Joint Optimization of Robot Design and Motion Parameters using the Implicit Function Theorem

We present a novel computational approach to optimizing the morphological design of robotic devices. Our framework takes as input a parameterized robot design, and a motion plan consisting of end-effector trajectories and/or a body trajectory. The algorithm we propose is used to optimize a set of design parameters including link lengths and actuator layout, while concurrently adjusting motion parameters such as joint trajectories, actuator forces, and contact forces. Our key insight is that the complex relationship between design and motion parameters can be made explicit through the implicit function theorem if movements are modeled as spatio-temporal solutions to optimal control problems. This explicitly modeled relationship allows us to formulate the task of optimizing robot designs using quadratic programming. We evaluate the model we propose by optimizing two simulated robots that employ linear actuators: a manipulator and a large quadruped. We further validate our framework by optimizing the design of a small quadrupedal robot and testing its performance using a hardware implementation.