Control of mechanical systems

1. A review paper on geometric methods in control theory for mechanical systems
   Reference: The bountiful intersection of differential geometry, geometric mechanics, and geometric control theory
2. Low-order controllability is connected with simple motion planning algorithms
   Reference: Low-order controllability and kinematic reductions for affine connection control systems
3. The mechanical meaning of ``linearly controllable''
   Reference: The linearisation of a simple mechanical control system
4. 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
5. Generalisation to systems with constraints of previous work
   Reference: Simple mechanical control systems with constraints
6. Single-input affine connection control systems are uncontrollable
   Reference: Local configuration controllability for a class of mechanical systems with a single input
7. 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
8. An explicit motion planning algorithm for the snakeboard
   Reference: Kinematic controllability and motion planning for the snakeboard
9. 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
10. An investigation of force and time-optimal control for a planar rigid body
    Reference: Optimal control for a simplified hovercraft model
11. 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
12. 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
13. 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
14. Integrability conditions for the partial differential equations of potential energy shaping
    Reference: Potential energy shaping after kinetic energy shaping
15. Formulation of the energy shaping partial differential equations using differential and affine differential geometry
    Reference: Notes on energy shaping