Control of mechanical systems
Back to my research page.
Table of Contents
Motion control algorithms
- Low-order controllability is connected with simple motion planning
Reference: Low-order controllability and kinematic reductions
for affine connection control systems.
- The mechanical meaning of ``linearly controllable.''
Reference: The linearisation of a simple mechanical control
- Basic discussion of controllability for ``simple mechanical control
systems.'' This work gives the necessary and sufficient conditions for
local configuration accessibility, and some too strong sufficient conditions
for local configuration controllability.
Reference: Configuration controllability of simple mechanical
- Generalisation to systems with constraints of previous work.
Reference: Simple mechanical control systems with
- Single-input affine connection control systems are uncontrollable.
Reference: Local configuration controllability for a class
of mechanical systems with a single input.
Motion control algorithms
- A discussion of the relationship between motion planning and low-order
local controllability for affine connection control systems.
Reference: Controllable kinematic reductions for mechanical
systems: concepts, computational tools, and examples.
- An explicit motion planning algorithm for the snakeboard.
Reference: Kinematic controllability and motion planning for
- Some motion control primitives for systems on Lie groups with certain
Reference: Controllability and motion algorithms for
underactuated Lagrangian systems on Lie groups.
- An investigation of force and time-optimal control for a planar rigid
Reference: Optimal control for a simplified hovercraft
- Basics of time-optimal control for affine connection control systems,
and an application to the robotic leg and the planar rigid body.
Reference: Time-optimal control of two simple mechanical
systems with three degrees of freedom and two inputs.
- The derivation of the ``adjoint Jacobi equation'' from the Pontryagin
maximum principle for affine connection control systems. The setting in
this paper is quite general.
Reference: The geometry of the maximum principle for affine
connection control systems.
- Integrability conditions for joint partial differential equations of
kinetic and potential energy shaping.
Reference: A geometric framework for stabilization by energy
shaping: Sufficient conditions for existence of solutions.
- Integrability conditions for the partial differential equations of
potential energy shaping.
Reference: Potential energy shaping after kinetic energy
- Formulation of the energy shaping partial differential equations using
differential and affine differential geometry.
Reference: Notes on energy shaping.
Andrew D. Lewis (andrew at mast.queensu.ca)