Algorithms for Planning Smoothed Individual Trajectories of Ground Robots

摘要

The article is devoted to the development of an algorithm for constructing the trajectory of a robotic platform moving in an environment with obstacles. This algorithm is based on the application of a special local optimization procedure at each planning step and allows us to obtain feasible program trajectories without increasing the computational complexity of algorithms compared to existing methods. The algorithm is based on the application of the improved method of potential fields and subsequent smoothing of the resulting trajectory. The improving of the potential field method consists in a new way of detecting and avoiding local minima. When a local minimum is detected, it is added to the map as an additional obstacle, which makes it possible to avoid it during further trajectory planning. To circumvent obstacles that can be approximated by polygons, the method of the effective point to the obstacle is proposed, which is the equivalent of the latter in relation to the current location of the moving robotic platform when using this planning method. A two-stage technique for smoothing piecewise linear trajectories is proposed. It is assumed that there is some initial suboptimal curve found by any planning method. This curve is optimized using a functional that includes the length of the trajectory and the deviation of the optimized curve from the original curve. At the second stage, the linear segments of the planned straight line are conjugated with second-order curves. As a result, the planned trajectory of motion is a quadratic-linear curve with a smooth function of the trajectory velocity. At the same time, the proposed method of coupling rectilinear sections of the trajectory does not require sudden changes in speed when passing turns. Simulation results confirming the effectiveness of the proposed method of planning the trajectories of robots are considered and discussed.