Distance Computation Between Non-Holonomic Motions with Constant Accelerations

A method for computing the distance between two moving robots or between a mobile robot and a dynamic obstacle with linear or arc-like motions and with constant accelerations is presented in this paper. This distance is obtained without stepping or discretizing the motions of the robots or obstacles. The robots and obstacles are modelled by convex hulls. This technique obtains the future instant in time when two moving objects will be at their minimum translational distance - i.e., at their minimum separation or maximum penetration (if they will collide). This distance and the future instant in time are computed in parallel. This method is intended to be run each time new information from the world is received and, consequently, it can be used for generating collision-free trajectories for non-holonomic mobile robots.

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