The dynamics of legged locomotion in heterogeneous terrain: universality in scattering and sensitivity to initial conditions

Abstract

Abstract-Natural substrates are often composed of particulates of varying size, from fine sand to pebbles and boulders. Robot locomotion on such heterogeneous substrates is complicated in part due to large force and kinematic fluctuations introduced by heterogeneities. To systematically explore how heterogeneity affects locomotion, we study the movement of a hexapedal robot (15 cm, 150 g) in a trackway filled with ∼ 1 mm "sand", with a larger convex "boulder" of various shape and roughness embedded within. We investigate how the presence of the boulder affects the robot's trajectory. To do so we develop a fully-automated terrain creation system, the SCATTER (Systematic Creation of Arbitrary Terrain and Testing of Exploratory Robots), to control the initial conditions of the substrate, including sand compaction, boulder distribution, and substrate inclination. Analysis of the robot's trajectory indicates that the interaction with a boulder can be modeled as a scatterer with attractive and repulsive features. Depending on the contact position on the boulder, the robot will be scattered to different directions after the interaction. The trajectory of an individual interaction depends sensitively on the initial conditions, but remarkably this dependence of scattering angle upon initial contact location is universal over a wide range of boulder properties. For a larger heterogeneous field with multiple "scatterers", the trajectory of the robot can be estimated using a superposition of the scattering angles from each scatterer. This scattering superposition can be applied to a variety of complex terrains, including heterogeneities of different geometry, orientation, and texture. Our results can aid in development of both deterministic and statistical descriptions of robot locomotion, control and path planning in complex terrain.

A review on locomotion robophysics: the study of movement at the intersection of robotics, soft matter and dynamical systems

“…The following study exemplifies automation's utility in the study locomotion of heterogeneous substrates. 1 S1 S1 S1 S1 S1 S S1 S1 Qian et al [225] have taken the first steps in this ambitious direction with the development of a fully-automated terrain creation system called Systematic Creation of Arbitrary Terrain and Testing of Exploratory Robots (SCATTER, Fig. 2c).…”

Anticipatory control using substrate manipulation enables trajectory control of legged locomotion on heterogeneous granular media

“…Using SCATTER, we investigated the locomotor dynamics during interaction with a single 3D printed convex objects of different geometries, textures, burial depths and mobilities. 1 Our study revealed that the complex interaction between a robot with a single boulder could be modelled as a scattering process -depending on the contact position on the boulder, the robot left the heterogeneity with a certain angle of trajectory deviation.…”

“…1 For example, we compare robot trajectories during interaction with a single spherical boulder fixed at different burial depths in the sand (Fig. 3A).…”

Modulation of Robot Orientation Via Leg-Obstacle Contact Positions

“…In contrast, robots typically avoid most collisions and contacts with their physical environments and treat large disturbances as "obstacles" because our limited understanding of contact reaction forces precludes their effective use. Without a better understanding of the dynamics of repeated locomotorobstacle interactions [3], [5], [6] obtaining such understanding from systematic experiments in simplified settings [7], [8], [9], [10], [11], [12], [5], [13]. While the vast parameter space presented by any natural environment presents daunting challenges to analysis, this paper seeks to build on recent progress in extracting a highly abstracted but physically revealing model of periodic legged gaits interacting with periodically structured obstacle fields [13].…”