Control of a mobile robot with a trailer based on nilpotent approximation

We consider a kinematic model of a mobile robot with a trailer moving on a homogeneous plane. The robot can move back and forth and make a pivot turn. For this model, we pose the following optimal control problem: transfer the “robot–trailer” system from an arbitrarily given initial configuration into an arbitrarily given final configuration so that the amount of maneuvering is minimal. By a maneuver we mean a functional that defines a trade-off between the linear and angular robot motion. Depending on the trailer–robot coupling, this problem corresponds to a two-parameter family of optimal control problems in the 4-dimensional space with a 2-dimensional control.
We propose a nilpotent approximation method for the approximate solution of the problem. A number of iterative algorithms and programs have been developed that successfully solve the posed problem in the ideal case, namely, with no state constraints. Based on these algorithms, we propose a dedicated reparking algorithm that solves a particular case of the problem where the initial and final robot position coincide and takes into account a state constraint on the trailer’s turning angle occurring in real systems.