Physically Consistent Lie Group Mesh Models for Robot Design and Motion Co-Optimization

With recent advances in rapid prototyping and mechatronics, the problem of simultaneous design and motion optimization, or the co-design problem, is becoming more and more relevant in robotics. For reasons of computational tractability, all existing methods use simplified approximations of a robot’s kinodynamic model. We empirically confirm that any model approximations that are not physically consistent, i.e., the kinodynamic model parameters do not accurately reflect the actual link shapes, can sometimes lead to large errors in the optimization. We then propose a physically consistent, Lie group-based mesh element model for robot links that (i) parametrizes a wide variety of link shapes, and (ii) provides closed-form analytic gradients for the mesh deformations. The latter property is key to developing efficient co-design optimization algorithms that significantly improve numerical convergence and stability. Our co-design methodology is validated through extensive numerical and hardware experiments involving 3D-printed serial and parallel robots.