Push based Manipulation of a Cubic Block using a Nonholonmically Constrained Planar Pusher

Abstract

This work aims to study the nonprehensile planar manipulation of a cubic block using a nonholonomic MuSHR race car equipped with a flat planar bumper/pusher. The underactuated and nonholonomic nature of our setup and the uncertainty of physical parameters like friction coefficients between contact surfaces, the pressure distribution of the cubic block, etc. pose challenges for planning and control. To tackle these challenges and the sliding motion of the block along the pusher, our method uses an analytical model to output a set of stable pushes in velocity space to generate trajectories from the block’s start to it’s goal position using a graph-based planner under a quasi-static assumption. Stable pushes are defined as push actions in velocity space that do not cause sliding motion of the block w.r.t. the pusher. We then deploy an LSTM based MPC with added stochasticity to approximate the pushing dynamics and track the planner trajectories. We conduct pushing experiments and compare our LSTM based MPC against a first-order Markov Gaussian Process and stable pushing-based MPCs for adaptability to different pushing experiments and robustness to initial sliding displacements. Our results suggest that the LSTM based MPC is more robust to initial sliding displacements compared to baseline alternatives and can be used to track planner and non-planner outputted trajectories.