Potential Field
- Also called: artificial potential field, APF
- Category: Planning & manipulation › Motion planning
- Tags: motion-planning, obstacle-avoidance, reactive-control, navigation, gradient-descent
A planning and control method in which the goal attracts and obstacles repel, and the robot follows the gradient of the combined potential; simple and reactive, but prone to local minima.
Definition
In the artificial potential field method, the robot is treated as a particle moving in a scalar field U(q) defined over its workspace or configuration space. An attractive potential, often quadratic in the distance to the goal, pulls it toward the target. Repulsive potentials, which grow sharply as the robot approaches an obstacle and vanish beyond an influence distance, push it away from obstacles. The robot is commanded to follow the negative gradient −∇U, which acts as a virtual force. Khatib (1986) introduced the approach for real-time obstacle avoidance by manipulators and mobile robots, applying the virtual forces at points on the arm and mapping them to joint torques through the Jacobian transpose.
The appeal is that the computation is local and cheap. Each step needs only the current distances to nearby obstacles, so the method reacts immediately to moving obstacles and runs at control rates. The main limitation is that following the gradient stops at any local minimum of U, where attractive and repulsive forces cancel: a robot can be trapped inside a U-shaped obstacle or in front of a gap between two close obstacles. Potential fields can also oscillate in narrow passages, and when an obstacle sits close to the goal, the repulsion can keep the robot from reaching it.
Several remedies exist. Navigation functions, introduced by Rimon and Koditschek, are potentials constructed to have a single minimum at the goal for certain classes of environment, and harmonic potential functions avoid spurious minima by construction. More often, potential fields are combined with a global planner that supplies intermediate waypoints, with random motions to escape minima, or used as one term in an optimization-based controller. The same idea of descending the gradient of a cost built from goals and obstacles appears in current work under other names, such as signed-distance-field costs in trajectory optimizers and dynamically composed cost landscapes for reactive manipulation.
Why it matters
Potential fields are one of the simplest ways to obtain reactive obstacle avoidance, and their local-minimum problem is the standard illustration of why reactive control and global planning are combined. Gradient-following on goal and obstacle costs remains at the core of many reactive controllers and trajectory optimizers.
Key applications
- Reactive obstacle avoidance for mobile robots
- Real-time collision avoidance for manipulators near people or moving objects
- Multi-robot and swarm coordination with inter-robot repulsion
- Drone navigation in cluttered spaces
- Local control layers beneath a global path planner
- Cost terms in trajectory optimization and reactive manipulation
In practice
A small differential-drive robot uses a 2D lidar to move through a lab. At each scan, the controller computes an attractive force toward the next waypoint and a repulsive force from every lidar return inside a set influence distance, sums them, and converts the result into linear and angular velocity commands. The robot steers around people walking past without replanning. When it gets stuck in a corner formed by two desks, the team detects the stall from near-zero velocity while the goal is still far away, and has the global planner insert an intermediate waypoint around the obstacle. They also cap the repulsive force and smooth the commanded velocities to stop the robot oscillating in doorways.
Common misconceptions
- Following the potential field always reaches the goal — gradient following can stop at local minima where attractive and repulsive forces cancel
- Potential fields are a complete planning method — they are local and reactive, and are usually paired with a global planner when a path must be guaranteed
- Stronger repulsion always makes the robot safer — overly strong or wide repulsion can block narrow passages and cause oscillation
Who should know this
- Mobile-robot and navigation engineers
- Manipulator control engineers working on collision avoidance
- Multi-robot and drone developers
- Students learning classical motion planning
Related technologies
- Navigation Functions
- Vector Field Histogram
- Dynamic Window Approach
- Signed Distance Fields
- Operational Space Formulation
Related terms
- Obstacle Avoidance
- Motion Planning
- Configuration Space
- Signed Distance Field
- Operational Space Control
- Control Barrier Function
Related projects
- Nav2: ROS 2 navigation stack with path planning and obstacle avoidance for mobile robots
- DimOS: Python robotics runtime with agents, SLAM and teleop, no ROS required
- ROS Motion Planning: One repo implementing 40+ classic and learning-based robot path planners as ROS plugins
- OMPL: Sampling-based motion planning library powering MoveIt and countless robotics applications
- MRPT: Comprehensive C++ toolkit for mobile robotics, SLAM, and sensor-based navigation
- MoveIt 2: Motion planning framework for ROS 2 robot arms, with kinematics and collision checking