Application of Chance-Constrained Optimal Control to Optimal Obstacle Avoidance

摘要

The problem of optimal obstacle avoidance in the presence of chance constraints is considered using the time minimization of a Dubin's car with a circular keep-out zone. Three cases of the Dubin's car problem are explored. For the first case, the only constraint is the circular keep out zone. For the second case, a three-sided box with side length equal to the diameter of the keep out zone is added as a second path constraint and for which the deterministic optimal control problem is unsolvable. The keep out zone is then transformed to have a probabilistic boundary, converting the problem from a deterministic to a chance-constrained optimal control problem. A Split-Bernstein approximation method is used to transform the chance constraint into a deterministic nonlinear constraint. The chance-constrained optimal control problem is solvable and the solution has a lower optimal cost than that of the first deterministic optimal control problem. Thus in certain applications there is a correlation between a lower optimal cost and higher risk that has numerous practical applications. Numerical results are shown that demonstrate the effectiveness of the technique.