Journal Publications

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Conference Publications

Piecewise-Linear Path Following for a Unicycle using Transverse Feedback Linearization

Rollen S. D'Souza and Christopher Nielsen

DOI

Path planning and following together constitute a critical part of the decision-making hierarchy in autonomous ground vehicles. One of the simplest instances of this architecture is when the path planner generates waypoints that define a sequence of collision free line segments from a start location to goal destination and when the vehicle's kinematic model is taken to be Dubin's vehicle. The low level feedback controller can then be design by treating the path following problem as a set stabilization problem; one such approach is called transverse feedback linearization (TFL). However, for a Dubin's vehicle with only one input, the direction of traversal along the path is completely determined by the vehicle's initial condition. In this paper we provide easily certifiable sufficient conditions and a systematic design procedure that guarantees the robot satisfies the initial condition requirements at transitions between line segments of the path. Our analysis relies on geometric properties of the path; as a result we construct a formal connection between the feasible motions generated by the planner and the path following controller's convergence properties.

Dual Conditions for Local Transverse Feedback Linearization

Rollen S. D'Souza and Christopher Nielsen

DOI

Given a control-affine system and a controlled invariant submanifold, the local transverse feedback linearization problem is to determine whether or not the system is locally feedback equivalent to a system whose dynamics transversal to the submanifold are linear and controllable. In this paper we present necessary and sufficient conditions for a single-input system to be locally transversally feedback linearizable to a given submanifold that dualize, in an algebraic sense, previously published conditions. These dual conditions are of interest in their own right and represent a first step towards a Gardner-Shadwick like algorithm for local transverse feedback linearization.


Other Work

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