The Effect of Limb Kinematics on the Speed of a Legged Robot on Granular Media

Abstract

Achieving effective locomotion on diverse terrestrial substrates can require subtle changes of limb kinematics.Biologically inspired legged robots (physical models of organisms) have shown impressive mobility on hard ground but suffer performance loss on unconsolidated granular materials like sand. Because comprehensive limbground interaction models are lacking, optimal gaits on complex yielding terrain have been determined empirically. To develop predictive models for legged devices and to provide hypotheses for biological locomotors, we systematically study the performance of SandBot, a small legged robot, on granular media as a function of gait parameters. High performance occurs only in a small region of parameter space. A previously introduced kinematic model of the robot combined with a new anisotropic granular penetration force law predicts the speed. Performance on granular media is maximized when gait parameters minimize body acceleration and limb interference, and utilize solidification features of granular media. INTRODUCTIONTo move effectively over a wide range of terrestrial terrain requires generation of propulsive forces through appropriate muscle function and limb kinematics [1,2]. Most biological locomotion studies have focused on steady rhythmic locomotion on hard, flat, non-slip ground. On these surfaces kinematic (gait) parameters like limb frequency, stride length, stance and swing durations, and duty factor can change as organisms walk, run, hop and gallop [1]. There have been fewer biological studies of gait parameter modulation on non-rigid and nonflat ground, although it is clear that gait parameters are modulated as the substrate changes during challenges like climbing [3,4], running on elastic/damped substrates [5], transitioning from running to swimming [6], and running on different preparations of granular media [7]. Even subtle kinematic changes in gait can lead to major differences in limb function [8]. A major challenge is to develop models of limb interaction with complex substrates and to develop hypotheses for how organisms vary gait parameters in response to substrate changes.The RHex class of model locomotors (robots) has proved useful to test hypotheses of limb use in biological organisms on hard ground [9] and recently on more complex ground with few footholds [10] or the ability to flow [11]. These hexapedal devices model the dynamically stable locomotion of a cockroach and were the first legged machines to achieve autonomous locomotion at speeds exceeding one body length/s. In these devices, complexity in limb motion is pared down to a few biologically relevant parameters controlling intra-cycle "stance" and "swing" phases of 1-dof rotating limbs (referred to as"gait" parameters hereafter; see detailed description in Methods and Results). When these gait parameters are appropriately adjusted, RHex shows performance comparable in speed and stability to organisms on a diversity of terrain [12]. However, because of the scarcity of existing models of limb interaction with com...

Multi-functional foot use during running in the zebra-tailed lizard (Callisaurus draconoides)

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Models for Slip Estimation and Soft Terrain Characterization With Multilegged Wheel–Legs

“…(24) correspond to the ratio of the other model's error variance (σ 2 S,T |V ) over the sum of both variances, as in Eq. (26). This fusion scheme agrees with the optimal gain of the Kalman filter measurement update for variance minimization.…”

“…Examples of related work generally consider rigid ground rather than soft soil [21], conventional articulated legs rather than rotary legs [22], [23], or assume very low sinkage and lack experimental validation [24]. However, there is a series of research publications that address the interaction and performance of robots with multiple singlelegged wheel-legs through systematic empirical studies [25], [26] and experimentally validated terradynamics modeling [11], [27].…”

A Forced Damped Oscillation Framework for Undulatory Swimming Provides New Insights into How Propulsion Arises in Active and Passive Swimming

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