We present a versatile framework for the computational co-design of legged robots and dynamic maneuvers. Current state-of-the-art approaches are typically based on random sampling or concurrent optimization. We propose a novel bilevel optimization approach that exploits the derivatives of the motion planning sub-problem (i.e., the lower level). These motion-planning derivatives allow us to incorporate arbitrary design constraints and costs in an general-purpose nonlinear program (i.e., the upper level). Our approach allows for the use of any differentiable motion planner in the lower level and also allows for an upper level that captures arbitrary design constraints and costs. It efficiently optimizes the robot's morphology, payload distribution and actuator parameters while considering its full dynamics, joint limits and physical constraints such as friction cones. We demonstrate these capabilities by designing quadruped robots that jump and trot. We show that our method is able to design a more energy-efficient Solo robot for these tasks.

翻译：我们为计算共设计脚步机器人和动态操控提供了一个多功能框架。 目前最先进的方法通常以随机抽样或同时优化为基础。 我们提出一个新的双级优化方法,利用运动规划子问题(即低层次)的衍生物。 这些运动规划衍生物使我们能够将任意设计的限制和成本纳入一个通用的非线性程序(即上层)。 我们的方法允许在较低层次使用任何不同的运动规划师,并允许有一个能捕捉任意设计制约和成本的上层。 它有效地优化机器人的形态、有效载荷分布和动作器参数,同时考虑其充分动态、联合限制和诸如摩擦锥体等物理限制。 我们通过设计跳跃和旋转式的四重机器人来展示这些能力。 我们证明我们的方法能够设计出一种更节能的机器人来完成这些任务。