An Extension to the Dynamic Window Approach for

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots Christian Mandel A 1[Robo. Map], 09/17/04

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. Overview • Rolland: new hardware platform • Motivation • Basic principles of the Dynamic Window Approach • DWA & the problem with non circular shaped robots • Implementation issues: Curve Segments Table, Collision Table • Computing the Trajectory • Computing the Velocity Profile • What remains to do • Preliminary Experiments SFB/IQN-Kolloquium 09/17/04 -0 - A 1[Robo. Map]

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. • Rolland: hardware platform § Meyra Champ wheelchair § omnidirectional camera system § controlling laptop connected via single usb cable § emergency stop button § 2 laser range finder § 2 incremental encoders SFB/IQN-Kolloquium 09/17/04 -1 - A 1[Robo. Map]

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. A 1[Robo. Map] Motivation decision points voronoi edges Wheelchair in its environment Metrical & topological representation. How to navigate between decision points while taking care of dynamic obstacles? SFB/IQN-Kolloquium 09/17/04 -2 -

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. A 1[Robo. Map] Basic principles of the Dynamic Window Approach 1 • Local navigation combined with reactive collision avoidance. • DWA assumes: Robot velocity is a piecewise constant function in time. • DWA considers: Robot has initial velocity and limited accelerations. • DWA computes optimal circular arc in every time step. • DWA looks one curve ahead. 1 [Fox, Burgard, Thrun] „The Dynamic Window Approach To Collision Avoidance“ SFB/IQN-Kolloquium 09/17/04 -3 -

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. A 1[Robo. Map] DWA & the problem with non circular shaped robots current pose computed arc headed pose current pose collision computed arc current pose computed arc 2 computed arc 1 SFB/IQN-Kolloquium 09/17/04 -4 -

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. A 1[Robo. Map] Curve Segments Table SFB/IQN-Kolloquium 09/17/04 -5 - start curvature prime direction 0 + MAX backwards 0 - MAX forwards 0 + MAX forwards 0 - MAX backwards 0 0 forwards 0 0 backwards . . poses . . .

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. A 1[Robo. Map] Collision Table arclength (t) 0 . . . offset between occupied cells ({(x 1, y 1 1), . . . , (x n, yn n)}) 1 n ({(x 1, y 1), . . . , (xn, yn)}) {(-1, 1), (-1, -1), (1, -1), (2, -1)} {(0, -1), (1, 0), (0, -1), (1, -1), {(-1, 1), (-1, -1), (1, -1), (2, -1), (0, 1), (1, 0), (0, -1)} (3, -1), (3, -2), (4, -1), (4, -2)} . . . t=8 t=7 t=0 SFB/IQN-Kolloquium 09/17/04 t=1 t=2 t=3 t=4 -6 - t=5 t=6

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. A 1[Robo. Map] Algorithmic Refinements 1 Goal: reduce Size of Precompute and store only paths whose first pose has zero heading. Curve Segments Table Test-for-Collision-Operation has to rotate CT-entries. Collision Table Precompute additional table which holds rotated offsets between occupied cells. SFB/IQN-Kolloquium 09/17/04 -7 -

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. Score Function A 1[Robo. Map] start. Pose headed. Pose path goal. Pose SFB/IQN-Kolloquium 09/17/04 -8 -

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. Computing the Optimal Path Input Algorithm (basic idea) Local Evidence Grid, Odometry Pose, Goal Pose Curve Segments Table Collision Table SFB/IQN-Kolloquium 09/17/04 -9 - A 1[Robo. Map]

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. A 1[Robo. Map] Algorithmic Refinements 2 Goal: reduce complexity of computation Computing the optimal path w. r. t. objective function SFB/IQN-Kolloquium 09/17/04 Algorithm (with (basicconstant idea) arc 2. length) set arc 1. curvature, arc 2. length = MAX_arc 2. length arc 1. length, arc 1. direction do arc 1. curvature, arc 1. length, arc 1. direction do arc 2. curvature, arc 2. length, arc 2. direction do arc 2. curvature, arc 2. direction do • construct path • test for collision and prune if necessary • calc score • minimise path. score • if (path. score < best. Path. score) • if set (path. score best. Path<=best. Path. score) path set best. Path = path - 10 -

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. Algorithmic Refinements 3 Algorithm (witch constant arc 2. length) minimise path. score potentialarc 2 goal. Pose pose do • arc 2 calcdo score with goal. Pose • calc score = pose store goal. Pose • • store with minimal score with SFB/IQN-Kolloquium 09/17/04 - 11 - A 1[Robo. Map]

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. A 1[Robo. Map] Computing the Velocity Profile Input Algorithm FOR EVERY DO: COMPUTE MAXIMUM velocity FOR EVERY Solution Path DO: INCORPORATE LONGITUDINAL ACCELERATION LIMIT Velocities in Start & Goal Lateral Acceleration Limit Longitudinal Acceleration Limit Rotational Velocity Limit Longitudinal Velocity Limit SFB/IQN-Kolloquium 09/17/04 FOR WHICH HOLDS: - 12 - :

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. What remains to do • current implementation considers only binary information from the evidence grid while doing the collision test • better: collision test should also return minimal distance to obstacles for tested path SFB/IQN-Kolloquium 09/17/04 - 13 - A 1[Robo. Map]

An Extension to the Dynamic Window Approach for arbitrarily shaped Robots. Preliminary Experiments SFB/IQN-Kolloquium 09/17/04 - 14 - A 1[Robo. Map]