Transition Curves for Kinematic Feasibility in Robotic Roadmaps
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Solution Overview
Problem
Existing roadmaps for robotic navigation in environments like warehouses often include sharp intersections that can lead to rapid changes in velocity and acceleration, causing kinematically infeasible paths and potential collisions with obstacles or other devices.
Innovation Solution
The introduction of transition curves, composed of Euler spiral and circular curve segments, to replace intersections, ensuring kinematically feasible paths by limiting curvature changes based on robotic device constraints, such as maximum velocity and acceleration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If sharp intersections are used in roadmaps for robotic navigation, then the roadmap structure is simple and easy to generate, but the robotic device experiences rapid changes in velocity and acceleration leading to kinematically infeasible paths
Solution Approach 1:
The patent applies curvature by replacing sharp intersections with transition curves that have continuous, bounded curvature. The transition curves use Euler spiral segments with linearly varying curvature and circular arc segments with constant curvature, ensuring that the curvature remains finite and continuous throughout the path, thereby achieving kinematically feasible trajectories for robotic devices.
Solution Approach 2:
The patent changes the curvature parameter along the path by using Euler spiral segments where curvature varies linearly with arc length, and circular arc segments where curvature is constant. This controlled parameter change ensures that velocity and acceleration remain within kinematic constraints, resolving the contradiction between simple roadmap structure and kinematic feasibility.
2Reliability
If transition curves with Euler spiral and circular curve segments are used to replace intersections, then kinematic feasibility is improved by limiting curvature changes, but the roadmap generation and path planning become more complex
Solution Approach 1:
The patent segments the transition curve into distinct Euler spiral segments and circular arc segments. Each segment type has well-defined mathematical properties and can be independently computed and integrated into the roadmap, making the complex path generation process more manageable and systematic.
Solution Approach 2:
By using standard geometric curves (Euler spirals and circular arcs) with known mathematical formulations, the patent provides a systematic approach to generating smooth transitions. These curves have explicit parametric equations that can be efficiently computed, reducing the practical complexity despite the increased mathematical sophistication required.
Data Source
AI summary
Systems and methods related to roadmaps for mobile robotic devices are provided. A computing device can receive a roadmap. The roadmap can include an intersection between first and second edges. The computing device can determine a transition curve between the first and second edges and includes first, second, and third curve segments. The first and second curve segments can connect at a first curve junction point. The second and third curve segments can connect at a second curve junction point. The first and third curve segments each include a segment of an Euler spiral and the second curve segment can be a circular curve segment having a fixed radius. The computing device can update the roadmap by replacing the intersection between the first and second edges with the transition curve. The computing device can provide the updated roadmap.