The well-known algorithms for time-optimal trajectory planning are difficult to apply in practice because they rely on imperfect models of the robot dynamics, they take no account of controller dynamics, and they provide no connection to tracking accuracy. In this paper we propose two schemes for planning and implementing time-optimal control to enable robots under computed torque control to track paths to a prescribed tolerance. Experimental results confirm the theories, showing that both schemes track to a prescribed accuracy in a near time-optimal fashion. The second scheme is shown to perform better, achieving complete torque utilization nearly all of the time.

In this paper, we propose an approach to solving the problem of robust time-optimal path tracking control to meet a prescribed tolerance in the presence of plant uncertainty. Our approach involves identifying the modelling errors as disturbances in joint accelerations and using a theory that relates such disturbances to the tracking performance of a robot under computed-torque control. The theory allows us to calculate the torque levels that need to be held in reserve and the controller gains that are required to reject the expected levels of disturbance. Our experiments show that if these levels of torque are held in reserve and if the controllers are tuned in this way, then the robot performs near time-optimal tracking meeting the specified tolerance for tracking accuracy.

In previous work the authors (1996) developed a method for planning robust time-optimal reference trajectories for robots under computed-torque control. That scheme was based on the idea of holding enough torque on reserve during trajectory planning to ensure that actuators would not saturate due to disturbances. This, together with the correct controller gain settings, ensured that tracking was accurate to a specified tolerance. This work extends that approach to a less conservative "closed-loop" architecture for "online trajectory generation" which is similar to Dahl and Neilsen's scheme (1990) for "online trajectory time-scaling". We propose a feedback control law for setting the reference path acceleration such that path tracking is nearly time-optimal, robustly controllable, and accurate to a prescribed tolerance. We show how this law can be determined offline using shooting methods and implemented with little online memory. Experimental results demonstrate that the tracking times are reduced compared to our previous approach, while tracking accuracy and robustness remain approximately the same.

In this paper we investigate whether singular configurations may be good sites for high-speed pick or place operations. Motivation comes from the observation that the end effector velocity can be brought to zero at a singularity without stopping the mechanism. This allows the robot to keep some of its kinetic energy while accomplishing the pick or place task and can lead to faster cycle times compared to pick or place at nearby regular configurations.

This article develops a general technique for differential analysis that can be applied to singularities of three related problems: path tracking for nonredundant robots, self-motion analysis for robots with one degree of redundancy, and displacement analysis of single-loop mechanisms. For each of these problems, the locus of displacement solutions generally forms a set of one-dimensional manifolds in the space of variable parameters. However, if singularities occur, the manifolds may degenerate into isolated points, or into curves that include bifurcations at the singular points. Higher-order equations, derived from Taylor series expansion of the matrix equation of closure, are solved to identify singularity type and, in the case of bifurcations, to determine the number of intersecting branches as well as a Taylor series expansion of each branch about the point of bifurcation. To avoid unbounded mathematics, branch expansions are derived in terms of an introduced curve parameter. The results are useful for identifying singularity type, for numerical curve tracking with continuation past bifurcations on any chosen branch, and for determining exact rate relations for each branch at a bifurcation. The noniterative solution procedure involves configuration-dependent systems of equations that are evaluated by recursive algorithm, then solved using singular value decomposition, polynomial equation solution, and linear system solution. Examples show applications to RCRCR mechanisms and the Puma manipulator.>