Planning with purpose: Task-specific trajectory optimization

In this paper we propose an approach to trajectory planning based on the purpose of the task. For a redundant manipulator, many end effector poses in the task space can be achieved with multiple joint configurations. In planning the motion, we are free to choose the configuration that is optimal for the particular task requirement. Many previous motion-planning approaches have been proposed for the sole purpose of maximizing manipulability or minimizing effort. However, there is a lack of formulation that is flexible enough to allow the designer to purposefully define the motion and force priority of the planned trajectory. Our approach exploits both velocity and force manipulability, depending on the purpose of the task. In this formulation, the purpose of the task is defined by the motion preference (“fast” or “strong”), which can be characterized by a direction of the desired motion, or force. These two directions can be used to evaluate the compatibility of a chosen configuration with the given task. We first demonstrate the possibility of generating two distinct motion plans by the kinematic alignment of desired velocity and force directions with the manipulator’s velocity and force manipulability ellipses. Next, this configuration selection strategy is incorporated into a task-specific trajectory optimization formulation to generate dynamically feasible trajectories. Two distinct motions (force-oriented lifting motion and velocity-oriented ballistic motion) are planned. We also propose a blending method to generate a single motion plan that considers both force and velocity, each to a specified degree. Together the three motions (force, velocity, and blended) are successfully planned and executed on a three-link serial robotic manipulator. The paper concludes with discussion and future directions.