Dynamic Window Approach: Local Obstacle Avoidance

Planner Parameters

Max speed v_max 2.0 m/s

Max angular accel 3.0 rad/s²

Clearance weight 1.2

Live State

Speed v

0.00 m/s

Turn rate ω

0.00 rad/s

Min clearance to obstacle

— m

Distance to goal

— m

How it works

The Dynamic Window Approach (Fox, Burgard & Thrun, 1997) is a local, reactive planner for a differential-drive robot. Every control cycle it searches directly in velocity space (v, ω) instead of pose space, so the trajectories it evaluates are ones the robot can physically reach.

1. Dynamic window (reachable in one Δt given accel limits):
   V_d = [v - a_v·Δt, v + a_v·Δt] ∩ [0, v_max]
   W_d = [ω - a_w·Δt, ω + a_w·Δt] ∩ [-ω_max, ω_max]

2. Admissible velocities (can still stop before a collision):
   v ≤ √(2 · dist(v,ω) · a_v_brake)

3. For every sampled (v,ω), forward-simulate a short arc with
   the unicycle model:
     x' = x + v·cos(θ)·Δt
     z' = z + v·sin(θ)·Δt
     θ' = θ + ω·Δt

4. Objective function, maximised over the admissible set:
   G(v,ω) = α·heading(v,ω) + β·clearance(v,ω) + γ·velocity(v,ω)

heading rewards arcs whose end orientation points at the goal.
clearance rewards arcs that stay far from obstacles (β here is the "Clearance weight" slider).
velocity rewards faster forward motion, so the robot doesn't stall.
Any arc that intersects an obstacle before Δt elapses is discarded outright — collision-free trajectories only.

This is exactly the local layer that sits underneath a global planner (A*, RRT) in most real mobile-robot stacks: the global planner picks the route, the DWA loop re-solves the immediate next half-second at 5–10 Hz to dodge whatever the sensors see right now.

SEARCHING VELOCITY SPACE

Robot Static obstacle Goal Chosen arc

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