Potential Field 3D

Problem Statement

Potential-field planning computes motion by descending a synthetic scalar field that attracts toward goals and repels from obstacles.

Model and Formulation

Total potential:

$$U(q)=U_{att}(q)+U_{rep}(q)$$

Motion command:

$$\dot{q}=-\mathrm{\nabla }U(q)$$

Practical Notes

• Very fast and simple for local navigation.
• Sensitive to local minima in cluttered environments.
• Often combined with global planners for robust deployment.

Implementation and Execution

python -m flybots.simulations.path_planning.potential_field_3d

Evidence

References

• Khatib, Real-Time Obstacle Avoidance for Manipulators and Mobile Robots (1986)
• Ge and Cui, Dynamic Motion Planning for Mobile Robots Using Potential Field Method

Related Algorithms

• A* 3D
• Costmap Navigation