On Property Analysis of Optimal Solutions for Two Typical Motion Planning Problems

This paper considers the optimal solutions of two typical motion planning problems subject to the speed and acceleration constraints. The performance indexes of these two problems are maximizing the distance from a non-cooperative object and adjusting the target azimuth of the decision-making object with respect to the non-cooperative object in the shortest time, respectively. Although it is difficult to obtain explicit optimal solutions in general, this paper studies the properties of optimal solutions under some typical conditions. In particular, the explicit expressions for the optimal solutions of these two motion planning problems are given under the condition that distance between the decision-making object and the non-cooperative object is larger than a certain value. Without complicated calculation or special initial value, the optimal solutions only need the current information of non-cooperative object. Finally, the simulation results for some typical cases illustrate our theoretical results.