Obstacle avoidance using optimal control theory
H.L. Hagenaars · TU/e Research Portal · 2004
This report addresses the optimal control problem with non-convex state constraints.The specific application pursued is the obstacle avoidance problem.To solve the problem, discretization of time and space is used, which is often used in solving obstacle avoidance problems.During each time step, the optimal control using the standard continuous-time cost function is derived in an explicit form, including the optimal next step as a parameter.The optimal next step can be obtained by solving a discrete minimization problem.An efficient algorithm to solve this problem is presented.Numerical simulations are used to point out that the standard continuous-time cost function does not lead to satisfactory results.Next, a new cost function is proposed that includes the intermediate desired target states.This leads to a new approach that optimizes the continuous-time behavior as well as the discrete states simultaneously.The optimal control can be given in an explicit form that includes the intermediate target states as parameters, and the optimal intermediate target states can be obtained by solving a discrete optimization problem, making use of the algorithm presented before.This approach gives a sub-optimal solution to the initial problem.Finally, numerical simulations illustrate the effectiveness of the new approach.