跳跃机器人的研究

Biological Jumping Mechanism Analysis and Modeling for Frog RobotMeng Wang, Xizhe Zang, Jizhuang Fan, Jie ZhaoState Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, P. R. ChinaAbstractThis paper presents a mechanical model of jumping robot based on the biological mechanism analysis of frog. By biological observation and kinematic analysis the frog jump is divided into takeoffphase, aerial phase and landing phase. We find the similar trajectories of hindlimb joints during jump, the important effect of foot during takeoff and the role of forelimb in supporting the body. Based on the observation, the frog jump is simplified and a mechanical model is put forward. The robot leg is represented by a 4bar spring/linkage mechanism model, which has three Degrees of Freedom (DOF) at hip joint and one DOF (passive) at tarsometatarsal joint on the foot. The shoulder and elbow joints each has one DOF for the balancing function of arm. The ground reaction force of the model is analyzed and compared with that of frog during takeoff .The results show that the model has the same advantages of low likelihood of premature liftoff and high efficiency as the frog. Analysis results and the model can be employed to develop and control a robot capable of mimicking the jumping behavior of frog.Keywords: frog jump modality, kinematic analysis, mechanical model, jumping robot Copyright ) 2008, Jilin University. Published by Science Press and Elsevier Limited. All rights reserved.1 IntroductionBiological principles can improve the performance of robots. Raibert and colleagues developed one, two, and four leg hopping and running robots by incorporating biologically inspired dynamics into their designate.These robots have telescoping legs with an internal air spring for compliance, and hydraulic actuators. Researchers at Case Western Reserve University constructed a series of hexapod robots based on biological inspiration. Robots RI and RII were based upon stick insects that all the six legs are of the same construction. Robots RIII to RV modeled were on the Blaberus discoidalis that have a total of 24 DOF. Compared to the large R series of robots, a cricket microrobot can fit into a two inch cube, and could both walk and jump to navigate terrain with features much larger than itselft. Hyon and Mita developed a hopping robot "KenKen" inspired by dog. The robot has an articulated leg and uses two hydraulic actuators as muscles and a tensile spring as tendon. It could hop in a planer's. Yamakita et al. proposed a robotic system based on cat's behavior,which moves in a vertical direction as a cat kicks a wall to jump up to a roof.We select the frog as a model for the development of a jumping robot because of its remarkable jumping capability (a bullfrog can jump more than 15 times its body length). In order to produce such a robot, we need to identify a model that can jump. Kinematic observation and analysis of the frog can serve as the raw data for simulation and provide insights into the robot Construction.2 Biological observation and analysis2.1 Frog morphologyFive frogs (Rananigromaculata) were obtained from a commercial supplier. They werekept at approximately 20 0C in plastic containers measuring 35 cm (width) X 50 cm (length) X 30 cm (height), and provided with clean water. The frogs were fed with crickets at least twice a week. Immediately after obtaining the frogs from the supplier, each animal's body's mass (Mb) in grams, snoutvent length (LS,,), hindlimb length (Lhl) and forelimb length (L}), as well as the distance from thesacral joint to the vent (Lsa}) in millimeters were measured (Table 1).Frogs have evolved remarkable disparity in the relative size of their hindlimbs and forelimbs. The forelimbs that serve in supporting and steering are small and weak; while the hindlimbs are relatively large and strong,enabling them to propel the frog in both jumping andswimming.The jumping patterns of frogs differ from those of humans and other mammals in several important ways.In frogs, the hindlimb bones do not lie in a single plane throughout the jump, and hindlimb joint rotations other than extension are prominent. Further, the tarsometatarsal (TM) joint at the foot, which is nearly fixed in humans, is flexible in frogs, and may contribute greatlyto jumping}lo'I}}.The forelimb and hindlimb each has five distinct segments (Fig. 1 a). Starting from the body attachment point, the forelimb segments are humerus, radioulna,metacarpal, wrist and phalanx (without web between digits). The hindlimb segments are femur, tibiofibula,tarsal, metatarsal and phalange (with web between digits)}12}. We regard metacarpal, wrist and phalanx of forelimb as a whole segment, also metatarsal and phalange of hindlimb as a whole segment for the convenfence of observation. To realize complex positioning of the entire hindlimb, the hip joint has 3 DOF. The knee,ankle and TM (displacement of the tarsal relative to the metatarsal) joints are simple 1 DOF joints and act in the same plane. For the same reason, the shoulder joint has 3 DOF. Elbow and wrist are simple 1 DOF joints.Although the forelimb and hindlimb are not arranged in completely orthogonal planar fashion, we defined a relative x yz axis orientation to assist the analysis. By definition, the animal's horizontal, longitudinal headtotail line is the xaxis; the lateral, horizontal sidetoside line is the zaxis; and the vertical line direcred upward is the yaxis.Fig. 1 Skeleton of frog (a) Side view of frog with digitizing points marked and segments identified;(b) Dorsal (top) view of frog with digitizing points and joints identified.2.2 Experimental setupThe jumping movements of frog are explosive and involve coordination of its extremity. In order to observe and measure these movements, we built a platform to collect the necessary data such as individual joint angles.The platform consists of a highspeed video (100 frames per second), a mirror and a 3D staff gauge (Fig. 2). The mirror was mounted above the arena at 450 to allow simultaneously filming the side and top views. A 3D staff gauge that provides x (longitudinal), y (vertical), and:(lateral) orientation coordinates, helps us get accurate data. 3D information of the red dots locating thejoints of limbs and body was obtained from video images by program (Fig. 1 and Fig. 2). After correction of digitized data from the effect of perspective, the program reconstructed the true angles of the joints in 3D as frog jumped on the arena}l3}. The temperature was kept at 20 0C一25 0C during the experiment.2.3 Jumping performanceOn the basis of the actions and positions of the body, forelimbs and hindlimbs, three phases in the jump were identified from the video recordings (Fig. 3): (i) the takeoff phase, which lasts from the ` jumpready" or crouching position to the point at which the frog leaves the ground; (ii) the aerial phase, which lasts from this point to the first touching point of the ground; (iii) the landing phase, measured as the time from the first contact with the ground to the resumption of the "jumpready" position.Fig. 3The jumping movement is divided into three phases: takeoff phase, from image 1 to image 4; aerial phase, from image 4 to image 6; landing phase, from image 6 to image 8.At the beginning of the takeoff phase, the hip and knee are greatly flexed; in fact, the thigh and shank that bend underneath the body are completely folded. The TM joint is flexed about 1200 to elevate the ankle so that it is not in contact with the ground. The forelimbs support the body in position for takeoff.As the muscles shorten, the generated power leads to a rapid extension of the hindlimbs which, in turn, propels the frog into the air. While the hip, knee, and ankle extend during initial takeoff phase, most of the foot (metatarsals and phalanges) remains in contact withthe ground, and the TM joint extends just slightly. But while the TM joint extends, there is a concurrent dor soflexion at metatarsophalangeal (MP) joint that causes the tarsals to rock forward until to the distal toe joint, as in a human foot shifting from the heel to the ball of the foot}la}.During the initial takeoff, the elbow extends and the humerus retracts and adducts as the forelimbs come off the ground. It seems unlikely that this extension of the small forearm segments contributes much, if any, power to the jump. Nevertheless, the forelimbs probably supply balancing and steering as the animal initiates a dump.During the aerial phase, the hip, knee, ankle, and TM joints of hindlimbs begin flexing, and the forelimbs are extended to prepare for landing.In the final landing phase, the hindlimb flexion is completed. The forelimbs support and decelerate the frog before its body is pivoted ventrally about the shoulder until the hindlimbs contact the ground. At this point, the bulk of the body weight is transferred to the hindlimbs, and the frog is ready to jump again.During a jump, the duration of the takeoff phase is quite variable, ranging from 90 ms to 220 ms (40 jumps were chosen for research). The duration decreases with increasing jumping distance (linear regression, r2一0.28, t二一1.711+204, P<0.0001, t is takeoff duration (ms), l is jump distance (cm); Fig. 4). Because of its ballistic nature, jump performance, as measured by the linear horizontal distance traveled by the animal, is largely a function of takeoff velocity and angle. Given similar amount of limb extension, a jump with shorter takeoff phase should have higher accelerations of the center of mass and, given similar takeoff angles, the jump should cover a greater distance.Fig. 4 Scatterplot of 40 separate jumps-the relationship between jumping distance and takeoff duration.The long, soft and mufti一jointed foot is a critical element for successful jump performance. Its movement, with the legs keep most of the plantar surface in contact with the ground as long as possible, causes the site of push off to shift forward from the back of the foot. For an animal with feet as long as a frog's, this allows for more controlled extension. Keeping the broadest part of the foot in contact with the ground throughout propul sion also permits continuous adjustment of balance so that rapid changes in direction and/or trajectory could be made. Additionally, these movements maximize the velocity of limb extension and the final takeoff velocity by maximizing the contact of the foot (to keep pushing for the possible longest time as the upper limb segments extend) and by combining velocities of as many joints as possible}}5}. Thus, the elongated foot of the frog funclions to produce very large takeoff velocitiesllb}, and the foot with the TM joint should be considered in robot design.2.4 Analysis of joint trajectoryIn order to find the characteristics of the jump, we compared and analyzed the joint trajectory based on the kinematic data from the experiment. Five similar jumps (the takeoff angle is about 300 and jumping distance is about 0.5 m, takeoff angle was measured from the frame at takeoff and corrected geometrically for the deviation of the jumping plane from the focal plane of camera) were selected. Fig. 5a and Sb show the mean joint angles of the forelimb and hindlimb respectively.From Fig. 5a, the shoulder and elbow joints change greatly from the time that the frog touches the ground. But the former has more extension, perhaps because it contributes more to support and decelerate the frog.Fig. 5 The mean joint angles of 5 jumps: (a) Elbow and shoulder joints of forelimb; (b) Hip, knee, ankle and TM joint angles of hindlimb; The time of take off from the ground is about 360ms.During the takeoff phase, joint extension appears to be temporally staggered, with the hip and knee beginning to extend prior to or initially faster than the more distal ankle joint (Fig. 5b). The hip and knee joints finish extending near the point of takeoff (when the feet leave the ground), while the ankle joint still extends for some time (about 30 ms). However, the hip, knee and ankle joints of hindlimbs have very similar trajectory and range during the whole jump (Table 2).The TM joint has relatively small range and extends until the end of takeoff phase. This movement pushes the tarsus upward and forward throughout propulsion to realize the function of foot mentioned above.2.5 Biological summaryKinematic analysis of a frog jumping provides critical 3D space point data for modeling. Notably, the role of the forelimb (in supporting and positioning more than in taking off), the similar trajectories of hindlimb joints during the jump and the function of the foot during takeoff phase are issues that must be addressed in design.3 A dynamic model of frogWe developed a dynamic model of frog to help us understand the biological data and to aid the design of the robot (Fig. 6). There are 18 DOF in the model; five for each of the hindlimbs and four for each of forelimbs. Each hindlimb has 3 DOF at the hip joint, 1 DOF at the knee joint, and 1 DOF at the ankle joint. Each forelimb has 3 DOF at the shoulder joint, and 1 DOF at the elbow joint.The inputs to the simulation include the lengths and inertias of the hindlimb and forelimb segments and the body, the joint angle trajectories obtained from the observation of frog jump. We choose the parameters of frog No. O 1, shown in Table 1, as the inputs to the model. The outputs from the simulation are the overall body movement and ground reaction forces.Fig. 7 shows the ground forces during takeoff phase. The result displays a similar time course to those recorded by Calow and Alxander}l}}. In the early stage of takeoff, the forces exerted on the ground are low (the ground force in Fig. 7 at onset includes the gravity of frog) and thenincrease to a peak before falling rapidly as the frog approaches takeoff. The high peak force in the late stage of takeoff could be explained by the redis tribution of power output by elastic elements, for example tendons, in series with muscles}'g}. This characteristic is very important in the design of a mechanism.4 A mechanical model of frogAccording to the kinematic analysis of frog jumping, in which the hip, knee and ankle joints of the hindlimbs have similar trajectory, we put forward a kind of model to mimic the movement of hindlimb (Fig. 8). Like the elastic elements that are used as energy storage, we employed springs as a convenient and robust storage mechanism. Three joints could be simplified and com pressed by one motor via a cable.The main part of the model is a 4bar spring/linkage mechanism. We can obtain the relationship of the thrust force and linkage displacement for this mechanism as follows. From Fig.9 one can easily derive an expression for y as a function of x:This equation can be solved for x:The principle of virtual work states that for an infinitesimal displacement of the mechanism, FXdx=FYdy FX is the spring force along xaxis, andFYis the thrust force in the ydirection. From this we obtain:where k and so are the spring constant and undistorted length respectively. An expression for FY as a function of y can be obtained by substituting Eq. (2) into Eq. (3). For the particular case, where a=b (the length of thigh is equal to that of shank).Fig. 10 plotsFYvs y for the case where the spring constant is normalized, k=1, and so= a=1.5.One can find that the model has ground reaction force similar to the frog during takeoff phase by comparing Fig. 10 with Fig. 7. At the onset of takeoff, the thrust force is quite low and then increases to its maximum before falling as the mechanism approaches the end of takeoff. The jump with this characteristic possesses the advantages of low likelihood of premature liftoff and high efficiency}l9}.Besides the linkage mechanism as the main part of robot's leg, there should be 1 DOF (passive) at the TM joint on the foot for its important role in frog jump. It could also prevent slipping and enhance stability by keeping the plantar surface in contact with the ground as long as possible during takeoff. Moreover, the leg requires another 3 DOF (rotation about xaxis, yaxis and zaxis, Fig. 11) at hip joint for adjusting the direction and trajectory.Because the function of the forelimb is balancing and steering, we need only 1 DOF (rotation about zaxis, Fig. 11) at the shoulder joint to simplify the mechanism. There is also 1 DOF (passive) at the elbow joint to support and decelerate the robot during the landing phase.Hence, we get the whole model of frog for robot design (half of the symmetrical body showed in Fig. 11). The desired stance for takeoff can be achieved by controlling the shoulder and hip joints. When the cable is released, the leg could push the robot into the air. During the aerial phase, the leg will be retracted by cable and the shoulder joint will be adjusted to prepare for landing.5 ConclusionThe biological kinematic data of a jumping frog were obtained. These data and the function of the main joints at each phase were analyzed. A kind of mechanism model was put forward and studied. The forces exerted on the ground by a frog during the takeoff phase of jump were derived from the simulation, and compared with that of the model. The result shows that the mechanical model could be used as a part of robot leg. The model has five actuators which could all be fixed on the body. The relatively light leg could reduce the energy loss of jumplt9l, and the passive joint at elbow and TM could absorb the impact during landing phase.Continuing work will involve the design of jump robot, and corresponding control methods.AcknowledgementThis work was financially supported by the National High Technology Research and Development Program of China NO.0.2006AA04Z245), and partially supported by Program for ChangJiang fang Scholars and Innovative Research Team in University (PCSIRT)(IRT0423).References[1] Raibert M H. Legged Robots that Balanced, The MIT Press, Cambrige, MA, USA, 1986.[2] Nelson G M, Quinn R D, Bachmann R J, Flannigan W C, Ritzmann R E, Watson J T. Design and simulation of a cockroachlike hexapod robot. Proceedings of the IEEE In ternational Conference on Robotics and Automation, 1997, 2,11061111.[3] Kingsley D A. 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