On the Use of Ellipsoidal Estimation Techniques in the RRT Suboptimal Pathfinding Algorithm

The article is devoted to the development of an algorithm for the approximate solution of the time-optimal control problem for a system of ordinary differential equations, under the condition of avoiding collisions with stationary obstacles and subject to the specified point-wise constraints on the possible values of the control parameters. The main idea is to use a modification of the algorithm for finding suboptimal paths using rapidly growing random trees (RRT*). The most difficult part of this algorithm is to find the optimal trajectories for the problems of transferring the system from one fixed position to another, close to it, without taking into account state constraints. This subproblem is proposed to be solved using the methods of ellipsoidal calculus. This approach makes it possible to efficiently search suboptimal trajectories both for linear systems with large state space dimension and for systems with nonlinear dynamics. Algorithms for the linear and non-linear cases are sequentially analyzed in the paper, and the corresponding examples of calculations are presented.