Robot Control Using On-Line Modification of Reference Trajectories

In practice, the robot motion is specified according to physical constraints, such as limited torque input. Thus, the computation of the desired trajectory is constrained to attain the physical limit of actuator saturations. See, e.g., (Pfeiffer & Johanni, 1987), for a review of trajectory planning algorithms considering the robot model parameters and torque saturation. Besides, trajectories can also be planned irrespectively of the estimated robot model, i.e., simply by using constraints of position, velocity and acceleration at each time instant, see, e.g., (Cao et al., 1997; Macfarlane & Croft, 2003). Once that the reference trajectory is specified, the task execution is achieved in real time by using a trajectory tracking controller. However, if parametric errors in the estimated model are presented, and considering that the desired trajectories require to use the maximum torque, no margin to suppress the tracking error will be available. As consequence, the manipulator deviates from the desired trajectory and poor execution of the task is obtained. On-line time-scaling of trajectories has been studied in the literature as an alternative to solve the problem of trajectory tracking control considering constrained torques and model uncertainties. A technique for time-scaling of off-line planned trajectories is introduced by Hollerbach (1984). The method provides a way to determine whether a planned trajectory is dynamically realizable given actuator torque limits, and a mode to bring it to one realizable. However, this method assumes that the robot dynamics is perfectly known and robustness issues were not considered. It is noteworthy that this approach has been extended to the cases of multiple robots in cooperative tasks (Moon & Ahmad, 1991) and robot manipulators with elastic joints (De Luca & Farina, 2002). In order to tackle the drawback of the assumption that the robot model in exactly known, Dahl and Nielsen (1990) proposed a control algorithm that result in the tracking of a time-scaled trajectory obtained from a specified geometric path and a modified on-line velocity profile. The method considers an internal loop that limits the slope of the path velocity when the torque input is saturated. Other solutions have been proposed in, e.g., (Arai et al., 1994; Eom et al., 2001; Niu & Tomizuka, 2001). In this chapter, an algorithm for tracking control of manipulators under the practical situation of limited torques and model uncertainties is introduced. The proposed approach consists of using a trajectory tracking controller and an algorithm to obtain on-line time-