Page 107 - Dynamic Vision for Perception and Control of Motion

3.4 Behavioral Capabilities for Locomotion 91

creased, the measured longitudinal deceleration (a x < 0) will be lower than ex-
pected. However, due to the torque developed by the different braking forces on
both sides of the vehicle, there also will be a rotational onset around the vertical
axis and maybe a slight banking (rolling) motion around the longitudinal axis. This
situation is rather common, and therefore, one standard automotive test procedure
is the so-called “ȝ-split braking” behavior of vehicles (testing exactly this).
Because of the importance of these effects for safe driving, they have to be
taken into account in visual scene interpretation. The 4-D approach to vision has
the advantage of allowing us to integrate this knowledge into visual perception
right from the beginning. Typical motion behaviors are represented by generic
models that are available to the recursive estimation processes for prediction–error
feedback when interpreting image sequences (see Chapter 6). This points to the
fact that humans developing dynamic vision systems for ground vehicles should
have a good intuition with respect to understanding how vehicles behave after spe-
cific control inputs; maybe they should have experience, at least to some degree, in
test driving.

3.4.5.1 Longitudinal Road Vehicle Guidance

The basic differential equation for locomotion in longitudinal degrees of freedom
(dof) has been given in a coarse form in Equation 3.8. However, longitudinal dof
encompass one more translation (vertical motion or “heave”), dominated by Earth
gravity, and an additional rotation (pitch) around the y-axis (parallel to the rear
axle and going through the cg).
Vertical curvature effects: Normally, Earth gravity (g § 9.81 m/s²) keeps the
wheels in touch with the ground and the suspension system compressed to an aver-
age level. On a flat horizontal surface, there will be almost no vertical wheel and
body motion (except for acceleration and deceleration). However, due to local sur-
face slopes and curvatures, the vertical forces on a wheel will vary individually.
Depending on the combination of local slopes and bumps, the vehicle will experi-
ence all kinds of motion in all degrees of freedom. Roads are designed as networks
of surface “bands” having horizontal curvatures (in vertical projection) in a limited
range of values. However, for the vertical components of the surface, minimal cur-
vatures in both lateral and longitudinal directions are attempted by road building.
In hilly terrain and in mountainous areas, vertical curvatures C V may still have
relatively large values because of the costs of road building. This will limit top
speed allowed on hilly roads since at the lift-off speed V L, the centrifugal accelera-
tion will compensate for gravity. From V ˜ L 2 C V g there follows
V / g C . (3.23)
L V
Driving at higher speed, the vehicle will lift off the ground (lose instant controlla-
bility). Only a small fraction of weight is allowed to be lost due to vertical cen-
trifugal forces V²·C V for safe driving. At V = 30 m/s (108 km/h), the vertical radius
of curvature for liftoff will be R V = 1/C V § 92 m; to lose at most 20% of normal
weight as contact force, the maximal vertical radius of curvature would be 450 m.
Going cross-country at 5 m/s (18 km/h), local vertical radii of curvature of about