Minimum-Time Optimal Control of Many Robots that Move in the Same Direction at Different Speeds

摘要: In this paper, we solve the minimum-time optimal control problem for a group of robots that can move at different speeds but must all in same direction. We are motivated to because constraints sort common micro-scale and nano-scale robotic systems. By application minimum principle, obtain necessary conditions optimality use them guess candidate policy. showing corresponding value function is viscosity solution Hamilton-Jacobi-Bellman equation, verify our optimal. The complexity finding policy arbitrary initial only quasilinear number robots, fact dominated by computation planar convex hull. extend result consider obstacle avoidance explicit parameterization possible policies, show examples simulation.