Path Relaxation

Concept

Path relaxation simplifies the discrete path by removing or adjusting redundant waypoints while maintaining low traversal cost and obstacle clearance.
It can be viewed as a local optimization process that "relaxes" the original path shape into a smoother, simpler form.

Process

1. Identify Redundant Points

   • Evaluate intermediate waypoints whose removal does not increase overall path cost (e.g., distance, curvature, or risk).
   • Ensure that skipping these points still keeps the path in safe, low-cost regions of the costmap.

2. Collapse Intermediate Points

   • Merge or remove these redundant nodes, effectively simplifying the path without losing safety guarantees.

3. Shift Points Locally

   • Slightly adjust remaining points within their neighborhood to reduce curvature or sudden heading changes.
   • These shifts create smoother geometric transitions between segments.

4. Iterate the Process

   • Repeat relaxation until further simplification no longer improves smoothness or violates constraints.

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Path Interpolation

Concept

Path interpolation takes a (possibly relaxed) discrete set of waypoints and fits a continuous mathematical curve through them.
This provides a differentiable representation of the path — suitable for smooth control, velocity profiling, and dynamic re-planning.

Process

1. Compute a Continuous Function

   • Fit a function that passes through or near a trajectory's waypoints. Some possible approaches are with:
     • Polynomial splines (cubic, quintic)
     • B-splines
     • Bezier curves

2. Short-Horizon Interpolation for Dynamic Environments

   • In environments with changing costmaps, recompute only a local segment of the path using short-horizon B-spline interpolation.
   • This enables faster re-planning while preserving global smoothness.

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Implementation

Almost every state(ignoring Done/Off states) will use A* to produce a trajectory that it wants the rover to follow, and currently that resides in an A* class. We should rework this such that there is a general path planning class that will take care of both A* planning and the smoothing post-processing.

Run git fetch and then git checkout nav/path-smoothing to checkout the shared path smoothing project branch.