Abstract: The present invention relates to computing reachable areas given a first point. More specifically, the present invention relates to the computation of an intersection between a first surface and a second surface for determining a set of points that are reachable from a first point. Using the present invention, a user can determine either (1) a locus of target sites that can be struck by a ballistic projectile from a given launch site, or (2) a locus of launch sites that can be used to hit a given target site. The disclosed system and method employs graphics hardware to determine an intersection between a first surface defined by trajectory paths, and a second surface defined by terrain.

Abstract: Methods and apparatus to incorporate user feedback during planning. In one embodiment, first and second plans are generated for which user feedback is obtained and used to generate a revised plan.

Abstract: A planner generates a plan having actions based upon domain and problem definition information provided by a user. The planner stores a rationale for decisions made for each one of the series of actions. A user can query the planner to retrieve rationale information from an action. A user can modify and/or add constraints to the plan and the planner can generate a new plan using a portion of the plan affected by the new constraints.

Abstract: A path planning system and method for an object, such as a vehicle, provides a randomized adaptive path planning that handles real-time path planning for a vehicle operating under kinodynamic constraints in dynamically changing and uncertain environments with probabilistic knowledge of vehicle and obstacle movement.