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Local Minima (in motion planning)

A trap condition where the robot gets stuck in a sub-optimal position—like a ball rolling into a small dip when there’s a deeper valley elsewhere. Good planning algorithms help avoid these traps.


Local minima occur when a robot becomes trapped in a suboptimal position and can't escape using only local information.

Visual Analogy

Imagine a landscape with multiple valleys:

  1. The robot's goal is the deepest valley (global minimum)
  2. But it gets stuck in a shallow dip nearby (local minimum)
  3. It can't "climb out" because moving in any direction increases energy
     Goal (Global Min)
        ↓
      ___
    /     \         ← Robot stuck here (Local Min)
   /       \___   /
  /            \_/

Why It Happens

Using potential energy gradients, the robot follows the steepest descent. When surrounded by obstacles that create repulsive forces, it can become wedged between conflicting forces:

  1. Attracted toward goal in one direction
  2. Repelled by obstacles in all escape routes
  3. Result: Paralysis

Real-World Example

A robot navigating around two close obstacles might get pushed into the gap between them, unable to move forward or backward.

Solutions

Good planning algorithms avoid this by:

  1. Using global path planning (knowing the whole map first)
  2. Adding randomized escape movements
  3. Applying potential field modifications
  4. Using hybrid methods combining local + global approaches

Key Takeaway

Local minima are the main weakness of purely reactive navigation—they work great in open spaces but fail in complex obstacle configurations.

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Contents Visual Analogy Why It Happens Real-World Example Solutions Key Takeaway