Controller design for robot manipulators based on reachability

This paper presents an alternative way to design controllers for robot manipulator systems based on the concept of reachability. Led by the definition of reachability, controller design contains two steps: the kinematics design and the dynamics design. In the kinematics design, the desired trajectory of acceleration is planned to satisfy the constraints of specific control tasks. And in the dynamics design, the controller is designed to realize the planned acceleration based on the system model. Thus, reachability is achieved through this two-step design. All the parameters of the proposed controller are calculated on-line. In particular, the inertia matrix is estimated using the measured acceleration signal and the lumped uncertain term including the Coriolis force, the gravity force, and the disturbance force is obtained through the observer. The estimation error is reflected in the position and velocity. The present velocity and position of the robot are then used as initial conditions to re-plan the new desired acceleration for the next control action. Simulation results conducted on two-link planar robotic arm show that the performance of the closed-loop system has five order of precision improvements on angular position errors compared with traditional computed-torque plus proportional-derivative (PD) control, and one order of precision improvement compared with sliding mode control both in low speed tracking (< 5 rad/s) and high speed tracking (< 70 rad/s).