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

摘要

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.