Optimal Trajectory Planning for Delta Robot Based on Three-Parameter Lamé Curve

This paper presents a method of optimal trajectory planning for Delta robot based on three-parameter Lamé curve. Using the curve to smoothen the corners of adept motion in Cartesian space. A 6th order polynomial with asymmetrical acceleration and deceleration is adopted to generate the motion profile. The general formulations of displacement, velocity and acceleration are derived at discrete time. To make the overall trajectory as smooth as possible under the constraints of joint velocity, acceleration and torque, a genetic algorithm with elitist strategy is applied to optimize the three parameters under a cost function which is defined by the mean value of joint torque time-derivative. Simulation results show that this optimal trajectory planning method can gain smooth trajectory in Cartesian space and allows high-speed pick-and-place operation for Delta robot with small tracking errors.