Modular robots can be tailored to achieve specific tasks and rearranged to achieve previously infeasible ones. The challenge is choosing an appropriate design from a large search space. In this work, we describe a framework that automatically synthesizes the design and controls for a serial chain modular manipulator given a task description. The task includes points to be reached in the 3D space, time constraints, a load to be sustained at the end-effector, and obstacles to be avoided in the environment. These specifications are encoded as a constrained optimization in the robots kinematics and dynamics and, if a solution is found, the formulation returns the specific design and controls to perform the task. Finally, we demonstrate our approach on a complex specification in which the robot navigates a constrained environment while holding an object.
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