Motion planning for systems with constraints on controls or the need for relatively straight paths for real-time actions presents challenges for modern planners. This paper presents an approach which addresses these types of systems by building on existing motion planning approaches. Guided Expansive Spaces Trees are introduced to search for a low cost and relatively straight path in a space with motion constraints. Path Gradient Descent, which builds on the idea of Elastic Strips, finds the locally optimal path for an existing path. These techniques are tested on simulations of rendezvous and docking of the space shuttle to the International Space Station and of a 4-foot fan-controlled blimp in a factory setting.

An existing nonlinear design methodology developed by Krener (1984, 1987), approximate feedback linearization, is applied to the control of underactuated single-input-single-output nonlinear systems. A computational approach to test for the order of linearization as well as a method to compute the approximate output function is derived. A method to simplify the dynamics using partial precompensation which uses the constraint equations of motion is presented. This approach is applied to a simple example. Simulation results showed a substantial improvement in the operating range of the linear controller by using this approach.>

A general methodology is presented for the classification of redundant spatial manipulator singular configurations. The techniques derived are shown to be independent of attitude description, measurement units, and coordinate reference frame provided by the forward kinematic equations. Conditions for null vector admissibility and escapability, i.e, reconfiguration into a nonsingular posture via self-motion, are derived through analysis of the manipulator Jacobian matrix only. A general approach to singularity classification based on perturbation techniques is presented. For one-degree-of freedom redundant manipulators, a singularity characterization procedure based on methods from dynamical systems theory is derived.>

A general methodology for the classification of kinematically redundant spatial manipulator singular configurations is presented. The singular configurations are classified based on the possibility of reconfiguration into a nonsingular posture using self-motion. For one degree-of-freedom redundancy manipulators, an alignment condition is introduced, and methods from dynamical systems analysis and the center manifold theorem are used to characterize singularities. >

A general methodology is presented for the singularity analysis of kinematically redundant manipulators. The singular configurations are classified based on the possibility of reconfiguration into a nonsingular posture using self-motion. A procedure is presented to test for the possibility of self-motion at a singular configuration. Necessary and sufficient conditions for admissible tangent vectors at the singular configuration are presented, as well as a method to construct such vectors. Sufficient conditions are derived for instances when the singular system can be reconfigured into a nonsingular state by displacements along the admissible null vectors.>