Motion Control of a Planar Spider-like Robot in a Two-dimensional Gravitational Field

Mobile robots are generally required to pass through non-flat terrains which may contain holes and obstacles. Robots which are adequate for performing this task are limbed robots. The goal of this research is to navigate a multi-limbed robot under gravitational field effects. The navigation of the robot is achieved by quasistatic gaiting. In quasistatic motion, inertial effects due to moving parts of the robot are kept small relative to gravity forces and forces of interaction with the environment. The navigation of multi-limbed mechanisms in two dimensions using quasistatic motion was studied by [1], [2]. However, gravitational field effects were not included. Or and Rimon [3] characterized robust equilibrium postures in a two-dimensional gravitational field where the mechanism was modeled as a single rigid body. In this work, however, we are concerned with the analysis of stable equilibrium stances while accounting for the compliance induced by the mechanism's joints. A planar spider-like robot is described. The robot consists of an unactuated central base which is attached to k limbs. Each limb consists of n links and n actuated revolute joints. The robot thus has a total of degrees of freedom. We assume that the robot's footpads contact a piecewise linear terrain with known geometry and that each contact is frictional with a known lower bound on the coefficient of friction. 3 + ⋅ n k