DiffSDFSim: Differentiable Rigid-Body Dynamics With Implicit Shapes

Abstract

Differentiable physics is a powerful tool in computer vision and robotics for scene understanding and reasoning about interactions. Existing approaches have frequently been limited to objects with simple shape or shapes that are known in advance. In this paper, we propose a novel approach to differentiable physics with frictional contacts which represents object shapes implicitly using signed distance fields (SDFs). Our simulation supports contact point calculation even when the involved shapes are nonconvex. Moreover, we propose ways for differentiating the dynamics for the object shape to facilitate shape optimization using gradient-based methods. In our experiments, we demonstrate that our approach allows for model-based inference of physical parameters such as friction coefficients, mass, forces or shape parameters from trajectory and depth image observations in several challenging synthetic scenarios and a real image sequence.• We develop a novel formulation of differentiable time

Non-inertial torques and the Euler equation

“…Dynamics of rigid bodies is well studied and presented in standard textbooks [1,2], and despite being an old subject, has resulted in a wide range of modern investigations such as their mathematical underpinnings [5]- [11], applications in computer graphics [3]- [4] and in various broader studies [12]- [18]. However, in this short article we have a rather narrow focus on the dynamical equation itself and how it can be derived from the non-inertial torques.…”