11 papers
Delay effects on the discontinuous stabilization of the nonholonomic integrator and its generalizations
William Clark, Anthony Bloch
The nonholonomic integrator is a famous example in feedback design - although it is small-time locally controllable to the origin, no continuous feedback law exists. Therefore, any…
Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance
Alexandre Anahory Simoes, Anthony Bloch, Leonardo Colombo
It was shown in \cite{bloch2000optimal} that an optimal control formulation for incompressible ideal fluid flow yields Euler's equations. In this paper, we consider a variational o…
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…
Stable Walking for Bipedal Locomotion under Foot-Slip via Virtual Nonholonomic Constraints
Leonardo Colombo, Ãlvaro RodrÃguez Abella, Alexandre Anahory Simoes +1
Foot slip is a major source of instability in bipedal locomotion on low-friction or uncertain terrain. Standard control approaches typically assume no-slip contact and therefore de…
Virtual Holonomic and Nonholonomic Constraints on Lie groups
A. Anahory Simoes, A. Bloch, L. Colombo +1
This paper develops a geometric framework for virtual constraints on Lie groups, with emphasis on mechanical systems modeled as affine connection systems. Virtual holonomic and vir…
Learning Nonholonomic Dynamics with Constraint Discovery
Baiyue Wang, Anthony Bloch
We consider learning nonholonomic dynamical systems while discovering the constraints, and describe in detail the case of the rolling disk. A nonholonomic system is a system subjec…