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UBC Theses and Dissertations

On-line smooth trajectory planning for manipulators Macfarlane, Sonja


This work proposes a smooth, on-line, trajectory generation method for manipulators. The ability to compute a trajectory on-line increases the ease and speed with which manipulator programming can be done. It also reduces a manipulator's downtime and provides a certain amount of autonomy to the manipulator. These properties are especially desirable in industrial applications. Smooth trajectories are used to avoid controller and actuator saturation thereby reducing actuator wear, and improving tracking accuracy. They also improve manipulator motion times. Existing trajectory generation strategies can be divided into two groups: those based on the dynamic model of the manipulator, and those based on the kinematic limits of the actuators. Trajectory generation methods based on the dynamic model of the manipulator typically cannot be implemented on-line due to the required optimization processes, which can have widely varying computational requirements. Furthermore, their complexity is prohibitive for industrial implementation. Those based on the kinematic limits of the actuators provide computationally simpler solutions and can be used on-line. However existing kinematic-based trajectory planning algorithms that are suitable for use on-line, either do not incorporate jerk limits or involve the use of transcendental functions to limit jerk. The latter method increases the computational load. The trajectories proposed herein can be tracked using typical industrial controllers. The solution is based on forming a fifth order polynomial (quintic) trajectory following a sine-wave template, such that the velocity, acceleration and jerk limits are respected throughout the trajectory. All trajectories between two points can be planned by calculating the time, position, speed and acceleration at a maximum of seven control points, which describe the trajectory. This provides a tractable near time-optimal trajectory which can easily be generated on-line. The trajectory paths consist of straight lines joined by splines (blends) to ensure that the manipulator does not stop at each way-point. Limitations on the blend speed are proposed to ensure that the acceleration and jerk limits are respected during the blend. In addition, a high level planning architecture is provided for on-line trajectory planning. An implementation of the proposed trajectory generation technique and its comparison to an industrial technique show improved motion times, consistent kinematic profiles and improved path tracking.

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