Local Optimal Tracking Control for Manipulators with Restrictive Joint Velocity and Acceleration Limits

Velocity based tracking control of manipulators under speed and acceleration limitations has been subject of intensive research from the very beginning of industrial robots. Especially in the vicinity of singularities these limitations severely degrade control performance. Although many different control approaches exist, still none of them has been implemented in industrial manipulators. Often, heuristics in parametrization and control structure as well as stability issues due to switching impede a practical implementation.In this paper we present the novel control method PDLC to overcome these drawbacks. For active velocity or acceleration constraints it behaves locally optimal in a sense that at each time step it realizes end-effector speeds with minimal control errors. Two sets of end-effector variables can be configured: One set contains variables that must follow the reference trajectory as close as possible. The other set contains released variables that are allowed to show tracking errors when constraints are active. Thus specific accuracy requirements of the underlying manipulation task can be taken into account by the user.PDLC does not require heuristics and does not switch. Analytic solutions for the optimization based control algorithm can be derived, minimizing real time computational costs.The proposed control method is applied in simulation to a 3-DoF SCARA-type manipulator. By means of a case study the features of PDLC are demonstrated and explained in detail.