Motion planning with constraints using configuration space approximations

Robots executing practical tasks in real environments are often subject to multiple constraints. These constraints include orientation constraints: e.g., keeping a glass of water upright, torque constraints: e.g., not exceeding the torque limits for an arm lifting heavy objects, visibility constraints: e.g., keeping an object in view while moving a robot arm, etc. Rejection sampling, Jacobian projection techniques and optimization-based approaches are just some of the methods that have been used to address such constraints while computing motion plans for robots performing manipulation tasks. In this work, we present an approach to handling certain types of constraints in a manner that significantly increases the efficiency of existing methods. Our approach focuses on the sampling step of a motion planner. We implement this step as the drawing of samples from a set that has been computed in advance instead of the direct sampling of constraints. We show how our approach can be applied to different constraints: orientation constraints on the end-effector of an arm, visibility constraints and dual-arm constraints. We present simulated results to validate our method, comparing it to approaches that use direct sampling of constraints.