Now showing items 1-10 of 15
Mechanical Systems with Partial Damping: Two Examples
We discuss the problem of constructing steady state motions of mechanical systems with partial damping. A planar three bar linkage with viscous damping at one of the joints is considered as an example. We show that for a ...
Geometric Phases, Anholonomy, and Optimal Movement
In the search for useful strategies for movement of robotic systems (e.g. manipulators, platforms) in constrained environments (e.g. in space, underwater), there appear to be new principles emerging from a deeper geometric ...
Optimal Control and Poisson Reduction
In this paper we make explicit a reduction of G-invariant optimal control problems on a Lie group G.
Steady Rigid-Body Motions in a Central Gravitational Field
In recent work, the exact dynamic equations for the motion of a finite rigid body in a central gravitational field were shown to be of Hamiltonian form with a noncanonical structure. In this paper, the notion of relative ...
Stabilization of Rigid Body Dynamics by Internal and External Torques
In this paper we discuss the stabilization of the rigid body dynamics by external torques (gas jets) and internal torques (momentum wheels). We compare the stabilizing quadratic quadratic feedback law for a single external ...
Gyroscopic Control and Stabilization
In this paper, we consider the geometry of gyroscopic systems with symmetry, starting from an intrinsic Lagrangian viewpoint. We note that natural mechanical systems with exogenous forces can be transformed into gyroscopic ...
High-Order Averaging on Lie Groups and Control of an Autonomous Underwater Vehicle
In this paper we extend our earlier results on the use of periodic forcing and averaging to solve the constructive controllability problem for drift-free left-invariant systems on Lie groups with fewer controls than state ...
Motion Control of Drift-Free, Left-Invariant Systems on Lie Groups
In this paper we address the constructive controllability problem for drift free, left-invariant systems on finite-dimensional Lie groups with fewer controls than state dimension. We consider small (e) amplitude, low-frequency, ...
Dissipation Induced Instabilities
The main goal of this paper is to prove that if the energy- momentum (or energy-Casimir) method predicts formal instability of a relative equilibrium in a Hamiltonian system with symmetry, then with the addition of ...
Motion Control of Drift-Free, Left-Invariant Systems on Lie Groups, Part II: A General Constructive Control Algorithm
In this paper we present a general algorithm for constructing open-loop controls to solve the complete constructive controllability problem for drift-free invariant systems on Lie groups that satisfy the Lie algebra ...