Pointwise Angle Minimization: A Method for Guiding Wheeled Robots Based on Constrained Directions

Abstract

In this paper we consider the point-to-point steering of a two wheeled differential drive mobile robot subject to constrained control inputs where the robot is expected to follow a given path between initial and final points. Formulation of this steering task as a constrained optimal control problem leads to nonlinear two-point boundary value problems. To avoid dealing with boundary value problems while alleviating the complications in analysis of systems with holonomic/non-holonomic constraints, we tackle the problem from a different perspective. This paper proposes a general framework for guiding wheeled robots using constrained direction method. The proposed scheme is equipped with pointwise angle minimization, a search algorithm useful in devising control strategies for steering problems. In addition to computational efficiency, one of the main advantages of the proposed scheme is that it does not impose any restrictive assumptions on the robot’s model. In this paper, kinematics of the robot under the assumption of rolling without slipping has been used as the model of the system and the efficiency of the proposed navigation scheme is illustrated through simulation results. However, the proposed scheme can be applied to more complicated models representing the two wheeled differential robots such as dynamics under slip occurrence.