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Abstract

We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies.

DefGraspNets: Grasp Planning on 3D Fields with Graph Neural Nets

“…Differentiable simulators for rigid and deformable bodies allow gradients of output variables (e.g., poses, velocities, or deformation fields of objects) to be computed with respect to input variables (e.g., control inputs or material parameters) [40][41][42][43][44][45][46]. Such simulators enable gradient-based optimization for control optimization [14,[45][46][47][48], parameter estimation [13,46,48], and inverse design [46,49].…”

“…There are 4 main strategies to realize a differentiable simulator or equivalent model: 1) finite-differencing a nondifferentiable simulator, which has unfavorable O(n) scaling to an n-dimensional input space [50,51], 2) analytically or automatically differentiating a simulator that smoothly approximates spatial or kinetic discontinuities (e.g., penaltybased contact forces and smooth friction models [13,48], which may introduce inaccuracies or require tuning), 3) training a deep network with physically-based loss functions [52,53], which has seen limited use for contact dynamics [54], and 4) training a deep network on datasets from a nondifferentiable simulator, primarily with graph-based inductive biases [31,32,34,55].…”

An inextensible model for the robotic manipulation of textiles

“…Despite their mentioned limitations, penalty methods are still widely used because of their ease of implementation (see, e.g. [9]).…”

Differentiable Depth for Real2Sim Calibration of Soft Body Simulations

“…Recently, many works have presented differentiable simulators for rigid bodies, articulated rigid bodies, cloth and fluids [dABPSA*18, SF18, LLK19, DHDw19, LL20, LLKL*20, KAMS20, SB20, HMZS20]. Recent work addressed multi‐body simulations of both rigid and soft bodies [MEM*20, GHZ*20]. In our work, we focus on hyper‐elastic soft materials that are connected to rigid fixed objects.…”