Nonlinear modeling and control of slosh in liquid container transfer via a PPR robot

This paper studies the point-to-point liquid container transfer control problem for a PPR robot. The robot manipulator is represented as three rigid links, and the liquid slosh dynamics are included using a multi-mass-spring model. It is assumed that two forces and a torque applied to the prismatic joints and the revolute joint, respectively, are available as control inputs. The objective is to control the robot end-effector movement while suppressing the sloshing modes. A nonlinear mathematical model that reflects all of these assumptions is first introduced. Then, Lyapunov-based feedback controllers are designed to achieve the control objective. Two cases are considered: partial-state feedback that does not use slosh state information and full-state feedback that uses both robot state and slosh state measurements or estimations. Computer simulations are included to illustrate the effectiveness of the proposed control laws.