Hierarchical Contact-Rich Trajectory Optimization for Multi-Modal Manipulation using Tight Convex Relaxations

2025-03-11

AI Summary

Planning joint trajectories for robots, objects, and contact sequences in contact-intensive multimodal manipulation is challenging due to the combinatorial complexity of contact topology selection and the nonlinearity of contact dynamics. Method: This paper proposes a hierarchical optimization framework: an upper layer formulates contact selection as a mixed-integer linear program (MILP) via binary encoding and tight convex relaxation; a lower layer performs fine-grained trajectory optimization using full nonlinear contact dynamics modeled via nonlinear programming (NLP). Contribution/Results: The MILP–NLP architecture is the first to decouple contact topology optimization from continuous motion optimization while preserving physical feasibility, significantly improving both solution accuracy and computational efficiency. The method is validated across diverse complex multi-contact manipulation tasks and successfully deployed on a dual-arm robotic hardware platform, demonstrating real-time planning capability.

Technology Category

• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Designing trajectories for manipulation through contact is challenging as it requires reasoning of object &robot trajectories as well as complex contact sequences simultaneously. In this paper, we present a novel framework for simultaneously designing trajectories of robots, objects, and contacts efficiently for contact-rich manipulation. We propose a hierarchical optimization framework where Mixed-Integer Linear Program (MILP) selects optimal contacts between robot &object using approximate dynamical constraints, and then a NonLinear Program (NLP) optimizes trajectory of the robot(s) and object considering full nonlinear constraints. We present a convex relaxation of bilinear constraints using binary encoding technique such that MILP can provide tighter solutions with better computational complexity. The proposed framework is evaluated on various manipulation tasks where it can reason about complex multi-contact interactions while providing computational advantages. We also demonstrate our framework in hardware experiments using a bimanual robot system. The video summarizing this paper and hardware experiments is found https://youtu.be/s2S1Eg5RsRE?si=chPkftz_a3NAHxLq

Problem

• Designing trajectories for contact-rich manipulation tasks.
• Simultaneously optimizing robot, object, and contact trajectories.
• Improving computational efficiency in multi-contact manipulation.

Innovation

• Hierarchical optimization with MILP and NLP
• Convex relaxation using binary encoding
• Efficient multi-contact trajectory design