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Simulation modeling of robots, objects, and environments is the backbone forall model-based control and learning. It is leveraged broadly across dynamicprogramming and model-predictive control, as well as data generation forimitation, transfer, and reinforcement learning. In addition to fidelity, keyfeatures of models in these control and learning contexts are speed, stability,and native differentiability. However, many popular simulation platforms forrobotics today lack at least one of the features above. More recently,position-based dynamics (PBD) has become a very popular simulation tool formodeling complex scenes of rigid and non-rigid object interactions, due to itsspeed and stability, and is starting to gain significant interest in roboticsfor its potential use in model-based control and learning. Thus, in this paper,we present a mathematical formulation for coupling position-based dynamics(PBD) simulation and optimal robot design, model-based motion control andsystem identification. Our framework breaks down PBD definitions andderivations for various types of joint-based articulated rigid bodies. Wepresent a back-propagation method with automatic differentiation, which canintegrate both positional and angular geometric constraints. Our framework cancritically provide the native gradient information and perform gradient-basedoptimization tasks. We also propose articulated joint model representations andsimulation workflow for our differentiable framework. We demonstrate thecapability of the framework in efficient optimal robot design, accuratetrajectory torque estimation and supporting spring stiffness estimation, wherewe achieve minor errors. We also implement impedance control in real robots todemonstrate the potential of our differentiable framework in human-in-the-loopapplications.

Parameter Identification and Motion Control for Articulated Rigid Body Robots Using Differentiable Position-based Dynamics