Piecewise-differentiable trajectory outcomes in mechanical systems subject to unilateral constraints

2016/10/17 by Andrew M. Pace, Pace, Andrew M., Samuel A. Burden +1 · 2 citations
Computer Science · Engineering · Mathematics · #Control and Dynamics of Mobile Robots #Dynamics and Control of Mechanical Systems #FOS: Computer and information sciences #FOS: Mathematics #Hydraulic and Pneumatic Systems #Optimization and Control (math.OC) #Robotics (cs.RO) #Vehicle Dynamics and Control Systems #cs.RO #math.OC

paper · pdf · doi:10.48550/arxiv.1610.05645

arXiv admin note: text overlap with arXiv:1609.04056

arxiv created 2016/10/17 · openalex publication_date 2016/10/17 · arxiv updated 2016/10/19 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We provide conditions under which trajectory outcomes in mechanical systems subject to unilateral constraints depend piecewise-differentiably on initial conditions, even as the sequence of constraint activations and deactivations varies. This builds on prior work that provided conditions ensuring existence, uniqueness, and continuity of trajectory outcomes, and extends previous differentiability results that applied only to fixed constraint (de)activation sequences. We discuss extensions of our result and implications for assessing stability and controllability.

Citations

• Multiple Lyapunov functions and other analysis tools for switched and hybrid systems
• Decoupled limbs yield differentiable trajectory outcomes through intermittent contact in locomotion and manipulation

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• Optimal Control for Nonlinear Hybrid Systems via Convex Relaxations

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