Control of mechanical systems
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Table of Contents
Motion control algorithms
- A review paper on geometric methods in control theory for mechanical
Reference: The bountiful intersection of differential
geometry, geometric mechanics, and geometric control theory.
- 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
control for a simplified hovercraft model.
- 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.
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)