Control of mechanical systems

Table of Contents

1. Low-order controllability is connected with simple motion planning algorithms.
   Reference: Low-order controllability and kinematic reductions for affine connection control systems.
2. The mechanical meaning of ``linearly controllable.''
   Reference: The linearisation of a simple mechanical control system.
3. 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 systems.
4. Generalisation to systems with constraints of previous work.
   Reference: Simple mechanical control systems with constraints.
5. Single-input affine connection control systems are uncontrollable.
   Reference: Local configuration controllability for a class of mechanical systems with a single input.

1. 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.
2. An explicit motion planning algorithm for the snakeboard.
   Reference: Kinematic controllability and motion planning for the snakeboard.
3. Some motion control primitives for systems on Lie groups with certain controllability properties.
   Reference: Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups.

1. An investigation of force and time-optimal control for a planar rigid body.
   Reference: Optimal control for a simplified hovercraft model.
2. 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.
3. 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.

1. 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.
2. Integrability conditions for the partial differential equations of potential energy shaping.
   Reference: Potential energy shaping after kinetic energy shaping.
3. Formulation of the energy shaping partial differential equations using differential and affine differential geometry.
   Reference: Notes on energy shaping.