As the field of autonomous mobile robot motion planning reaches maturity, researchers are seeking new frontiers that will expand their range of applications and improve their safety record. An important example is self driving cars that will soon allow vehicles to be piloted at speeds up to 50 km/h in urban environments cohabited by human-driven cars, bicyclists and pedestrians.
The talk will focus on the synthesis of high speed paths for autonomous mobile robots subject to velocity dependent safety constraints. Calculus of variations seems to provide an ideal toolbox for synthesising such paths in the mobile robot’s position-and-velocity state space. In particular, 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 mobile robot’s braking safety constraint as a force field surrounding each obstacle, the the Brachistochrone problem can be generalized into safe time optimal navigation of a mobile robot in environments populated by obstacles.
Based on this insight, the talk will describe how calculus of variation can be used to solve two classical autonomous mobile robot problems. The first problem concerns *time optimal navigation* among obstacles subject to uniform braking safety constraints. Convexity of the safe travel time functional, a path dependent function, allows efficient computation of safe high speed paths as a convex optimization problem in O(n^2log(1/e)) steps, where n is the number of obstacle features in the environment and e is the desired solution accuracy. The second problem concerns *time optimal docking* of a mobile robot against an obstacle boundary along safe time paths. Here, too, convexity of the safe travel time functional allows efficient computation of the time optimal docking path. The results will be illustrated with examples and on-going validation experiments will be described.