defined as the time interval needed significant differences among third instar, fourth instar, and for a L. migratoria individual to prepare to jump, from con- adult locusts. The release time of third instar locusts was sig- tracting the hind legs backward (T ) to being ready to jump nificantly longer than adult and fourth instar locusts (T ). The takeoff time is the time interval from the first (Figure 2(c)). The trajectory of the body center during the observed movement of the hind leg (T ) to the detection of takeoff phase of L. migratoria was close to a straight line, hind legs losing contact with the ground ðT Þ. The release and takeoff angle was defined as the slope angle of the body time is the time interval from the moment in which the hind center trajectory of the tested locusts during takeoff [54, legs lose contact with ground ðT Þ to the moment when the 55]. Considering the takeoff angle, no significant differences hind legs stop moving and are kept in a fixed position relative were detected in third instar, fourth instar, and adult locusts to body ðT Þ. ðF =0:8065 ; P =0:4502Þ . 2,80 Images of the jumping at T , T , T , and T , respectively, 1 2 3 4 θ and θ were significantly affected by the insect were carefully picked out from sequential images to evaluate 1 2 instars at T . Both θ (F =3:1813 ; P <0:05, the geometrical and temporal parameters (i.e., θ , θ , θ , θ , 2 1 2,80 1 2 3 4 Figure S1b, in supplementary materials attached) and θ cocking time, takeoff time, and release time) via Microsoft (F =3:5052 ; P <0:05)of adult locusts were significantly Office Visio. The centroid of each locust was tracked during 2,80 smaller than fourth instar locusts. θ (F =7:5272 ; P <0:05, each jump by considering it positioned between the base of 3 2,80 the middle and hind legs and bilaterally symmetrical from Figure S1c) of fourth instar locusts at T was significantly the vertical view [54]. higher than that of third instar locusts. θ 3 4 Applied Bionics and Biomechanics 400 30 Third instar Fourth instar Adult Third instar Fourth instar Adult (a) (b) AB Third instar Fourth instar Adult Third instar Fourth instar Adult (c) (d) Figure 2: Mean cocking time (a), takeoff time (b), release time (c), and takeoff angles (d) of third instar, fourth instar, and adult L. migratoria. Different letters above each column indicate significant differences (P <0:05). Whiskers represent standard errors. (F =3:8030 ; P <0:05) of third instar locusts at T was (F =4:3591 ; P <0:05) and more than twice those of 2,80 4 2,80 significantly smaller than fourth instar ones. θ adults (3.3%) and fourth instars (2.19%) (Table 2). (F =5:8588 ; P <0:05)and θ (F =4:6958 ; P <0:05, The elasticity of the hind legs is simplified as a torsional 2,80 4 2,80 spring (torsional stiffness: K) at femur-tibiae joints [56], the Figure S1d) of fourth instar locusts were significantly smaller displacement in the vertical direction at T and T are h than third instar ones at T . Based on the established 3 4 3 and h , the mass of locust is m, and the gravitational acceler- simplified model in Figure 1, mean configurations of tested adult fourth instar and third instar locusts at T , T , T ,and T ation is g, equals to 9.81 m/s . The velocity of the mass center 1 2 3 4 at T was set as 0 m/s, and the velocity of the mass center is v are plotted (Figures S2a, S2b, and S2c in supplementary 2 3 materials) using the mean dimension parameters (Table 1), and v at T and T , respectively. The values of θ at T , T , 4 3 4 3 2 3 and T are θ , θ , and θ , respectively. θ was considered center position tracking results, and mean angle data (Figure S1). 4 32 33 34 34 to be the free position of the torsional spring. Based on energy conservation, the following formulas were used: 3.2. Velocities at T and T and Elastic Element Parameter of 3 4 Tested Locusts. The velocity at T (F =9:8738 ; P <0:05) 3 2,80 E = mgh +0:5mv , 3 3 3 and T (F =10:5871 ; P <0:0001) were significantly 4 2,80 ð1Þ E = mgh +0:5mv , affected by the tested L. migratoria instar. The velocity at 4 4 4 T and T of third instar individuals was significantly 3 4 smaller when compared to that of adults and fourth instars 2 2 ð2Þ mgh + mv =0:5KðÞ θ − θ −ðÞ θ − θ : (Figures 3(a) and 3(b)). For the third instar, fourth instar, 3 3 32 34 33 34 and adult locusts, the mean velocities at T were bigger than the mean velocities at T . The velocity decrease percentage The energy of locusts at T and T were defined in Equa- 3 4 from T to T of third instars (7.7%) is significantly higher tion (1) individually, and the corresponding values were 3 4 Time (ms) Time (ms) Angle (°) Time (ms) Applied Bionics and Biomechanics 5 3 3 2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 0 0 Third instar Fourth instar Adult Third instar Fourth instar Adult (a) (b) 2.5 1.5 –1 0.5 –2 0 12 3 4 Third instar Fourth instar Adult 2 2 2 0.5[(𝜃 −𝜃 ) −(𝜃 −𝜃 ) ] [rad ] 32 34 33 34 Adult Fourth instar Third instar (c) (d) Figure 3: Mean velocities of third instar, fourth instar, and adult L. migratoria at T (a) and T (b). (c) Mean K value calculated based on 3 4 Equation (2) of all tested third instar, fourth instar, and adult locusts separately. Different letters above each bar indicate significant differences (P <0:05). Whiskers represent standard errors. (d) The relationship between the jump energy of locusts after takeoff phase at 2 2 T moment and 0:5½ðθ − θ Þ − ðθ − θ Þ  of all tested third instar, fourth instar, and adult locusts’ jumps. 3 32 34 33 34 Table 2: Mean velocity and energy of tested L. migratoria at T and T moments. 3 4 Type Weight (g) E mJ E mJ v (m/s) v (m/s) v − v /v ðÞ ðÞ ðÞ 3 4 3 4 3 4 3 Third instar 0:24 ± 0:06 0:27 ± 0:15 0:24 ± 0:15 1:43 ± 0:42 1:32 ± 0:43 7.7% 0:32 ± 0:09 0:55 ± 0:24 0:55 ± 0:27 1:82 ± 0:25 1:78 ± 0:32 Fourth instar 2.19% Adult 1:65 ± 0:36 3:89 ± 2:21 3:71 ± 2:38 2:12 ± 0:65 2:05 ± 0:69 3.30% listed in Table 2. Based on Equation (2), elastic param- 3.3. Hind Leg Length of Tested Locusts. The tibiae length of eter K values of all tested jumps were calculated with hind legs was significantly affected by L. migratoria instar known kinematic data and angle data. Elastic parameter (F =24:4218 ; P <0:001). The tibiae length of adults was 2,80 K was significantly affected by the insect instars significantly longer than that of fourth and third instars (F =5:2980 ; P <0:05), and K of tested adult locust (Figure S3a, in supplementary materials attached). The 2,80 jumps was significantly higher than that of fourth instar femur length of hind legs was significantly affected by L. and third instar locust jumps (Figures 3(c) and 3(d)). migratoria instar (F =18:3199 ; P <0:001). This femur 2,80 Velocity (m/s) K (Nmm/rad) Energy (mJ) Velocity (m/s) 6 Applied Bionics and Biomechanics 1 7 0 3 –1 –2 0.5 1 1.5 2 –1 0 1 –1 0 1 10 10 10 10 10 10 Mass (g) Mass (g) Mass (g) Adult Adult Third instar Adult Third instar Fourth instar Fourth instar Fitted result Fourth instar Fitted result Third instar (a) (b) (c) Figure 4: (a) The allometric relationship between jump energy and body mass of all tested third instar, fourth instar, and adult locust jumps. 1:342±0:16 2 All tested jumps were included in the regression: E =1:8018m (R =0:8288). (b) The allometric relationship between mass-specific work (the ratio of jump energy divided by body mass) and body mass of all tested third instar, fourth instar, and adult locusts’ jumps. All 0:342±0:136 2 tested jumps were included in the regression: E =1:8018m (R =0:2388). (c) The allometric relationship between mass-specific work and body mass of all tested third instar, fourth instar, and adult locust jumps. The straight red, blue, and black lines are the average ratio of jumping energy divided by body mass of all tested third instar, fourth instar, and adult locusts individually. length of adults was significantly longer than that of fourth effect, small size jumpers, such as fourth and third instar and third instars (Figure S3b, in supplementary materials locusts, should reach similar (or slightly higher) takeoff attached). The ratio of tibiae length to femur length of velocities if compared to adult locusts. However, experimen- hind legs was not significantly affected by L. migratoria tal results disagree with both conclusions. Firstly, mass- instars (F =0:1378 ; P =0:8715). The relation between specific works showed an increasing trend during growing 2,80 mass and hind leg femur length and tibiae length of tested (Figures 4(b) and 4(c)). Secondly, even though adult locusts third instar, fourth instar, and adult locusts were included have bigger masses than younger instar ones (Table 2), adults 0:3144±0:0259 in the regression L =16:7880m ðR =0:8806Þ have significantly larger takeoff velocities (Figure 3(a)). These femur 0:3299±0:0241 and L =15:5597m ðR =0:9033Þ individually apparent paradoxes showed that L. migratoria locusts at dif- tibiae (Figure S4a and Figure S4b, in supplementary materials ferent developmental instars cannot be expected to perform attached). as geometrically similar jumpers. The relation between mass and energy of all tested jumps 4. Discussion of third instar, fourth instar, and adult locusts (Figure 4(a)) 1:342±0:16 was included in the regression: E =1:8018m How locust morphology can vary to fit the mutable (R =0:8288). Similar regression values were concluded in mechanical demands of increasing body size and mass 1:14±0:09 2 two separate studies: E =1:91m (R =0:96) for L. has been investigated by specific scaling models or allom- 1:114 2 migratoria juveniles [39] and E =1:7906m (R =0:939) etries [27–29]. In our study, jumping performance related [29] for S. gregaria juveniles. In both published research, to some specific parameters (viz. tibiae length, body adult locusts’ jumps have greater kinetic energy than the weight, and main joint angles) of L. migratoria individuals value predicted using the regression that concluded using at different life stages were analyzed. Results showed that only juveniles; for example, S. gregaria adults produces the jumping performance of L. migratoria adults outper- around four times as much kinetic energy as the regression formed those of young instars, both in terms of absolute predicted for juveniles using adult body mass [29]. In our velocity (Figure 3(a)) and mass specific work (Figure 3(f)). experiment, the regression included tested jumps of both Suppose L. migratoria locusts at different developmental adult and instar locusts, because the regression using only instars follow a geometrically similar jump model [57], where 1:8018±0:4840 2 juveniles is E =3:5278m (R =0:5473) and the both skeletal and muscular properties obey the laws of geo- coefficient of determination R is 0.5473, which is relatively metric scaling—“muscle work”—which means the energy lower than that including both adult and instar locusts delivered during the push-off should scale at the same rate of mass and mass-specific works are independent of scale. (R =0:939). If we adopt the regression using only juveniles to predict the kinetic jumping energy of adults, the pre- Two conclusions should be obtained based on this model: (i) The specific energy (E /m) should be the same for all dicted jumping energy is greater than the real kinetic energy, which is different from previous published results. tested instars and adults of L. migratoria. (ii) Due to a size E (mJ) E /m (mJ/g) E /m (mJ/g) 3 Applied Bionics and Biomechanics 7 96 10.5 9.5 90 9 88 8.5 86 8 7.5 82 7 5 10 15 20 5 10 15 20 25 30 Age Age Male Male Female Female (a) (b) Figure 5: (a) The development curve of skelic index and age [69]. (b) The development curve of average velocity of 100 m sprint best record and age [70]. Considering the state of the art, the authors examined the spring rather than a rigid bending lever in S. gregaria [42]. scaling ofjumpingperformance inL. migratoria to understand The obvious deflection of tibiae during takeoff [60] can store whether there is a connection between functional and mor- at least 10% of the total kinetic energy of the jump [42]. The phological designs. Even though adult locusts have body effect of leg compliance on jumping performance is also masses bigger than fourth instar and third instar locusts investigated in jumping robots [61, 62], and results demon- (Table 2), adults have significantly higher velocity and energy strated that proper leg compliance can improve the perfor- after takeoff (Table 2). This result is comparable with existing mance of a jumping robot using the initially stored energy research focused on S. gregaria. Juvenile S. gregaria locusts in the compliant legs to be used. Based on this, the significant increase in tibiae length were considered meaningful to produce takeoff velocities of 0.9-1.2 m/s, while adult locusts show takeoff velocities around twice as high as that of juveniles improve jumping performances of adult locusts. (2.5 m/s) [29]. In addition, the kinetic energy of the jump in S. Secondly, the established mechanical model revealed gregaria have values that range from a low of 0.004 mJ in afirst- that locust adults have a significantly bigger K value if instar locust to as high as 15.99 mJ in an adult [29]. The greater compared to fourth instar and third instar individuals (Figure 3(c)). This seems directly connected with the better takeoff velocity in adult locusts and excellent jumping perfor- mance can be explained by different reasons. jumping performance characterizing adult locusts. A sharp Firstly, the lengths of the femur and tibiae show a signif- improvement of velocity and energy in adults is reported icant increase in L. migratoria individuals during its devel- to be a result of the combination of a bigger mean cross- opment, in a comparable manner to results previously sectional area of the femur muscle [28, 63, 64] coupled with the fact that a rather long life span gives adult locusts lon- achieved on S. gregaria [42]. Jump distance is demonstrated to be proportional to the distance through which the force ger time to stiffen their semilunar process and extensor acts [41, 58, 59], which is related directly to limb length. cuticle [27, 32, 40, 65, 66]. A stiffer spring system in adults Thus, the relatively longer legs (including the femur and tib- was also estimated by the abovementioned modeling, where iae) of older juveniles likely provide the approaches to propel the elasticity of the hind legs of locusts was supposed to be modeled as a torsional spring located at the femur-tibiae these animals farther and with greater jump energy [39]. In addition, the muscle mass in the femurs of adult locusts joint [56], neglecting other elastic contributions [67, 68]. shows a higher percentage of body mass compared to those The results showed that the stiffness of fourth instar and in young instar locust [27] and shows an aligned increase in third instar locusts are close, and rather smaller than that the angle of muscle pennation [28]; both lead to a greater of adults, differing by orders of magnitude. Finally, due to the viscoelasticity of muscular tissues, longer capacity for energy storage and greater jump velocity [28]. The importance of tibiae mechanical property has been takeoff times in adults L. migratoria decrease the energy con- investigated [29, 42], and the authors pointed out that the sumption during takeoff caused by internal dissipative forces. increase of tibiae length in S. gregaria during growth can help There is an interestingly similar phenomenon in locusts 2 2 locusts to adapt to the acceleration decrease caused by the and humans. The value of 0:5½ðθ − θ Þ − ðθ − θ Þ  in 32 34 33 34 increase of body mass [42] with an enlarged takeoff time in fourth instar locusts showed an increasing trend compared adults. James et al. also reported that the increased relative to third instar ones, while for adult locusts it showed a hind limb length and relative mass of jumping muscles decreasing trend (Figure 3(d)). This is very similar to the ensure the improvement of jumping performance [58]. In skelic index (standing height minus sitting height divided contrast, Katz and Gosline stressed that tibiae play an impor- by sitting height and multiplied by 100) development trend in human beings (Figure 5(a)); the skelic index has its tant role during the takeoff phase and work like a bending Skelic index Average velocity (m/s) 8 Applied Bionics and Biomechanics is compensated by peculiar morphological design and stiff- maximum value at around 15 years old and then decreases. Both the takeoff velocity of tested locusts (Figure 3(a)) and ness. Longer hind legs boost the acceleration time and com- average velocity of 100 m sprint best record (Figure 5(b)) pensate for the supposed acceleration decrease [29, 42]. A showed an increasing trend until becoming adults. The best bigger tibiae-to-femur ratio means a relatively longer tibiae, locomotion performance for both locusts and humans hap- supporting the prediction that the tibia works as a leaf spring pens in adults. It likely conveys that the locomotion perfor- and the deflection of tibiae can store a significant part of mance is a combined result of both geometrical parameters energy needed by each jump. The spring system of locust and material property. For adults, the best geometrical hind legs is composed by elastic cuticles and a semilunar pro- 2 2 cess. The thickness of the semilunar process and extensor parameters (0:5½ðθ − θ Þ − ðθ − θ Þ  for locusts and 32 34 33 34 skelic index for humans) and best material property (muscle resilin show a general increasing trend during development, occupation rate and elastic parameters) are achieved simulta- while decreasing during molting [32]. The stronger spring neously and result in the best locomotion performance. system in adult locusts is consistent with the calculation Interestingly, the percentage velocity difference from T results based on a simplified mathematical model proposed to T strongly increases as the body size decreases, from here. The stiffer spring system and bigger muscle occupation adults (3.3%) and fourth instar (2.19%) to third instar rate work together to improve the adult locust jumping per- locusts (7.7%) (Table 2). This phenomenon may be con- formance [32]. This study adds basic knowledge on the nected to the fact that smaller instars have a higher frontal jumping mechanisms in various developmental instars of L. area-to-body mass ratio compared to larger instars, which migratoria locusts considering a different leg configuration makes them more susceptible to the effects of aerodynamic as well as body mass, length of hind legs, velocity, and energy. drag [39, 71]. Another possible reason is the longer release We also proposed a simplified mathematical model to calcu- time in third instar locusts. The takeoff angles in all tested late the elastic features of each jump in young instars and locusts are similar, close to 45 , helping to maximize the adults of L. migratoria. jumping distance [39, 72, 73]. The ontogenetic jumping performance of locusts In agreement with the findings obtained studying S. reported here can inspire roboticists to select the most suit- americana [34], the compromise between power and endur- able instars as a model organism to design advanced jumping ance was noticed in the present research. Indeed, L. migra- robots. Firstly, jumping represents the only locomotion toria adults took a longer time than 10 minutes to be ready mode (e.g., early instar locusts) or can be coupled with flap- for the next jump. In several instances, after recording a pow- ping and gliding wings (e.g., adult locusts). Secondly, the erful jump in an adult locust, it was hard to record another mass (Table 1), the consumed energy (Table 2), and the elas- one, while the situation was different for fourth instar and tic parameter K (Figure 3(c)) increase around one order of third instar locusts. After a less powerful jump, it took less magnitude from third instar to adult locusts, which con- time before the next one was ready for another jump and they vinces us that size and weight are key parameters in jumping were willing to jump another time if stimulated again within robot design together with the elastic and actuation systems. a short time interval. Thirdly, it is important to consider geometrical parameters in Overall, we detected a longer takeoff time in adult locusts, robots’ design, due to the significant variation of geometrical if compared to young instars, although the velocity was param eters (e.g., joint angles, tibiae length and the ratio of higher and the release time shorter, probably to allow the tibiae length to femur length of hind legs) in locusts and their spread of wings to start the flight. Locusts can learn motor impact on jumping performance. actions at the level of the single ganglia [74]. Therefore, a lon- ger takeoff time, as well as a higher velocity and a shorter Data Availability release time, could be chieflyinfluenced by their increasing motor experience from young instar to adult. Furthermore, The excel data used to support the findings of this study are the specialization of leg control seems to be related to partic- available from the corresponding author upon request. ular neural circuits involved in sensory-motor mechanisms occurring within the prothoracic ganglion of these insects Conflicts of Interest [75, 76]. In addition, adults were found to be more efficient in storing energy in their hind legs and releasing it during The authors declare that there is no conflict of interest the jump. Indeed, K of tested adults’ jumps were significantly regarding the publication of this paper. higher compared to that of fourth and third instars: this could be related to a more efficient composite storage device, Acknowledgments consisting of a greater mass of soft resilin and a thicker hard cuticle in adult locomotor structures due to growth, contrib- The authors want to thank the BioRobotics Institute, San- uting to adults with enhanced performances during the t’Anna School of Advanced Studies and the China Scholar- jumping behavior [77–79]. Further research is still needed ship Council (CSC) for funding this research. This research to shed light on the abovementioned issue. was also supported by the National Key Research and Devel- In conclusion, velocity after takeoff and energy per jump opment Program of China under Grant 2017YFB1300101 are significantly higher in adult locusts over the fourth and and the EU H2020 Project “Submarine cultures perform third instars, while the body mass of adult locusts is a half long-term robotic exploration of unconventional environ- magnitude bigger than the fourth and third instar ones. This mental niches” (subCULTron) (640967FP7). Applied Bionics and Biomechanics 9 [9] J. Westerga and A. Gramsbergen, “The development of loco- Supplementary Materials motion in the rat,” Developmental Brain Research, vol. 57, Figure S1: (a) the mean values of θ , θ , θ , and θ of tested no. 2, pp. 163–174, 1990. 1 2 3 4 adult, fourth instar, and third instar locusts separately at T 1 [10] G. A. Cavagna, P. Franzetti, and T. Fuchimoto, “The mechan- (a), T (b), T (c), and T (d). 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