Robust Time Optimal Obstacle Avoidance Problem for Constrained Discrete Time Systems

This paper presents algorithms for the computation of the set of states that can be robustly steered in a finite number of steps via state feedback control to a given target set while avoiding pre–specified zones or obstacles. The paper therefore extends standard results in (robust) time optimal control. A general procedure is given for the case when the system is discrete-time, nonlinear and time-invariant, and subject to constraints on the state and input. Furthermore, the paper shows how the necessary set computations may be performed using polyhedral algebra, linear programming and computational geometry software, when the system is piecewise affine with additive state disturbances.