Trajectory Optimization for Manipulation of Deformable Objects: Assembly of Belt Drive Units

TL;DR

This paper introduces a novel trajectory optimization method using complementarity constraints for robotic assembly of belt drive units, effectively handling contact and deformable object dynamics in simulation and real-world experiments.

Contribution

It formulates the assembly task as a trajectory optimization problem with complementarity constraints, avoiding explicit contact mode sequencing and improving efficiency.

Findings

Successful simulation validation with physics engine

Real-world robotic experiments demonstrate feasibility

Efficient trajectory solutions for complex contact dynamics

Abstract

This paper presents a novel trajectory optimization formulation to solve the robotic assembly of the belt drive unit. Robotic manipulations involving contacts and deformable objects are challenging in both dynamic modeling and trajectory planning. For modeling, variations in the belt tension and contact forces between the belt and the pulley could dramatically change the system dynamics. For trajectory planning, it is computationally expensive to plan trajectories for such hybrid dynamical systems as it usually requires planning for discrete modes separately. In this work, we formulate the belt drive unit assembly task as a trajectory optimization problem with complementarity constraints to avoid explicitly imposing contact mode sequences. The problem is solved as a mathematical program with complementarity constraints (MPCC) to obtain feasible and efficient assembly trajectories. We validate the proposed method both in simulations with a physics engine and in real-world experiments with a robotic manipulator.