  Differentiable physics simulation provides an avenue to tackle previously
intractable challenges through gradient-based optimization, thereby greatly
improving the efficiency of solving robotics-related problems. To apply
differentiable simulation in diverse robotic manipulation scenarios, a key
challenge is to integrate various materials in a unified framework. We present
SoftMAC, a differentiable simulation framework that couples soft bodies with
articulated rigid bodies and clothes. SoftMAC simulates soft bodies with the
continuum-mechanics-based Material Point Method (MPM). We provide a novel
forecast-based contact model for MPM, which effectively reduces penetration
without introducing other artifacts like unnatural rebound. To couple MPM
particles with deformable and non-volumetric clothes meshes, we also propose a
penetration tracing algorithm that reconstructs the signed distance field in
local area. Diverging from previous works, SoftMAC simulates the complete
dynamics of each modality and incorporates them into a cohesive system with an
explicit and differentiable coupling mechanism. The feature empowers SoftMAC to
handle a broader spectrum of interactions, such as soft bodies serving as
manipulators and engaging with underactuated systems. We conducted
comprehensive experiments to validate the effectiveness and accuracy of the
proposed differentiable pipeline in downstream robotic manipulation
applications. Supplementary materials and videos are available on our project
website at https://damianliumin.github.io/SoftMAC.
