Multi-Agent Path Planning via Boolean Satisfiability

The patent replaces complex kinematic and geometric reasoning with a discrete graph representation where edges encode feasible transitions. Instead of continuously representing vehicle kinematics with Euler spirals and track transition curves, the system discretizes the configuration space into nodes and edges, where each edge represents a valid motion primitive. This substitution of continuous mechanical models with discrete graph structures reduces computational complexity while preserving adaptability to different vehicle types.

The patent changes the representation parameters from continuous kinematic models to discrete graph states. Each node in the discrete graph represents a discretized pose (position and orientation), and edges represent valid transitions between poses. This parameter transformation allows the system to handle varying vehicle footprints and directions by simply updating the discrete transition rules rather than reconfiguring continuous kinematic models.

The patent segments the continuous configuration space into discrete nodes and edges, creating a graph structure that can be efficiently processed. Each edge represents a discretized motion primitive with an associated cost. This segmentation enables the use of SAT solvers and other discrete optimization algorithms that operate on finite state spaces, dramatically improving computational efficiency compared to continuous optimization methods.

The patent transforms the continuous cost function into discrete edge weights in the graph representation. While this discretization enables efficient computation using SAT solvers and discrete optimization techniques, it introduces quantization effects that reduce the precision of cost representation. The uniform edge cost assumption further simplifies computation but loses information about varying terrain, obstacles, and motion difficulties.