Kinematic Control of a Nonholonomic Wheeled Mobile Manipulator – a Differential Flatness Approach

This paper presents an integrated motion planning and control framework for a nonholonomic wheeled mobile manipulator (WMM) system taking advantage of the (differential) flatness property. We first develop the kinematic model of the system and analyze its flatness properties. Subsequently, a statically feedback linearizable system description is developed by appropriately choosing the flat outputs. Motion-planning can now be achieved by polynomial curve fitting to satisfying the terminal conditions in the flat output space while control design reduces to a pole-placement problem for a linear system. A case study of point-to-point motion is considered to study the effectiveness of pose stabilization in the WMM. The simulation and experimental results highlight the ease-of-implementation of proposed method for online real-time integrated motionplanning/control within a hardware-in-the-loop (HIL) electro-mechanical testing. NOMENCLATURE WMR Wheeled Mobile Robot WMM Wheeled Mobile Manipulator ( ) , x y Cartesian coordinates of the center of the wheel axle of the WMR φ Orientation of the WMR with respect to the global frame 1 2 , θ θ Relative angles to describe the configuration of the two-link manipulator , r l θ θ Angular positions of the right and left wheel, respectively , v ω Forward and angular velocity inputs to WMR 1 2 , u u Velocity inputs to first and second joints of the manipulator, respectively η Acceleration of the WMR, v η = q Vector of generalized coordinates of the system. F Flat outputs ( ) F t Actual trajectories in the flat output space ( ) d F t Desired trajectories in the flat output space ξ Change of inputs for feedback linearization e Error between the desired and the actual trajectories in the flat output space T Final time