Karen I. Trovato

The geometrical representation of path planning problems

Abstract The path planning problem for arbitrary devices is first and foremost a geometrical problem. For the field of control theory, advanced mathematical techniques have been developed to describe and use geometrical structure. In this paper we use the notions of the flow of vector fields and geodesics in metric spaces to formalize and unify path planning problems. A path planning algorithm based on flow propagation is briefly discussed. Applications of the theory to motion planning for a robot arm, a maneuvering car, and Rubiks Cube are given. These very different problems (holomic, non-holomic and discrete, respectively) are all solved by the same unified procedure.

Autonomous vehicle maneuvering

This paper describes a method to automatically generate optimal, collision-free maneuvers for a vehicle to follow. The technique requires information about the vehicle dimensions, wheel layout and turning radius, so that the vehicles kinematic capabilities can be computed automatically. Locations of obstacles in the maneuvering environment must also be given. The maneuver computed is kinematically feasible, and is given in terms of the control parameters of the vehicle, namely steering angle and forward/backward motion. The method includes techniques for transforming obstacles, performing cost wave propagation, and using kinematically correct neighborhoods to generate an augmented configuration space specific to a vehicle. With this structure, the vehicle can move from any starting position, correct for run-time deviations, and drive to the goal position. A 1/10 scale radio-controlled testbed is used to verify that the theoretical path can indeed be carried out in practice.

Automated RFA planning for complete coverage of large tumors

Radiofrequency ablation (RFA) is a minimally invasive procedure used for the treatment of small-to-moderate sized tumors most commonly in the liver, kidney and lung. An RFA procedure for successfully treating large or complex shape tumors may require many ablations, in a non-obvious pattern. Tumor size > 3cm predisposes to incomplete treatment [1] and potential recurrence, therefore RFA is less often successful and less often used for treating large tumors. A mental solution is the current clinical practice standard, but is a daunting task for defining the complete 3D geometrical coverage of a tumor and margin (planned target volume, PTV) with the fewest ellipsoidal ablation volumes, while also minimizing collateral damage to healthy tissue. In order to generate a repeatable and reliable result, a solution must quantify precise locations. A new interactive planning system with an automated coverage algorithm is described. The planning system allows the interventional radiologist to segment the potentially complex PTV, select an RFA needle (which determines the specific 3D ablation shape), and identify the skin entry location that defines the shapes orientation. The algorithm generates a cluster of overlapping ablations from the periphery of the PTV, filling toward the center. The cluster is first tightened toward the center to reduce the overall number of ablations and collateral damage, and then pulled toward optimal attractors to further reduce the number of ablations. For most clinical applications, computation requires less than 15 seconds. This fast ablation planning enables rapid scenario assessment, including proper probe selection, skin entry location, collateral damage and procedure duration. The plan can be executed by transferring target locations to a navigation system.

Differential A*: an adaptive search method illustrated with robot path planning for moving obstacles and goals, and an uncertain environment

Differential A* is presented. It is a method that builds on the A*/configuration-space approach to adapt quickly to changes in the space by determining and updating the localized regions affected by those changes rather than regenerating the entire space. This is particularly effective with moving obstacles or goals and in an uncertain environment because only small parts of the space are affected at a time. This technique can provide significant speed improvements over, with the same desired results, as complete space regeneration. The A* search algorithm and its relationship to the configuration space method of path planning are presented. The connection of A* to wave propagation in configuration space for path planning is described. The differential A* method is outlined, with the focus on path planning. Examples of moving obstacles and goals and planning in an uncertain environment are presented.<<ETX>>