Task and Motion Planning for Manipulator Arms With Metric Temporal Logic Specifications

The aim is to synthesize control inputs for robotic manipulator arms that ensure a desired task specification is executed while optimizing a desired performance objective. We use metric temporal logic (MTL) to express the task specifications defined in terms of manipulating objects and implemented a hierarchical method combining mixed integer-linear programming (at high-level) to obtain a candidate MTL task specification defined in terms of the location of the arm end-effector and gradient descent based optimization (at low-level) for automatic synthesis of the motion plans to execute such candidate task specifications. The gradient descent algorithm is performed over the feasible input space to optimize the manipulator arm trajectory from a given arbitrary initial condition to perform the task at hand. We demonstrate the efficacy of our method by simulating a task specification on a Baxter robot.