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UBC Theses and Dissertations

Smooth time optimal trajectory planning for industrial manipulators Constantinescu, Daniela


This work proposes and demonstrates a strategy for planning smooth path-constrained time-optimal trajectories for manipulators. Such trajectories are obtained by limiting the actuator jerks required by the planned motion. Existing planning strategies incorporate the smoothness requirement either as smoothness of the actuator torques or as smoothness of the joint trajectories. The smoothness requirement is desirable for reducing strain on robot actuators while still requiring low cycle times. In this work, the trajectory smoothness is defined in the phase plane and the planning observes the limits on the actuator jerks. The solution proposed for determining the optimal trajectories consists of approximating the time optimal control problem by a nonlinear parameter optimization problem which is solved using the flexible tolerance method. It is shown that the approximate solution converges to the time optimal motion when the actuator jerks become very high. A number of simulations are performed to demonstrate the proposed strategy. These simulations show that actuator jerk limits have a negative impact on robot motion time, but they do not give any indication about robot trajectory feasibility. This aspect is studied through further simulations and experiments on an industrial robot. The results of this work show that the tracking accuracy is directly related to the actuator jerk limits. Therefore, it is necessary to impose such limits when planning feasible optimal trajectories. Finally, the performance of the smooth time optimal motion is compared to the performance of both the non-jerk limited optimal trajectory, as well as a smooth quintic trajectory. For similar actuator jerks and controller effort, the smooth path-constrained time-optimal trajectory results in a significantly shorter motion time with nearly the same tracking accuracy as a quintic polynomial. Based on the results in this work, actuator jerk limits are shown to provide an improved method of achieving a compromise between high tracking accuracy, smooth joint behaviour, and optimal motion time.

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