A geometric approach to consideration of control variable limits for wheeled mobile robots with kinematic constraints

Abstract: Subject of this paper is a method for consideration of control variable limits of single actuators in a redundant driven kinematic structure of a wheeled mobile robot (wmr). It is assumed that the desired robot state is given by the translational and rotational velocity of a coordinate system fixed to the robot frame. With the assumption of rigid body elements, motion is possible only when the kinematic constraints due to redundancy in actuation are met. According to the kinematic design the wmr reference point motion results in different set value characteristics for the steering actuators. This way limited actuation dynamics of single actuators influence the reachable state region for the complete structure. In case of a wmr moving in the horizontal plane the instantaneous center of rotation of all wheels must coincide, which limits the change of wmr state to a region determined by the dynamics of the steering actuators. By determination of the non feasible states of the single actuators a combination of all non feasible states by inversion results in the valid set value region. This method can be used in command generation for dynamically demanding feasible trajectories, as well as to limit set values generated by higher level control loops to feasible ones. In case the limits for valid commands are violated an alternative command can be generated, which in this example is closest to the original command. Furthermore this procedure provides a solution for singular operating points, when the instantaneous center of rotation approaches one of the steered wheels as the dynamic constraints of this wheel are considered in the final command. The paper describes the determination of the valid region for actuating commands in detail. Furthermore the generation of alternative feasible commands is presented. The efficient implementation to a μ-controller is described. Experimental results with an 8-DOF wheeled mobile robot prove the effectiveness of this approach.