Page 119 - Dynamic Vision for Perception and Control of Motion

3.4 Behavioral Capabilities for Locomotion 103

4 4
y (m) 3.5 y (m)
3 3
ȥ/° 2.5
2 · 2
ȥ (°/s)
1 1.5 œ|a y |dt
ȕ/° 1
0 0.5 v y (m/s) in m/s
Ȝ/° 0
-1 · -0.5
·
Control Ȝ (°/s) ȥ (°/s) a y (m/s 2 )
-2 -1
0 1 2 3 4 5 6 t /s 8 0 50 100 150 l (m) 250
Ȝ = 0
(a) Control input time T LC = 6 seconds, no central 0-input arc
10 · 5
8 ȥ/°/s 4 œ|a y |dt
6 ȥ/° y (m) in m/s y/m
4 3
2 2
0 v y (m/s)
-2 ȕ/° Ȝ/° · ȥ (°/s) 1
-4 0
-6 ·
-8 Control Ȝ (°/s) -1 a y (m/s 2 )
-2
0 0.5 1 1.5 2 2.5 3 t /s 4 0 20 40 60 80 l (m) 120
Ȝ = 0
(b) Control input time T LC = 2 seconds, no central 0-input arc
10 · 5
8 ȥ/° 4 œ|a y |dt
6 ȥ/° y (m) in (m/s)
4 3
2 2 v y (m/s)
0
-2 1
-4 ȕ/° Ȝ/° 0
-6 · ·
-8 Control Ȝ (°/s) ȥ/ °/s -1 a y (m/s 2 )
-2
0 0.5 1 1.5 2 2.5 3 t /s 4 0 20 40 60 80 l (m) 120
Ȝ = 0
(c) Control input time T LC = 2 seconds like (b), but 0.4 seconds (20 %) central 0-input arc;
note that maneuver time is almost 2·T LC = 4 seconds
Figure 3.27. Comparison of lane change maneuvers with fifth-order dynamic model at a
speed of V = 100 km/h (27.8 m/s) and realistic steer rate inputs. The amplitude A is ad-
justed such that the lateral offset y f is exactly one lane width of 3.75 m after the tran-
sients have settled. Left column shows the variables (over time): dȜ/dt = steer rate
( ) in (°/s); angle Ȝ ( ); slip angle ȕ ( ) in (°); dȥ/dt = yaw rate ( ) in (°/s), angle ȥ
( ). Right column the variables (over distance): lateral acceleration a y ( ) in (m/s²) and
the integral of its magnitude over time ( ); lateral velocity v y ( ), offset y ( ); integral of
magnitude of a y (dash-dotted line).
(column 8): compared to (a), maneuver time for the complete state transition is re-
duced from 7.9 to 4.4 s (by ~ 45%).
Inserting a central section of 20% duration (0.4 seconds) with zero control input
(last row in the table corresponding to Figure 3.27c requires an increase in steering
rate by about 30% for the same lateral offset y f = 3.75 m at the end of the maneu-
ver. This leads to the same maximal steering angle (column 2) as the case without
the central 0-input section. However, the maximal values of lateral acceleration
and of the other state variables (ȥ, ȕ, v y) are reduced slightly.