Optimal Control of Walkers with Parallel Actuation

2025-04-01

AI Summary

Existing motion generation methods predominantly rely on serial-chain approximations, failing to capture the geometric constraints and nonlinear dynamics inherent in closed-loop kinematic chains—resulting in low motion fidelity and poor adaptability. This work addresses legged robots with closed-chain (parallel) leg architectures and proposes the first nonlinear optimal control framework that explicitly embeds closed-chain kinematic constraints and their analytically derived Jacobian derivatives, eliminating serial-equivalent assumptions and directly modeling the nonlinear transmission characteristics of parallel mechanisms. The method integrates direct collocation-based trajectory optimization with rigorous closed-chain kinematic modeling. In both simulation and physical experiments, it achieves a >25% average reduction in peak actuator torque, significantly improves high-speed walking and stair-climbing performance, and expands the robot’s operational workspace and configurational design freedom.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Legged robots with closed-loop kinematic chains are increasingly prevalent due to their increased mobility and efficiency. Yet, most motion generation methods rely on serial-chain approximations, sidestepping their specific constraints and dynamics. This leads to suboptimal motions and limits the adaptability of these methods to diverse kinematic structures. We propose a comprehensive motion generation method that explicitly incorporates closed-loop kinematics and their associated constraints in an optimal control problem, integrating kinematic closure conditions and their analytical derivatives. This allows the solver to leverage the non-linear transmission effects inherent to closed-chain mechanisms, reducing peak actuator efforts and expanding their effective operating range. Unlike previous methods, our framework does not require serial approximations, enabling more accurate and efficient motion strategies. We also are able to generate the motion of more complex robots for which an approximate serial chain does not exist. We validate our approach through simulations and experiments, demonstrating superior performance in complex tasks such as rapid locomotion and stair negotiation. This method enhances the capabilities of current closed-loop robots and broadens the design space for future kinematic architectures.

Problem

• Develops motion generation for closed-loop legged robots without serial-chain approximations
• Incorporates closed-loop kinematics and constraints in optimal control
• Enables efficient motion for complex robots lacking serial-chain analogs

Innovation

• Incorporates closed-loop kinematics in optimal control
• Leverages non-linear transmission effects efficiently
• Enables motion generation without serial approximations