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

2016/10/17 by Andrew M. Pace, Pace, Andrew M., Samuel A. Burden +1 · 2 citations
Engineering · #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

paper · pdf · doi:10.48550/arxiv.1610.05645

openalex publication_date 2016/10/17 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We provide conditions under which trajectory outcomes in mechanical systems\nsubject to unilateral constraints depend piecewise-differentiably on initial\nconditions, even as the sequence of constraint activations and deactivations\nvaries. This builds on prior work that provided conditions ensuring existence,\nuniqueness, and continuity of trajectory outcomes, and extends previous\ndifferentiability results that applied only to fixed constraint (de)activation\nsequences. We discuss extensions of our result and implications for assessing\nstability and controllability.\n

Citations

• Multiple Lyapunov functions and other analysis tools for switched and hybrid systems

Cited by

• Gait Transitions in Load-Pulling Quadrupeds: Insights from Sled Dogs and a Minimal SLIP Model
• Optimal Control for Nonlinear Hybrid Systems via Convex Relaxations

Related

• Decoupled limbs yield differentiable trajectory outcomes through intermittent contact in locomotion and manipulation
• Nonsmooth optimal value and policy functions in mechanical systems\n subject to unilateral constraints
• Prioritized Inverse Kinematics: Nonsmoothness, Trajectory Existence, Task Convergence, Stability
• Prioritized Inverse Kinematics: Desired Task Trajectories in Nonsingular Task Spaces
• On the transpositional relation for nonholonomic systems