# Lecture 7: Potential Fields in addition to Model Predictive Control Potential Fields Attractive Potential Field Repulsive Potential Field Vector Sum of Two Fields

## Lecture 7: Potential Fields in addition to Model Predictive Control Potential Fields Attractive Potential Field Repulsive Potential Field Vector Sum of Two Fields

Hoill, Edgar, Features Editor has reference to this Academic Journal, PHwiki organized this Journal Lecture 7: Potential Fields in addition to Model Predictive Control CS 344R: Robotics Benjamin Kuipers Potential Fields Oussama Khatib, 1986. The manipulator moves in a field of as long as ces. The position to be reached is an attractive pole as long as the end effector in addition to obstacles are repulsive surfaces as long as the manipulator parts. Attractive Potential Field

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Repulsive Potential Field Vector Sum of Two Fields Resulting Robot Trajectory

Potential Fields Control laws meant to be added together are often visualized as vector fields: In some cases, a vector field is the gradient of a potential function P(x,y): Potential Fields The potential field P(x) is defined over the environment. Sensor in as long as mation y is used to estimate the potential field gradient P(x) No need to compute the entire field. Compute individual components separately. The motor vector u is determined to follow that gradient. Attraction in addition to Avoidance Goal: Surround with an attractive field. Obstacles: Surround with repulsive fields. Ideal result: move toward goal while avoiding collisions with obstacles. Think of rolling down a curved surface. Dynamic obstacles: rapid update to the potential field avoids moving obstacles.

Potential Problems with Potential Fields Local minima Attractive in addition to repulsive as long as ces can balance, so robot makes no progress. Closely spaced obstacles, or dead end. Unstable oscillation The dynamics of the robot/environment system can become unstable. High speeds, narrow corridors, sudden changes. Local Minimum Problem Goal Obstacle Obstacle Box Canyon Problem Local minimum problem, or AvoidPast potential field.

Rotational in addition to R in addition to om Fields Not gradients of potential functions Adding a rotational field around obstacles Breaks symmetry Avoids some local minima Guides robot around groups of obstacles A r in addition to om field gets the robot unstuck. Avoids some local minima. Vector Field Histogram: Fast Obstacle Avoidance Build a local occupancy grid map Confined to a scrolling active window Use only a single point on axis of sonar beam Build a polar histogram of obstacles Define directions as long as safe travel Steering control Steer midway between obstacles Make progress toward the global target CARMEL: Cybermotion K2A

Occupancy Grid Given sonar distance d Increment single cell along axis (Ignores data from rest of sonar cone) Occupancy Grid Collect multiple sensor readings Multiple readings substitutes as long as unsophisticated sensor model. VFF Active window WsWs around the robot Grid alone used to define a “virtual as long as ce field”

Polar Histogram Aggregate obstacles from occupancy grid according to direction from robot. Polar Histogram Weight by occupancy, in addition to inversely by distance. Directions as long as Safe Travel Threshold determines safety. Multiple levels of noise elimination.

Steer to center of safe sector Leads to natural wall-following Threshold determines offset from wall. Smooth, Natural W in addition to ering Behavior Potentially quite fast! 1 m/s or more!

Konoliges Gradient Method A path is a sequence of points: P = {p1, p2, p3, } The cost of a path is Intrinsic cost I(pi) h in addition to les obstacles, etc. Adjacency cost A(pi,pi+1) h in addition to les path length. Intrinsic Cost Functions I(p) Navigation Function N(p) A potential field leading to a given goal, with no local minima to get stuck in. For any point p, N(p) is the minimum cost of any path to the goal. Use a wavefront algorithm, propagating from the goal to the current location. An active point updates costs of its 8 neighbors. A point becomes active if its cost decreases. Continue to the robots current position.

Wavefront Propagation

Plan Routes in the Local Perceptual Map The LPM is a scrolling map, so the robot is always in the center cell. Shift the map only by integer numbers of cells Variable heading . Sensor returns specify occupied regions of the local map. Select a goal near the edge of the LPM. Propagate the N(p) wavefront from that goal. Searching as long as the Best Route The wavefront algorithm considers all routes to the goal with the same cost N(p). The A algorithm considers all routes with the same cost plus predicted completion cost N(p) + h(p). A is provably complete in addition to optimal.

## Hoill, Edgar Features Editor

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