4 papers
A Dynamical Systems view of Feedback Synthesis
William Clark
Control theory and dynamical systems are closely intertwined fields. Pontryagin's maximum principal offers a strong connection by providing a constructive way to synthesize feedbac…
LieIPM: Lie Group Interior Point Method for Direct Trajectory Optimization of Rigid Bodies
Sangli Teng, Ruiqi Zhang, Tzu-Yuan Lin +5
Designing dynamically feasible trajectories for rigid bodies is a fundamental problem in robotics. While direct methods are widely used, the existing constrained optimizers typical…
Dissipation-assisted stabilization of periodic orbits via actuated exterior impacts in hybrid mechanical systems with symmetry
William Clark, Leonardo Colombo, Anthony Bloch
Impulsive mechanical systems exhibit discontinuous jumps in their state, and when such jumps are triggered by spatial events, the geometry of the impact surface carries information…
Symplectic Geometry in Hybrid and Impulsive Optimal Control
William Clark, Maria Oprea
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory was applied to these systems and a hybrid…