potentialfield

Potential field methods, or potentialfield approaches, are a class of robot motion planning and obstacle avoidance techniques that represent goals and obstacles as a scalar potential field over the robot’s configuration space. The robot is guided toward low potential regions by following the negative gradient of the field, effectively performing a gradient descent toward the goal while being repelled from obstacles.

A common formulation splits the potential into attractive and repulsive components. The attractive potential U_att(q) encourages movement toward the goal q_goal, often written as U_att(q) = (1/2) ζ ||q − q_goal||^2, where ζ is a positive gain. The repulsive potential U_rep(q) discourages proximity to obstacles, typically defined as U_rep(q) = (1/2) η (1/d(q) − 1/d0)^2 for d(q) ≤ d0 and U_rep(q) = 0 otherwise, where d(q) is the distance to the nearest obstacle, d0 is the influence distance, and η is a positive gain. The total potential is U(q) = U_att(q) + U_rep(q), and the robot’s motion is commanded by the negative gradient, −∇U(q).

Potential field methods are simple to implement and provide real-time reactive behavior, but they have notable limitations. Local minima can trap the robot away from the goal, and narrow passages or dynamic environments can challenge performance. Extensions include harmonic potential fields that satisfy ∇^2U = 0 to reduce local minima, navigation functions with global convergence guarantees under certain conditions, and time-varying or dynamic potentials to handle moving obstacles. Hybrid strategies often combine potential fields with global planners to improve robustness.

The approach originated in early work on robot navigation, notably by Khatib in the 1980s, and remains a foundational idea in mobile robotics and automated manipulation.