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

Abstract

Abstract-We present a novel computational approach to optimizing the morphological design of robots. Our framework takes as input a parameterized robot design and a motion plan consisting of trajectories for end-effectors, as well as optionally, for its body. The algorithm we propose is used to optimize design parameters, namely link lengths and the placement of actuators, while concurrently adjusting motion parameters such as joint trajectories, actuator inputs, and contact forces. Our key insight is that the complex relationship between design and motion parameters can be established via sensitivity analysis if the robot's movements are modeled as spatio-temporal solutions to optimal control problems. This relationship between form and function allows us to automatically optimize robot designs based on specifications expressed as a function of range of motion or actuator forces. We evaluate our model by computationally 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.

Skaterbots

“…Building on a growing body of literature [Coros et al 2013;Ha et al 2017;Megaro et al 2017;Pérez et al 2017;Umentani et al 2015], we leverage sensitivity analysis to establish a relationship between the motions a robot can generate and its physical design parameters. In particular, the method described in [Ha et al 2017] nicely complements our work: while their formulation fine-tunes robot designs such that actuation forces are reduced, the suite of computational tools that we propose are specifically developed to support motion-aware manual, semi-automatic and fully automatic design exploration and optimization. Our work also draws inspiration from a number of specific, hybrid robot designs presented in the robotics literature [BostonDynamics 2017;Endo and Hirose 2008;Smith et al 2006].…”

Asymptotically optimal kinematic design of robots using motion planning

“…Recent work includes approaches that simultaneously optimize the design and motion of the robot with respect to a given objective. Ha et al introduce a design optimization procedure that leverages the Implicit Function Theorem to computationally optimize the morphological design of manipulators and quadruped robots [15]. Taylor et al present a nonlinear optimization based approach to simultaneous design and motion optimization of dynamic planar manipulators [38].…”

Jointly Learning to Construct and Control Agents using Deep Reinforcement Learning

“…Some designs may render locomotion impossible for a target environment (e.g., a robot with short legs may be unable to locomote quickly), while others may make the underlying control problem easy to solve and naturally efficient (e.g., certain bipedal designs enable passive walking [1][2][3] ayan@wustl.edu gait in isolation, it is therefore beneficial to consider them together as part of a joint optimization problem. Thus, many researchers have explored approaches that jointly reason over physical design and control [4][5][6]. Most recent methods are aimed at "model-based" approaches to control-in that they require a model of the robot dynamics or a near-ideal motion trajectory, which is chosen based on expert intuition about a specific domain and task.…”