Physics Residual Dynamics and Reduced Order Whole-Body Planning for Obstacle Aware Human Robot Cloth CoTransportation

Human--robot co-transportation of deformable objects requires predicting object deformation during motion, since obstacle clearance depends on both the grasp points and the unactuated interior. We present a hierarchical planning framework that combines a learned cloth model with a reduced-order whole-body model of a dual-arm mobile manipulator. A physics-residual conditional recurrent variational autoencoder (p-cRVAE) predicts the full cloth configuration from grasp-point observations by learning a residual correction to a computationally efficient linearized physics model, limiting error accumulation over 40-step planning horizon. The predicted cloth dynamics are embedded in a model predictive path integral (MPPI) planner using a reduced-order representation of a dual-arm mobile manipulator that preserves the non-holonomic base constraint and arm workspace limits. An MPC layer subsequently refines the sampled motion into smooth, executable references for whole-body control. The reduced-order formulation achieves tracking performance comparable to the full 17-DoF model while reducing computation time by approximately 80%. Across four co-transportation scenarios and two carrying speeds, the proposed framework maintains cloth-obstacle clearance where a corner-following baseline results in collisions, while whole-body refinement reduces final cloth deformation from 0.93\,m to 0.28\,m.