Abstract
The initial position and velocity of a robot is given, and the problem posed is to make it stop at the origin in the shortest possible time, given a maximum acceleration and speed. The robot can control its acceleration vector, and hence the full optimization problem can be specified as a Hamiltonian system where the solution will minimize the transit time. This problem is discussed in both the one- and two-dimensional cases. The key control parameter is the acceleration direction; reducing the problem to a one-dimensional optimization opens up several areas of exploration. The direction can be optimized using a global search algorithm, or can be updated periodically using a local search algorithm with a penalty function. Numerical solutions are presented in these cases, including when physical obstacles are included in the penalty function. The one-dimensional optimization also allows the use of reinforced learning to minimize the transit time.
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