1. Control of a Mobile Robot with a Trailer Based on Nilpotent Approximation
- Author
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A. A. Ardentov and Alexey Mashtakov
- Subjects
0209 industrial biotechnology ,Computer science ,Plane (geometry) ,010102 general mathematics ,Trailer ,Mobile robot ,02 engineering and technology ,State (functional analysis) ,Kinematics ,Optimal control ,01 natural sciences ,Computer Science::Robotics ,Nilpotent ,020901 industrial engineering & automation ,Control and Systems Engineering ,Control theory ,Robot ,0101 mathematics ,Electrical and Electronic Engineering - Abstract
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.
- Published
- 2021
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