Control of A 2R Planar Horizontal Underactuated Manipulator

This paper presents a new method for trajectory planning and control of a 2R planar horizontal robotic arm with only the first joint actuated, which is known to be controllable but not asymptotically stabilizable with smooth feedback controllers. The main idea is to first determine an admissible trajectory that satisfies both the constraints of system dynamics and boundary value conditions, and then design a feedforward controller for the system. For complex and highly nonlinear systems, an optimization method is applied to determine the trajectory. Moreover, a time-scaling method can be used to control the magnitude of the inputs and also make it easier to find a solution in the optimization procedure. To further improve the robustness of the controller, a feedback controller is designed along the planned trajectory. Position to position control of the robot is simulated to demonstrate the effectiveness of the method.