Optimal control approach for trajectory determination to suppress residual frame vibrations of delta robots in pick and place tasks

• Validated approach to determine time-optimal and vibration-reducing trajectories. • Holistic (path and motion law) trajectory optimization for a complex multi-DOF system. • Experimental system identification to tune a multi-body simulation for optimization. • Mathematical description of constraints required for a robotic pick and place task. This paper proposes an optimal control approach to reduce frame vibrations in robotic pick and place tasks, caused by rapid acceleration and deceleration of the robot. The objective of the proposed optimal control approach is to determine time-optimal trajectories that cancel out residual frame vibrations after trajectory execution. The control problem is defined for a delta robot but can be adapted to any type of robot used for pick and place tasks. To solve the optimal control problem numerically, it is transformed into a nonlinear programming problem using the Legendre-Gauss-Lobatto collocation method. To validate the approach, experiments are conducted to compare the residual frame vibrations of optimized trajectories with typical pick and place trajectories. The novelty of the paper is the vibration reduction with an optimization-based approach on a complex multi-degree-of-freedom robot system whose dynamic parameters are identified with experimental data. In addition, a mathematical description of all constraints required for a robotic pick and place task is proposed for the optimization.