Loop Closure Optimization Using Relative State Space
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Solution Overview
Problem
Existing methods for addressing the loop closure problem in simultaneous localization and mapping (SLAM) and bundle adjustment are computationally expensive and limited in handling large map sizes, as they treat the issue as nonlinear least squares or require numerous iterations.
Innovation Solution
The use of a two-phased optimization approach involving non-stochastic gradient descent in a relative state space followed by refinement in a global state space, which optimizes pose graphs and corrects mapping data efficiently, allowing for faster convergence and more accurate results.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional nonlinear least squares methods are used to solve loop closure, then measurement precision is improved, but computational complexity increases and map size is limited
Solution Approach 1:
The patent segments the loop closure problem into two distinct phases: (1) a fast phase using relative state space and stochastic gradient descent to obtain an approximate solution, and (2) a refinement phase using global state space to achieve high precision. This segmentation allows the system to handle large maps efficiently while maintaining accuracy for smaller maps.
Solution Approach 2:
The patent changes the parameter space from global state space to relative state space during the fast phase. By representing poses relative to their predecessors rather than in a global coordinate system, the computational complexity is reduced from O(n³) to O(n), enabling handling of tens of millions of nodes.
2Measurement precision
If direct minimization of objective function is used, then measurement precision is improved, but productivity decreases due to numerous iterations required
Solution Approach 1:
The patent performs preliminary optimization in the fast phase using relative state space before proceeding to the refinement phase. This preliminary action brings the solution close to the optimal value, reducing the number of iterations needed in the subsequent refinement phase and improving overall convergence speed by more than an order of magnitude.
3Measurement precision
If traditional methods are used for large scale mapping, then measurement precision may be maintained, but productivity decreases due to computational limitations
Solution Approach 1:
The patent introduces dynamic adaptivity by automatically selecting between two different computational approaches based on map size and computational resources. For large maps, the system uses the efficient relative state space method; for smaller maps or when higher precision is needed, it transitions to the global state space refinement method.
Data Source
AI summary
The subject disclosure is generally directed towards a relatively fast and accurate technology that corrects mobile device (e.g., mobile robot) mapping data into corrected map data based upon detection of loop closure. A variation of stochastic gradient descent (with constraints in a deterministic order) may be used in a first correction phase to provide an updated graph in a relatively fast manner by operating in a relative state space. A graph-based variant of Gauss-Seidel that operates in a global state space may be used in a later phase to refine the updated graph into a more exact graph.