Stiffness control of a legged robot equipped with a serial manipulator in stance phase

The ability to perform different tasks by a serial manipulator mounted on legged robots, increases the capabilities of the robot. The position/force control problem of such a robot in the stance phase with point contacts on the ground is investigated here. A target plane with known stiffness is specified in the workspace. Active joints of the legs and serial manipulator are used to exert the desired normal force on the plane while tracking a desired trajectory on the plane. First, the equations of motion of the robot and contact forces of the feet on the ground are derived. A controller is then proposed which tracks the desired trajectory while keeping the feet contacts on the ground and prevent slipping. An optimization problem is solved in each control loop to minimize the actuation effort. This minimization is subject to position tracking for the end-effect or (using inverse dynamics controller), force requirements of the feet contacts with the ground, and actuators capabilities. Simulations are conducted for the simplified model of a quadruped robot with a 2-DOF serial manipulator. To test the controller, a 20 N normal force is applied onto the target plane while moving the tip of the end-effector. It is shown that the robot can perform the task effectively without losing the ground contact and slipping.