Step length as a function of derived from 2s ϭ 2v / reveals the condition for the onset of swimming for տ 0.6 as s/R Ϸ 1. The solid lines and symbols are for values of 0. 580, 0.590, 0.600, 0.611, 0.616, 0.622, and 0.633.

RHex is an untethered, compliant leg hexapod robot that travels at better than one body length per second over terrain few other robots can negotiate at all. Inspired by biomechanics insights into arthropod locomotion, RHex uses a clock excited alternating tripod gait to walk and run in a highly maneuverable and robust manner. We present empirical data establishing that RHex exhibits a dynamical ("bouncing") gait-its mass center moves in a manner * This work was supported in part by DARPA/SPAWAR under contract N66001-00-C-8026. Portions of the material reported here were first presented in a conference paper appearing in the collection (Altendorfer et al., 2000). 208 Altendorfer et al. well approximated by trajectories from a Spring Loaded Inverted Pendulum (SLIP)-characteristic of a large and diverse group of running animals, when its central clock, body mass, and leg stiffnesses are appropriately tuned. The SLIP template can function as a useful control guide in developing more complex autonomous locomotion behaviors such as registration via visual servoing, local exploration via visual odometry, obstacle avoidance, and, eventually, global mapping and localization.

Abstract-This paper reviews a template for dynamical climbing originating in biology, explores its stability properties in a numerical model, and presents empirical data from a physical prototype as evidence of the feasibility of adapting the dynamics of the template to robot that runs vertically upward.The recently proposed pendulous climbing model abstracts remarkable similarities in dynamic wall scaling behavior exhibited by radically different animal species. The present paper's first contribution summarizes a numerical study of this model to hypothesize that these animals' apparently wasteful commitments to lateral oscillations may be justified by a significant gain in the dynamical stability and, hence, the robustness of their resulting climbing capability. The paper's second contribution documents the design and offers preliminary empirical data arising from a physical instantiation of this model. Notwithstanding the substantial differences between the proposed bio-inspired template and this physical manifestation, initial data suggest the mechanical climber may be capable of reproducing both the motions and ground reaction forces characteristic of dynamical climbing animals. Even without proper tuning, the robot's steady state trajectories manifest a substantial exchange of kinetic and potential energy, resulting in vertical speeds of 0.30 m/s (0.75 bl/s) and claiming its place as the first bio-inspired dynamical legged climbing platform.

This paper presents the first evidence that the Spring Loaded Inverted Pendulum (SLIP) may be "anchored " in our recently designed compliant leg hexapod robot, RHex. Experimentally measured RHex center of mass trajectories are fit to the SLIP model and an analysis of the fitting error is performed. The fitting results are corroborated by numerical simulations. The "anchoring " of SLIP dynamics in RHex offers exciting possibilities for hierarchical control of hexapod robots.

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...