Convergent evolution and locomotion through complex terrain by insects, vertebrates and robots

Arthropods are the most successful members of the animal kingdom largely because of their ability to move efficiently through a range of environments. Their agility has not been lost on engineers seeking to design agile legged robots. However, one cannot simply copy mechanical and neural control systems from insects into robotic designs. Rather one has to select the properties that are critical for specific behaviors that the engineer wants to capture in a particular robot. Convergent evolution provides an important clue to the properties of legged locomotion that are critical for success. Arthropods and vertebrates evolved legged locomotion independently. Nevertheless, many neural control properties and mechanical schemes are remarkably similar. Here we describe three aspects of legged locomotion that are found in both insects and vertebrates and that provide enhancements to legged robots. They are leg specialization, body flexion and the development of a complex head structure. Although these properties are commonly seen in legged animals, most robotic vehicles have similar legs throughout, rigid bodies and rudimentary sensors on what would be considered the head region. We describe these convergent properties in the context of robots that we developed to capture the agility of insects in moving through complex terrain.     

Distributed mechanical feedback in arthropods and robots simplifies control of rapid running on challenging terrain

Terrestrial arthropods negotiate demanding terrain more effectively than any search-and-rescue robot. Slow, precise stepping using distributed neural feedback is one strategy for dealing with challenging terrain. Alternatively, arthropods could simplify control on demanding surfaces by rapid running that uses kinetic energy to bridge gaps between footholds. We demonstrate that this is achieved using distributed mechanical feedback, resulting from passive contacts along legs positioned by pre-programmed trajectories favorable to their attachment mechanisms. We used wire-mesh experimental surfaces to determine how a decrease in foothold probability affects speed and stability. Spiders and insects attained high running speeds on simulated terrain with 90% of the surface contact area removed. Cockroaches maintained high speeds even with their tarsi ablated, by generating horizontally oriented leg trajectories. Spiders with more vertically directed leg placement used leg spines, which resulted in more effective distributed contact by interlocking with asperities during leg extension, but collapsing during flexion, preventing entanglement. Ghost crabs, which naturally lack leg spines, showed increased mobility on wire mesh after the addition of artificial, collapsible spines. A bioinspired robot, RHex, was redesigned to maximize effective distributed leg contact, by changing leg orientation and adding directional spines. These changes improved RHex's agility on challenging surfaces without adding sensors or changing the control system.     

Does a crouched leg posture enhance running stability and robustness?

Humans and birds both walk and run bipedally on compliant legs. However, differences in leg architecture may result in species-specific leg control strategies as indicated by the observed gait patterns. In this work, control strategies for stable running are derived based on a conceptual model and compared with experimental data on running humans and pheasants (Phasianus colchicus). From a model perspective, running with compliant legs can be represented by the planar spring mass model and stabilized by applying swing leg control. Here, linear adaptations of the three leg parameters, leg angle, leg length and leg stiffness during late swing phase are assumed. Experimentally observed kinematic control parameters (leg rotation and leg length change) of human and avian running are compared, and interpreted within the context of this model, with specific focus on stability and robustness characteristics. The results suggest differences in stability characteristics and applied control strategies of human and avian running, which may relate to differences in leg posture (straight leg posture in humans, and crouched leg posture in birds). It has been suggested that crouched leg postures may improve stability. However, as the system of control strategies is overdetermined, our model findings suggest that a crouched leg posture does not necessarily enhance running stability. The model also predicts different leg stiffness adaptation rates for human and avian running, and suggests that a crouched avian leg posture, which is capable of both leg shortening and lengthening, allows for stable running without adjusting leg stiffness. In contrast, in straight-legged human running, the preparation of the ground contact seems to be more critical, requiring leg stiffness adjustment to remain stable. Finally, analysis of a simple robustness measure, the normalized maximum drop, suggests that the crouched leg posture may provide greater robustness to changes in terrain height.     

BigDog-inspired studies in the locomotion of goats and dogs

Collision-based expenditure of mechanical energy and the compliance and geometry of the leg are fundamental, interrelated considerations in the mechanical design of legged runners. This article provides a basic context and rationale for experiments designed to inform each of these key areas in Boston Dynamic's BigDog robot. Although these principles have been investigated throughout the past few decades within different academic disciplines, BigDog required that they be considered together and in concert with an impressive set of control algorithms that are not discussed here. Although collision reduction is an important strategy for reducing mechanical cost of transport in the slowest and fastest quadrupedal gaits, walking and galloping, BigDog employed an intermediate-speed trotting gait without collision reduction. Trotting, instead, uses a spring-loaded inverted pendulum mechanism with potential for storage and return of elastic strain energy in appropriately compliant structures. Rather than tuning BigDog's built-in leg springs according to a spring-mass model-based virtual leg-spring constant , a much stiffer distal leg spring together with actuation of the adjacent joint provided good trotting dynamics and avoided functional limitations that might have been imposed by too much compliance in real-world terrain. Adjusting the directional compliance of the legs by adopting a knee-forward, elbow-back geometry led to more robust trotting dynamics by reducing perturbations about the pitch axis of the robot's center of mass (CoM). BigDog is the most successful large-scale, all-terrain trotting machine built to date and it continues to stimulate our understanding of legged locomotion in comparative biomechanics as well as in robotics.     

Bio-Inspired Controller for a Robot Cheetah with a Neural Mechanism Controlling Leg Muscles

The realization of a high-speed running robot is one of the most challenging problems in developing legged robots.The excellent performance of cheetahs provides inspiration for the control and mechanical design of such robots.This paper presents a three-dimensional model of a cheetah that predicts the locomotory behaviors of a running cheetah.Applying biological knowledge of the neural mechanism,we control the muscle flexion and extension during the stance phase,and control the positions of the joints in the flight phase via a PD controller to minimize complexity.The proposed control strategy is shown to achieve similar locomotion of a real cheetah.The simulation realizes good biological properties,such as the leg retraction,ground reaction force,and spring-like leg behavior.The stable bounding results show the promise of the controller in high-speed locomotion.The model can reach 2.7 m·s- 1 as the highest speed,and can accelerate from 0 to 1.5 m·s -1 in one stride cycle.A mechanical structure based on this simulation is designed to demonstrate the control approach,and the most recently developed hindlimb controlled by the proposed controller is presented in swinging-leg experiments and jump-force experiments.     

Human hopping on damped surfaces: strategies for adjusting leg mechanics

Fast-moving legged animals bounce along the ground with spring-like legs and agilely traverse variable terrain. Previous research has shown that hopping and running humans maintain the same bouncing movement of the body's centre of mass on a range of elastic surfaces by adjusting their spring-like legs to exactly offset changes in surface stiffness. This study investigated human hopping on damped surfaces that dissipated up to 72% of the hopper's mechanical energy. On these surfaces, the legs did not act like pure springs. Leg muscles performed up to 24-fold more net work to replace the energy lost by the damped surface. However, considering the leg and surface together, the combination appeared to behave like a constant stiffness spring on all damped surfaces. By conserving the mechanics of the leg-surface combination regardless of surface damping, hoppers also conserved centre-of-mass motions. Thus, the normal bouncing movements of the centre of mass in hopping are not always a direct result of spring-like leg behaviour. Conserving the trajectory of the centre of mass by maintaining spring-like mechanics of the leg-surface combination may be an important control strategy for fast-legged locomotion on variable terrain.     

Control of a Quadruped Robot with Bionic Springy Legs in Trotting Gait

Legged robots have better performance on discontinuous terrain than that of wheeled robots. However, the dynamic trotting and balance control of a quadruped robot is still a challenging problem, especially when the robot has multi-joint legs. This paper presents a three-dimensional model of a quadruped robot which has 6 Degrees of Freedom （DOF） on torso and 5 DOF on each leg. On the basis of the Spring-Loaded Inverted Pendulum （SLIP） model, body control algorithm is discussed in the first place to figure out how legs work in 3D trotting. Then, motivated by the principle of joint function separation and introducing certain biological characteristics, two joint coordination approaches are developed to produce the trot and provide balance. The robot reaches the highest speed of 2.0 m.s-1, and keeps balance under 250 Kg.m.s-1 lateral disturbance in the simulations. The effectiveness of these approaches is also verified on a prototype robot which runs to 0.83 m.s-1 on the treadmill, The simulations and experiments show that legged robots have good biological properties, such as the ground reaction force, and spring-like leg behavior.     

Leg recirculation in horizontal plane locomotion

A protocol prescribing leg motion during the swing phase is developed for the planar lateral leg spring model of locomotion. Inspired by experimental observations regarding insect leg function when running over rough terrain, the protocol prescribes the angular velocity of the swing-leg relative to the body in a feedforward manner, yielding natural variations in the leg touch-down angle in response to perturbations away from a periodic orbit. Analysis of the reduced order model reveals that periodic gait stability and robustness to external perturbations depends strongly upon the angular velocity of the leg at touch-down. While the leg angular velocity at touch-down provides control over gait stability and can be chosen to stabilize unstable gaits, the resulting basin of stability is much smaller than that observed for the original lateral leg spring model with a fixed leg touch-down angle. Comparisons to experimental leg angular velocity data for running cockroaches reveal that while the proposed protocol is qualitatively correct, smaller leg angular accelerations occur during the second half of the swing phase. Modifications made to the recirculation protocol to better match experimental observations yield large improvements in the basin of stability.     

Running in the real world: adjusting leg stiffness for different surfaces.

A running animal coordinates the actions of many muscles, tendons, and ligaments in its leg so that the overall leg behaves like a single mechanical spring during ground contact. Experimental observations have revealed that an animal''s leg stiffness is independent of both speed and gravity level, suggesting that it is dictated by inherent musculoskeletal properties. However, if leg stiffness was invariant, the biomechanics of running (e.g. peak ground reaction force and ground contact time) would change when an animal encountered different surfaces in the natural world. We found that human runners adjust their leg stiffness to accommodate changes in surface stiffness, allowing them to maintain similar running mechanics on different surfaces. These results provide important insight into mechanics and control of animal locomotion and suggest that incorporating an adjustable leg stiffness in the design of hopping and running robots is important if they are to match the agility and speed of animals on varied terrain.     

How well can spring-mass-like telescoping leg models fit multi-pedal sagittal-plane locomotion data?

Idealized mathematical models of animals, with point-mass bodies and spring-like legs, have been used by researchers to study various aspects of terrestrial legged locomotion. Here, we fit a bipedal spring-mass model to the ground reaction forces of human running, a horse trotting, and a cockroach running. We find that, in all three cases, while the model captures center-of-mass motions and vertical force variations well, horizontal forces are less well reproduced, primarily due to variations in net force vector directions that the model cannot accommodate. The fits result in different apparent leg stiffnesses in the three animals. Assuming a simple fixed leg-angle touch-down strategy, we find that the gaits of these models are stable in different speed-step length regimes that overlap with those used by humans and horses, but not with that used by cockroaches.     

Legged insects select the optimal locomotor pattern based on the energetic cost

 The gait transition in legged animals has attracted many researchers, and its relation to metabolic cost and mechanical work has been discussed in recent decades. We assumed that the energetic cost during locomotion is given by the sum of positive mechanical work and the heat energy loss that is proportional to the square of joint torque and examined the optimal locomotor pattern based on the energetic cost in a simple dynamical model of a hexapod by computer simulations. The obtained results well agree with characteristics in the locomotor patterns in legged animals; for example, the leg protraction time, step length, and the metabolic cost of transport are almost constant for many velocities, the leg cycling period decreases with velocity, and the energetic cost of locomotion induced by carrying loads linearly increases with mass loaded. This correspondence of the results of calculation to experimental results suggest that the heat energy loss for torque generation is proportional to the square of the torque during locomotion, and that the locomotor pattern in legged animals is highly optimized based on the energetic cost. Received: 22 December 1998 / Accepted: 14 April 2000     

A collisional model of the energetic cost of support work qualitatively explains leg sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition

Terrestrial legged locomotion requires repeated support forces to redirect the body's vertical velocity component from down to up. We assume that the redirection is accomplished by impulsive leg forces that cause small-angle glancing collisions of a point-mass model of the animal. We estimate the energetic costs of these collisions by assuming a metabolic cost proportional to positive muscle work involved in generating the impulses. The cost of bipedal running estimated from this collisional model becomes less than that of walking at a Froude number (v2/gl) of about 0.7. Two strategies to reduce locomotion costs associated with the motion redirection are: (1) having legs simulate purely elastic springs, as is observed in human running; and (2) sequencing the leg forces during the redirection phase; examples of this sequencing are the ba-da-dump pattern of a horse gallop and having push-off followed by heel-strike in human walking.     

Control of obstacle climbing in the cockroach, Blaberus discoidalis. I. Kinematics

An advantage of legged locomotion is the ability to climb over obstacles. We studied deathhead cockroaches as they climbed over plastic blocks in order to characterize the leg movements associated with climbing. Movements were recorded as animals surmounted 5.5-mm or 11-mm obstacles. The smaller obstacles were scaled with little change in running movements. The higher obstacles required altered gaits, leg positions and body posture. The most frequent sequence used was to first tilt the front of the body upward in a rearing stage, and then elevate the center of mass to the level of the top of the block. A horizontal running posture was re-assumed in a leveling-off stage. The action of the middle legs was redirected by rotations of the leg at the thoracal-coxal and the trochanteral-femoral joints. The subsequent extension movements of the coxal-trochanteral and femoral-tibial joints were within the range seen during horizontal running. The structure of proximal leg joints allows for flexibility in leg use by generating subtle, but effective changes in the direction of leg movement. This architecture, along with the resulting re-direction of movements, provides a range of strategies for both animals and walking machines.     

Piezoelectrically Actuated Biomimetic Self-Contained Quadruped Bounding Robot

This paper presents the development of a mesoscale self-contained quadruped mobile robot that employs two pieces ofpiezocomposite actuators for the bounding locomotion.The design of the robot leg is inspired by legged insects and animals,and the biomimetic concept is implemented in the robot in a simplified form,such that each leg of the robot has only one degreeof freedom.The lack of degree of freedom is compensated by a slope of the robot frame relative to the horizontal plane.For theimplementation of the self-contained mobile robot,a small power supply circuit is designed and installed on the robot.Experimentalresults show that the robot can locomote at about 50 mm·s^-1with the circuit on board,which can be considered as asignificant step toward the goal of building an autonomous legged robot actuated by piezoelectric actuators.     

A Biological Micro Actuator: Graded and Closed-Loop Control of Insect Leg Motion by Electrical Stimulation of Muscles

In this study, a biological microactuator was demonstrated by closed-loop motion control of the front leg of an insect (Mecynorrhina torquata, beetle) via electrical stimulation of the leg muscles. The three antagonistic pairs of muscle groups in the front leg enabled the actuator to have three degrees of freedom: protraction/retraction, levation/depression, and extension/flexion. We observed that the threshold amplitude (voltage) required to elicit leg motions was approximately 1.0 V; thus, we fixed the stimulation amplitude at 1.5 V to ensure a muscle response. The leg motions were finely graded by alternation of the stimulation frequencies: higher stimulation frequencies elicited larger leg angular displacement. A closed-loop control system was then developed, where the stimulation frequency was the manipulated variable for leg-muscle stimulation (output from the final control element to the leg muscle) and the angular displacement of the leg motion was the system response. This closed-loop control system, with an optimized proportional gain and update time, regulated the leg to set at predetermined angular positions. The average electrical stimulation power consumption per muscle group was 148 µW. These findings related to and demonstrations of the leg motion control offer promise for the future development of a reliable, low-power, biological legged machine (i.e., an insect–machine hybrid legged robot).     

Jumping robots: a biomimetic solution to locomotion across rough terrain

This paper introduces jumping robots as a means to traverse rough terrain; such terrain can pose problems for traditional wheeled, tracked and legged designs. The diversity of jumping mechanisms found in nature is explored to support the theory that jumping is a desirable ability for a robot locomotion system to incorporate, and then the size-related constraints are determined from first principles. A series of existing jumping robots are presented and their performance summarized. The authors present two new biologically inspired jumping robots, Jollbot and Glumper, both of which incorporate additional locomotion techniques of rolling and gliding respectively. Jollbot consists of metal hoop springs forming a 300 mm diameter sphere, and when jumping it raises its centre of gravity by 0.22 m and clears a height of 0.18 m. Glumper is of octahedral shape, with four 'legs' that each comprise two 500 mm lengths of CFRP tube articulating around torsion spring 'knees'. It is able to raise its centre of gravity by 1.60 m and clears a height of 1.17 m. The jumping performance of the jumping robot designs presented is discussed and compared against some specialized jumping animals. Specific power output is thought to be the performance-limiting factor for a jumping robot, which requires the maximization of the amount of energy that can be stored together with a minimization of mass. It is demonstrated that this can be achieved through optimization and careful materials selection.     

Stable walking with asymmetric legs

Asymmetric leg function is often an undesired side-effect in artificial legged systems and may reflect functional deficits or variations in the mechanical construction. It can also be found in legged locomotion in humans and animals such as after an accident or in specific gait patterns. So far, it is not clear to what extent differences in the leg function of contralateral limbs can be tolerated during walking or running. Here, we address this issue using a bipedal spring-mass model for simulating walking with compliant legs. With the help of the model, we show that considerable differences between contralateral legs can be tolerated and may even provide advantages to the robustness of the system dynamics. A better understanding of the mechanisms and potential benefits of asymmetric leg operation may help to guide the development of artificial limbs or the design novel therapeutic concepts and rehabilitation strategies.     

Stance leg control: variation of leg parameters supports stable hopping

The spring-loaded inverted pendulum describes the planar center-of-mass dynamics of legged locomotion. This model features linear springs with constant parameters as legs. In biological systems, however, spring-like properties of limbs can change over time. Therefore, in this study, it is asked how variation of spring parameters during ground contact would affect the dynamics of the spring-mass model. Neglecting damping initially, it is found that decreasing stiffness and increasing rest length of the leg during a stance phase are required for orbitally stable hopping. With damping, stable hopping is found for a larger region of rest-length rates and stiffness rates. Here, also increasing stiffness and decreasing rest length can result in stable hopping. Within the predicted range of leg parameter variations for stable hopping, there is no need for precise parameter tuning. Since hopping gaits form a subset of the running gaits (with vanishing horizontal velocity), these results may help to improve leg design in robots and prostheses.     

A Parallel Actuated Pantograph Leg for High-speed Locomotion

High-speed running is one of the most important topics in the field of legged robots which requires strict constraints on structural design and control.To solve the problems of high acceleration,high energy consumption,high pace frequency and ground impact during high-speed movement,this paper presents a parallel actuated pantograph leg with an approximately decoupled configuration.The articulated leg features in light weight,high load capacity,high mechanical efficiency and structural stability.The similarity features of force and position between the control point and the foot are analyzed.The key design parameters,K1 and K2,which concern the dynamic performances,are carefully optimized by comprehensive evaluation of the leg inertia and mass within the maximum foot trajectory.A control strategy that incorporates virtual Spring Loaded Inverted Pendulum (SLIP) model and active force is also proposed to test the design.The strategy can implement highly flexible impedance without mechanical springs,which substantially simplifies the design and satisfies the variable stiffness requirements during high-speed running.The rationality of the structure and the effectiveness of the control law are validated by simulation and experiments.