An obstacle avoidance model predictive control scheme: a sum-of-squares approach

The paper addresses the obstacle avoidance motion planning problem for ground vehicles operating in uncertain environments, i.e. time-varying obstacle scenarios are taken into consideration. By resorting to set-theoretic ideas and sum of squares (SOS) decomposition techniques, a receding horizon control algorithm is proposed for robots modelled by polynomial systems subject to input/state constraints. Sequences of inner ellipsoidal approximations of the exact one-step controllable sets are pre-computed for all the possible obstacle scenarios and then on-line exploited to determine the more adequate control action to be applied to the robot in a receding horizon fashion. The results here proposed are a significant generalization of existing algorithms which are tailored only for linear time invariant plant descriptions. The resulting framework guarantees Uniformly Ultimate Boundedness and constraints fulfilment regardless of any obstacle scenario occurrence.