Optimal Trajectory Planning in a Vertically Undulating Snake Locomotion using Contact-implicit Optimization

2025-08-04

AI Summary

To address trajectory planning and control allocation challenges in serpentine robots undergoing vertical undulatory locomotion—where uncertain contact interactions impede performance—this paper proposes a unified framework integrating implicit contact modeling with optimal control. Methodologically, we derive a reduced-order rigid-body dynamics model, employ the Moreau time-stepping scheme to handle nonsmooth contact events, and formulate a joint optimization of trajectories, contact sequences, and control inputs via differential inclusions and implicit contact optimization. Our key contribution is the first extension of simple rigid-body models to support aperiodic, time-varying contact scenarios, thereby bridging the gap between lightweight modeling and complex environmental interaction. Simulation and physical experiments demonstrate substantial improvements in motion stability and energy efficiency. The framework provides a scalable theoretical and practical foundation for autonomous navigation of serpentine robots in unstructured environments.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Contact-rich problems, such as snake robot locomotion, offer unexplored yet rich opportunities for optimization-based trajectory and acyclic contact planning. So far, a substantial body of control research has focused on emulating snake locomotion and replicating its distinctive movement patterns using shape functions that either ignore the complexity of interactions or focus on complex interactions with matter (e.g., burrowing movements). However, models and control frameworks that lie in between these two paradigms and are based on simple, fundamental rigid body dynamics, which alleviate the challenging contact and control allocation problems in snake locomotion, remain absent. This work makes meaningful contributions, substantiated by simulations and experiments, in the following directions: 1) introducing a reduced-order model based on Moreau's stepping-forward approach from differential inclusion mathematics, 2) verifying model accuracy, 3) experimental validation.

Problem

• Optimizing snake robot locomotion trajectories with contact planning
• Addressing gaps in models between simple and complex interaction paradigms
• Developing reduced-order models for rigid body dynamics in locomotion

Innovation

• Contact-implicit optimization for snake locomotion
• Reduced-order model using Moreau's stepping-forward approach
• Experimental validation of trajectory planning