Rigid-Body Dynamics with Friction and Impact
SIAM Review
Convex Programs for Temporal Verification of Nonlinear Dynamical Systems
SIAM Journal on Control and Optimization
Brief paper: Local stability analysis using simulations and sum-of-squares programming
Automatica (Journal of IFAC)
Stability and Convergence of Mechanical Systems with Unilateral Constraints
Stability and Convergence of Mechanical Systems with Unilateral Constraints
LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification
International Journal of Robotics Research
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Many critical tasks in robotics, such as locomotion or manipulation, involve collisions between a rigid body and the environment or between multiple bodies. Sums-of-squares (SOS) based methods for numerical computation of Lyapunov certificates are a powerful tool for analyzing the stability of continuous nonlinear systems, which can play a powerful role in motion planning and control design. Here, we present a method for applying sums-of-squares verification to rigid bodies with Coulomb friction undergoing discontinuous, inelastic impact events. The proposed algorithm explicitly generates Lyapunov certificates for stability, positive invariance, and reachability over admissible (non-penetrating) states and contact forces. We leverage the complementarity formulation of contact, which naturally generates the semialgebraic constraints that define this admissible region. The approach is demonstrated on multiple robotics examples, including simple models of a walking robot and a perching aircraft.