Jerk-optimal force and motion synchronous planning for a 3-DOF translational force-controlled end-effector

The 3-DOF Translational Force-controlled End-effector (TFE) based on 3-P(UU)₂ Parallel Mechanism (PM) and pneumoelectric actuator is developed for polishing process performed by industrial robots, in which synchronous force and motion planning is critical to enhance the polishing performance. However, conventional planning methods are mainly developed to generate the trajectory for robotic motion control. Utilizing periodic splines, a new jerk-optimal Force and Motion Synchronous Planning (FMSP) method is proposed for the 3-DOF TFE to improve the force control stability between the tool and environment. Both the kinematics of the 3-DOF translational PM and the dynamics of the hybrid serial-parallel and macro-mini robotic system are established through screw theory. By introducing septuple B-splines for motion trajectory and cubic splines for contact force with periodic boundary conditions, the jerk-optimal performance index of motion and force is employed to formulate the FMSP model in Cartesian space. Simulation and experimental results demonstrate that the high-order continuity of the active driving force, moving acceleration and jerk-optimal performance index generated by FMSP is preferable compared to the Trajectory Planning with Point-to-point Force (TPWPF) and the Force-motion Linear Interpolation (FMLI) methods. The unloaded force peaks caused by the motion impact are reduced by 21 % and 22.6 % along x and y direction, respectively. Furthermore, the peaks of the contact force between the tool and workpiece decrease by 31.5 % and 20.4 % owing to slighter systemic vibration and impact. The FMSP method for force-controlled end-effector shows great potential in robotic continuous contact operations.