Robot Path Planning With Bounded-Optimal Tree Search
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Solution Overview
Problem
Conventional path planning methods are inefficient in finding paths in large state spaces with unknown obstacles and fail to provide tractable solutions when obstacles are moving, often prioritizing asymptotic optimality over bounded optimal paths.
Innovation Solution
A method using a local growing tree search with bounded approximated optimal cost, where child nodes are generated within a certain distance to the parent node, and the cost of transitions is computed to select the node with the lowest overall cost, allowing for efficient exploration of obstacle-free space with a priority queue and consideration of time-evolving obstacles.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional path planning methods prioritize asymptotic optimality, then the solution approaches optimal cost in the limit, but the computation time becomes unacceptable for large state spaces with moving obstacles
Solution Approach 1:
The patent applies partial action by computing paths with bounded suboptimality rather than pursuing full asymptotic optimality. The algorithm terminates when a path within a predetermined bounded error of the optimal cost is found, accepting a partial solution that is sufficiently good for practical applications while dramatically reducing computation time for large state spaces with moving obstacles
Solution Approach 2:
The patent changes the optimality parameter from asymptotic (limit-based) to bounded (error-threshold-based). By introducing a bounded error parameter that defines acceptable deviation from optimal cost, the algorithm can terminate early with a satisfactory solution rather than continuing indefinitely to approach optimal cost asymptotically
2Reliability
If the state space is densely explored to ensure complete obstacle avoidance, then the path planning becomes more reliable, but the computational complexity increases significantly
Solution Approach 1:
The patent applies partial exploration by focusing computational resources on exploring only the necessary portions of the state space required to find a bounded-optimal path. Rather than exhaustively exploring all possible states, the algorithm terminates when sufficient exploration has been performed to guarantee a path within the bounded error threshold, reducing computational complexity while maintaining reliability
Solution Approach 2:
The algorithm performs self-assessment of exploration sufficiency by monitoring whether the current best path meets the bounded error criterion. When the exploration process determines that the optimal cost bound has been achieved or the state space has been sufficiently explored, the algorithm terminates automatically without requiring external intervention
Data Source
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AI summary
The present invention relates to a method for determining a path of an object like a robot, etc. for moving from a starting state to an end state set comprising one or more end states via one or more nodes each being defined as an obstacle free state that has been explored avoiding one or more obstacles, comprising the steps of a) Determining a plurality of child nodes to a parent node, wherein the starting node representing the starting state is the parent node when step a) is performed for the first time, and wherein the child nodes are within a certain distance to the parent node, b) Checking whether the transitions from the parent node to each of the child nodes are free of obstacles, and if not the corresponding child node and their partial path from the parent node to this child node is excluded, c) Computing a cost value for each of said partial paths, d) Add said computed cost value to a cost value from the starting node to the parent node, e) Add an estimated or expected cost value for the partial paths from each of the child nodes to an end node representing an end state, f) Determining the lowest overall cost value from the determined cost values according to steps d)-f) and selecting the child node as new parent node associated with the determined lowest cost, and g) Repeat performing the steps a)-g) until at least one termination condition is fulfilled including the termination condition if a selected child node is within a pregiven distance to the end node.