Preliminary Solutions for Autonomous Mobile Robot Docking Subject to Uniform Braking Safety Constraints
E. Rimon and G. Manor
https://doi.org/10.19124/ima.2015.001.27
Abstract
This paper considers the synthesis of time optimal paths for a mobile robot docking at targets located on the boundary of a polygonal obstacle in IR2. The robot must avoid the obstacle as well as satisfy velocity dependent braking safety constraints during the docking process. The classical Brachistochrone problem studies the time optimal path of a particle moving in an obstacle free environment subject to a constant force field. By encoding the braking safety constraint as a force field surrounding the obstacle, the paper generalizes the Brachistochrone problem into synthesis of time optimal paths for a mobile robot attempting to dock against an obstacle boundary. To solve the time optimal docking problem, the safe travel time functional, a path dependent function, is formulated. Convexity properties of this functional allow computation of the time optimal docking path as a convex optimization problem in O(n3 log(1/ϵ)) time, where n is the number of obstacle vertices and ϵ is the desired solution accuracy.