A reduced-order analytical solution to mobile robot trajectory generation in the presence of moving obstacles

In this paper, the problem of determining a collision-free trajectory for a car-like mobile robot moving in a dynamically changing environment is addressed. By explicitly considering the kinematic model of the robot, the family of feasible trajectories and their corresponding steering controls are derived in a closed form. In particular, feasible trajectories are parameterized as a family of fifth-order piecewise-constant polynomials and their solutions can be solved from the real-time updated boundary conditions and a set of new second-order polynomial inequalities formulated according to collision-avoidance conditions. The obtained solutions are analytical and can be updated in real time once a change in the environment is detected. Simulation shows that the proposed method is effective.