A General Framework for Optimal Tuning of PID-like Controllers for Minimum Jerk Robotic Trajectories - Oliveira, Phelipe W.; Barreto, Guilherme A.; Thé, George A. P. (Journal of intelligent & robotic systems, 2020)
The minimum jerk principle is commonly used for trajectory planning of robotic manipulators. However, since this principle is stated in terms of the robot’s kinematics, there is no guarantee that the joint controllers will actually track the planned acceleration and jerk profiles because the tuning of the controllers’ gains is decoupled from the trajectory planning. Bearing this in mind, in this paper we introduce a comprehensive framework for optimal estimation of the gains of PID-like controllers for tracking minimum-jerk (MJ) robot trajectories. The proposed methodology relies mainly on a novel variant of error-based performance indices (ISE, ITSE, IAE and ITAE) which are adapted to the tracking of MJ trajectories. Furthermore, the particle swarm optimization (PSO) algorithm is used to search for optimal values for the gains of the controllers of all joints simultaneously. The resulting approach is much simpler than recent developments based on more complex performance indices, in which joint controllers were individually optimized. The proposed approach is general enough to easily encompass the tuning of fractional PID controllers and a comprehensive set of experiments are reported comparing the performances of standard and fractional PID controllers for the task of interest.