Optimal Parking Maneuver Path Planning via HJB Equation
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Solution Overview
Problem
Existing methods for computing optimal parking maneuvers for road vehicles in known environments with static obstacles are limited by high computational costs and do not effectively account for direction changes and gear switching, which are crucial for efficient parking.
Innovation Solution
A method using a switched system of equations and a cost function that considers arrival time and direction changes, modeled through the Hamilton-Jacobi Bellman equation, to compute optimal parking maneuvers by dynamically switching between forward and reverse motion, with a penalty parameter to optimize trajectory planning.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If numerical solution of Hamilton-Jacobi-Bellman equation is used to compute optimal parking maneuvers, then deterministic solution is obtained, but computational cost increases significantly
Solution Approach 1:
The patent segments the continuous state space into a discrete multi-resolution lattice structure. This discretization allows the HJB equation to be solved numerically on a manageable grid, reducing computational complexity while maintaining deterministic solution properties. The lattice divides the configuration space into cells that can be systematically processed.
Solution Approach 2:
The patent implements dynamic switching between forward and reverse motion subsystems based on the vehicle's state and optimization requirements. This dynamic approach allows the system to adapt its computational model to the current parking scenario, improving efficiency while maintaining solution determinism through the switched system formulation.
2Productivity
If traditional path planning methods are used, then computational cost is reduced, but direction changes and gear switching are not effectively accounted for
Solution Approach 1:
The patent introduces a penalty parameter in the cost function that specifically penalizes direction changes and gear switching events. By modifying the cost function parameters to include these factors, the optimization process naturally accounts for operational complexity without requiring separate computational modules, thus maintaining efficiency while improving ease of operation.
Solution Approach 2:
The patent uses a switched system formulation as an intermediary model that bridges the gap between simple geometric path planning and complex dynamic vehicle behavior. This switched system acts as a mediator that incorporates direction changes and gear switching into the optimization framework while maintaining computational tractability.
3Productivity
If simple geometric algorithms are used for parallel parking, then computational efficiency is improved, but adaptability to various parking configurations is limited
Solution Approach 1:
The patent formulates a universal optimization framework based on the HJB equation that can handle multiple parking configurations (parallel parking, perpendicular parking, angled parking) through a single unified model. The switched system and cost function are designed to be configuration-agnostic, adapting automatically to different parking scenarios without requiring separate algorithms.
Solution Approach 2:
The patent employs dynamic switching between different motion subsystems (forward and reverse) that allows the same computational framework to adapt to various parking configurations. The system dynamically selects appropriate motion modes based on the current state and target configuration, providing versatility while maintaining computational efficiency through the unified HJB formulation.
Data Source
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AI summary
Path planning method for computing optimal parking maneuvers for road vehicles comprising operating according to a dynamic programming calculation procedure to compute a set of vehicle controls implementing an optimal parking maneuver, and computing a set of value functions of a cost function as a unique viscosity solution of a Hamilton Jacobi Bellman equation, said cost function taking in account an arrival time of the vehicle for a given parking maneuver and a number of direction changes of the road vehicle between forward motion and reverse motion.