Subject: [NEXTEL-1] GPS/INS-Vehicle Assessment

From: [email-masked]
Date: Tue, 05 Aug 2003 02:44:55 -0400

GPS/INS-Vehicle Assessment

July 1, 2003
By: Brendan Watts, Steve Neads
GPS World

Drivers can readily determine if a car is easy or difficult to maneuver, for
instance by driving it on twisting roads. But providing the absolute
numerical evaluation, necessary to identify the car as better and/or
safer, is not as straightforward. Engineers have developed a series of
tests that highlight important features of a car's suspension and steering
characteristics.

Our two companies developed a system that feeds back position to
ensure not merely that the car uses the same steering pattern, but that
it follows exactly the same road path, measuring road position and
guiding the steering mechanism with an inertial and GPS navigation
system. We applied the "path-following robot" to these exercises:

Circle Test. The car is driven on a constant
radius at gradually increasing speed until it
cannot grip the road any longer. This
assesses whether the car has too much
under-steer (the steering wheel has to be
turned more at higher speeds to stay on the
circle) or over-steer (the steering has to be
turned less as bending in the suspension and
tires causes the car to turn more than
expected).

Step-Steer Test. In an opposite maneuver to the circle test, engineers
examine the car's transient response instead of looking at its
steady-state response. The car is driven straight, then a sudden, fixed
shift in steering wheel position initiates a turn. The turn is held for a few
seconds until transient behavior - overshoot, damping, and so on - dies
away, and the car follows a constant radius trajectory; then the steering
wheel is let go.

Elk or Roll-Over Test. This determines if a car will roll over if the driver
steers suddenly to avoid an obstacle (turning both right then left to avoid
an oncoming vehicle - or an elk). Extending this to include several
sine-like trajectories can highlight any resonance in the roll mode. If the
resonance is too large, the car may roll over.

Test Requirements

Anthony Best Dynamics first addressed
repeatable car testing by developing a steering
robot. The steering robot (see photo inset above)
clamps onto existing steering wheels or replaces
the steering wheel entirely. An electric motor can
turn the steering wheel to any position, and a
motor controller plays predefined steering
patterns into the car's steering system.

However, the exact same steering pattern programmed into the steering
robot will still result in a slightly different course on the road next time it
is driven. Many factors, including wind and road camber, cause the car
to drift differently each time. Since road width is limited, drifting too far
presents a problem. The operator can correct the drift in the car's
position using a joystick.

For high-speed maneuvers with lateral accelerations exceeding 0.8G, it
is even more difficult to avoid drift. The friction of the tires on the road
becomes non-linear and highly unpredictable. The operator may not be
able to nudge the vehicle back on course quickly enough to guarantee
the tests can be compared reliably.

The Elk tests highlight a limitation of using a fixed
steering pattern. Here there are two conflicting
requirements: avoiding the obstacle and not rolling
over. Given a fixed steering pattern, the car can
be prevented from rolling over by making its
steering less responsive. In consequence, the car
is more likely to hit the elk.

To address this problem, Ford and Anthony Best
Dynamics developed a system that uses position
feedback to ensure that the car follows the same
path on the road, rather than simply using the same steering pattern.
Measuring the position on the road uses an inertial and GPS navigation
system from Oxford Technical Solutions. Commissioned originally for
Ford's Roll-Over test program, the system now participates in many
different car tests.

Other issues that need addressing for a robotic test system include
reliability and safety. A robotically guided vehicle clearly has great
potential for harming the test operator and other vehicles on the track.

Steering Robot Design

The steering robot was designed to fit quickly
into the vehicle. It uses a telescopic strut that
fits between the floor and the windscreen on
the passenger side. A steering motor is
mounted on the steering wheel, and two
parallel links restrain the motor housing and
measure the torque that the motor has to apply
to steer the vehicle (see inset photo, facing
page, and photo, this page).

The steering robot uses a direct-drive torque motor that can supply a
torque up to 30 Newton meters and can rotate the steering wheel at up
to 2000 degrees per second under no load, comparable to what a
human driver can achieve. An angular encoder measures the actual
position of the steering wheel with a resolution of 0.00075 degrees,
giving low noise for the feedback mechanism. The motor has no gearing
and provides little resistance if no power is supplied; this type of motor
is fitted so that the operator can drive normally when the robot is fitted
but not in use.

The motor is driven by a sophisticated motion controller with its own
dedicated real-time processor. This controller is interfaced to a PC that
runs the user interface software. A touch screen, essential in a vehicle
where a mouse is hard to use, can be mounted on the telescopic strut.

The operator retains control of the brake and accelerator
pedals; these are not included in the steering robot's
controller. The operator steers until the robot takes over.
For constant steering pattern tests, the operator holds a
joystick; if the operator releases the joystick then the
robot turns off immediately. This essential safety
mechanism allows the operator to take control of the
car if the robot fails. A master power button is provided
in case the software fails.

Turning the "steering robot" into a "path-following robot"
requires three additional components.

a method of measuring the position of the car on the road;
software to generate desired paths, or to replay paths that the
robot has learnt from the operator driving (see Figure 1);
a control algorithm to convert the position errors to steering
wheel positions.

Positioning System Requirements

Initial studies, simulation, and field trials gave some indications on the
required specifications for the positioning system. They include:

less than 10-millisecond latency
less than 5-centimeter position error
less than 1-centimeter high-frequency position noise
less than 0.3-degree heading error
100Hz Update Rate
robustness.

Human drivers have neither 100Hz reactions
nor 10-millisecond latency, yet we can still
drive. However, we cannot drive with
10-centimeter errors at 0.9G lateral
accelerations. To achieve these levels of
performance, the control algorithm is very
sensitive to any deviation in position from the
programmed path. The robot uses a gain that
gives a full 360-degree rotation of the steering
wheel if the error in the car's position is 50 centimeters relative to the
programmed path. If the measured position jumps by 50 centimeters,
then the robot will turn the steering wheel very rapidly. Having a low level
of high-frequency position noise is essential since this is transferred
directly to the steering wheel.

The robustness criterion is essential. If GPS alone was used and the
car was travelling at over 100 kilometers/hour, then any block in the
GPS signal could be catastrophic for the controller's behaviour. On
limited-width roads this would almost certainly cause the car to crash.
Even without overhead obstructions, multipath can cause the GPS to
temporarily drop out of real-time kinematic (RTK) mode; this too would
lead to problems for the controller. Using an inertial navigation system
(INS) allows the system to continue if GPS is blocked and gives the
driver time to take over if drift in the INS causes the position
measurement of the system to become too inaccurate.

INS/GPS System Design

The combined INS/GPS navigation system uses a
traditional approach as shown in Figure 2. A
strapdown navigator integrates the angular rate
sensors to give heading, pitch, and roll angles. These
are used to rotate the acceleration measurements
from the body-frame of the inertial array to a
North-East-Down frame where they can be integrated
to velocities and positions.

In the IMU the inertial sensors are fitted to a precision-machined block
so that the accelerations and angular rates are measured in three
orthogonal directions. Further alignment and additional correction is
performed through software calibration. Using technology similar to a
delta-sigma ADC, the 16-bit ADC is over-sampled and provides about 20
bits of resolution after the digital filter The sensors are sampled at
2.5kHz and integrated using a dedicated floating-point DSP to give
measurements of change in angle and change in velocity at 100Hz.

Sampling of the inertial sensors is aligned to GPS time using a digital
phase-locked loop. The advantage of this is that it is much easier to
compare the inertial and GPS measurements, because they occur at
the same time.

The strapdown navigator software runs on a 300-MHz Pentium-class
processor. A WGS-84 earth model makes it easy to combine the
outputs with GPS. The position is translated to a local metric coordinate
system, centered on the test site, for the robot's controller to use.

To achieve the lowest possible latency, the strapdown navigator
prepares constants, such as earth radii, for the next output cycle in
advance. The highest priority for the real-time operating system is to
output the measurements to the steering robot.

Kalman Filter. A 23-state Kalman filter estimates and
corrects the errors in the system. The filter states
(see Table 1) include position errors, velocity errors,
orientation errors, inertial sensor biases, and scale
factors. To simplify the configuration of the system for
the user when it is installed, five more states are used
to estimate the position of the GPS antenna
compared to the inertial sensors. If two GPS antennas
and receivers are fitted then the orientation of the
dual-antenna system compared with the inertial sensors is also
estimated.

To accurately track all car dynamics, the Kalman filter runs at 33Hz -
also the rate at which the errors are transferred from the error states to
the strapdown navigator. To ensure that the outputs never exhibit large
step changes (that would make the steering robot change the steering
wheel angle suddenly), a filter transfers the errors from the states to the
strapdown navigator. The rate that the errors are transferred from the
Kalman filter to the strapdown navigator (and output measurements) is
also limited for additional safety.

As another safety feature, the path-following robot's control algorithm
monitors the covariance of the position error states to give an indication
of position accuracy. The robot returns control to the operator if the
position becomes too inaccurate due to drift of the inertial system and
lack of GPS updates.

The GPS receiver cannot be used to update the system immediately
because its output latency is much higher (about 50 milliseconds) than
the 10-millisecond requirement. When a GPS measurement is made
the corresponding inertial measurement has already been output. A
buffer stores all the inertial measurements so that the correct values
can be compared to the GPS measurements. An algorithm then
translates and rotates the corrections from the (now) historical update to
the latest position and orientation.

GPS Environment. An L1/L2 GPS receiver gives an RTK position and
velocity correction signal for the system. Vehicle testing is usually
performed in an easy environment for GPS, as most test sites are old
airfields with complete open sky. Some purpose-built test tracks have
trees, but they are usually set back from the track. Resolving
carrier-phase integer ambiguities is generally required only a few times
during the day. Nevertheless, the system can work well in poorer
environments.

Another convenient point in this application is the base-station GPS
receiver. Whereas many survey applications require the precise location
of the base station to be known, the path-following robot only requires
relative position accuracy. The base station can be positioned close to
the test site and its position averaged for a few minutes. This gives
sufficient accuracy for relative positioning.

The base-station corrections are transmitted to the vehicle using
line-of-sight radio modems. Many countries provide a license-free band
at 450MHz where up to 1-watt transmitters can be used. This gives a
reliable 2-kilometer range, with the signal being useable up to 5
kilometers where there are no trees, buildings, or hills.

Generally an antenna with an integral ground-plane is used at the base
station to reduce the multi-path. These are too large to be used on cars
(without engineers complaining about aero-dynamic effects) so it is
necessary to rely on the car's metal roof as a ground-plane. Some
multi-path occurs from this but it is smaller than the positioning
requirements. The inertial sensors smooth it in any case.

Developing a Control Strategy

In designing the control algorithm that converts the
position errors from the navigation system to steering
wheel angles, we developed a pure mathematical
model using vehicle parameters such as tire cornering
stiffness, wheelbase steering ratio, and yaw inertial.
Many of these parameters are carried forward into the
final software, making it simple to change the control
algorithm to cope with different vehicles. Figure 3
shows an overview of the control strategy used in the robot.

Look-Ahead. The final control algorithm uses a Proportional-Differential
controller to control the steering wheel angle from the position error.
Rather than using the current position error, the algorithm uses
look-ahead to see if the vehicle is going to leave the path in the future,
rather than waiting until it has left the path before taking action.

The geometry of steering results in an additional integration, so the
Proportional-Differential controller actually results in an
Integral-Proportional control strategy. The integral action aims to remove
any offset from the path. Using look-ahead as an error signal also
damps the controller by providing some Differential action.

An area that causes problems for simple, textbook controllers is that
the gain of the controller changes with speed. This has to be
compensated correctly so that the control algorithm can work across a
range of speeds.

Start Gate. Other important developments included
managing the transition from operator to robotic
control. Using the path-following robot, a start gate is
always defined in the local coordinate system.
Although the test begins when the car crosses the
start gate, the path-following robot takes control before
this.

Whilst in motion at the desired speed, the operator
aims the vehicle towards the start gate and presses the start button.
The controller quickly computes a smooth curve to guide the vehicle to
the start gate. The curve has to have the vehicle arrive at the center of
the start gate and heading in the correct direction, otherwise there
would be a discontinuity at the start gate. The robot's reaction to this
discontinuity would inevitably be a severe steering angle input.

Although conceptually simple, there were many small, but significant,
refinements that needed to be developed before it was possible even to
test the path-following package.

Controller Gain. In a simple control strategy, the angle of the
steering wheel would be proportional to the distance of the car
from the programmed path. Figure 5A shows a car to the right
of the programmed path; the controller has turned the car to
the left to bring the car towards the path. The controller gain
determines how far the steering wheel should be turned when
there is a lateral error. Making the gain higher can result in a
faster response from the controller, but it can also make the
system unstable.

The problem with a proportion control strategy can be seen in
Figure 5B. Here the car has no lateral error, but it soon will.
The proportional controller will always bring the vehicle back to the track
at the wrong angle. It has no knowledge of the car's heading. The
proportional control strategy may work but it will always oscillate
left-right across the programmed path. A proportional control strategy
does not make use of any "future" information to help it. It will not react
to a turn before it occurs. It is like trying to drive a car while only looking
out of the side windows.

Look-Ahead Position. To combat these problems the system uses
look-ahead to predict whether the car will leave the path if it continues
moving straight from its current location. The actual position and
heading of the car are used to compute a look-ahead position as shown
in Figure 5C. The look-ahead position is used instead of the actual
position to control the angle of the steering wheel. Again, the gain of the
controller can be changed to adjust how quickly the car reacts to an
error.

In the example in Figure 6C, the look-ahead position is on the opposite
side of the programmed path compared to the car, so the controller will
turn the car left even though it is on the left-hand side of the
programmed path. If everything is adjusted correctly, the car will return
to the programmed path with the correct heading.

Fitting All Vehicles. Using a combination of non-linear simulation and
track testing, an optimum set of parameters has been found to minimize
the deviation of the car from the programmed path. As far as possible
the dynamics of the vehicle were separated from the control strategy so
that the robot works well with all types of vehicle. For each vehicle type
the tire cornering stiffness, wheelbase steering ratio, and yaw inertial
can be changed; this keeps the user from having to understand the
intricacies of control theory.

The look-ahead control strategy introduces several notable features:

It provides damping so that the car does not oscillate across the
programmed path.
It causes the car to turn onto the path as it arrives at the path.
It allows the controller to react before a corner.
The path of the car tends to cut corners (because it turns before
the corner arrives).

Results

The performance of the path-following robot is already impressive when
viewed alone. However, here we have compared the results to three
human drivers.

In this set of tests the car was driven through a Sine
Test. Cones were placed on the road along the desired
path. (The robot guided the car along the path at walking
speed and cones were dropped under the center of the
car.) The robot drove the course nine times. Three human
drivers drove the course three times each.

The car's position when the human drivers are in control
(Figure 6) varies by about 0.5 meters. On straight
sections humans tend to be more accurate than this, but
on turns close to the friction limit of the car it is a lot
more difficult to drive a repeatable path. By comparison,
the robot is able to keep within about 10 centimeters
(Figure 7).

The situation with the steering wheel angle is the same; the variation of
the driver (Figure 8) is much larger than that of the robot (Figure 9) .

If a different set of tires or even a different pressure in the
same tires were tested then it would be much easier to
see how it affects the steering angle when using the
robot. The effect would have to be much larger for it to be
obvious in the human driver trace. In general the human
driver would be able to identify the better tire, however it
would be a subjective view rather than a quantative one.

The variation of the roll angle between the human (Figure
10) and robot drivers (Figure 11) also shows that the
robot can repeat the same roll angle much better than
the human drivers. Roll stiffness is important for
determining vehicle comfort and critical for roll-over
testing. Being able to repeat the roll pattern of a car
along a path allows designers to make safer, more comfortable cars.

Finally, the body slip angle (Figures 12 and 13) shows the same
improvement in repeatability as the others. This parameter is useful for
ensuring that the driver "feels" that the car responds correctly. Many
cars are tuned to have a high slip angle, or under-steer, during tight
corners; this lets the driver know that they are approaching the limit of
friction. The alternative, over-steer, tends to be much harder for drivers to
recover from unless they have proper training.

From the graphs it is simple to see that the robot is far
more repeatable than the human drivers. In fact the main
variation in the robot's performance is speed variation
between the tests. The speed is currently still under
operator control.

The path-following robot accurately measures steering
angle and torque; roll angle; slip angle; accelerations and
velocities. All these are critical to vehicle testing
applications. Critical parameters, such as roll angle and
slip angle, are also much more repeatable using the
path-following robot.

In general the path-following robot can follow the same
path, at different speeds, accurate to about 15 centimeters. The largest
error in this is due to the look-ahead. Using look-ahead causes the
robot to cut corners (as human drivers usually do). The corner cutting is
not a problem for repeatability of the tests.

Assessing the performance of the navigation system is
more difficult. In this application there is no external
reference (like a camera) that can be used to provide some
statistics on the position accuracy.

A non-quantitative approach to determining the positioning
repeatability can be performed on nearly dry road surfaces.
Here the tracks left as the vehicle leaves wet patches and
moves to drier road can be compared. Using several tests
conducted like this, at speeds of about 100
kilometers/hour, the vehicle left an accumulated wet streak
over several passes only just wider than the tire (in our
case about 18 centimeters wide). The repeatability is
generally less than one tire width. Tracks left on muddy
sections also confirm this.

The path-following system has also been used extensively for roll-over
tests, constant radius tests, and more recently for repeating ride and
handling tests on twisty roads.

Acknowledgments

The authors would like to thank Ford for providing the opportunity to
develop the path-following system and for supplying a Ford Explorer and
Ford Focus for much of the test work.

Brendan Watts, managing director of Oxford Technical Solutions,
gained his Master of Engineering degree from Oxford University and has
more than 10 years experience working with inertial navigation systems
and GPS.

Steve Neads, director of suspension and steering test systems at
Anthony Best Dynamics (ABD), gained his Ph.D at Bath University and
has worked for ABD since 1986.

Manufacturers

The path-following robot uses an Anthony Best Dynamics
(Bradford-on-Avon, UK) SR30 steering robot, and an Oxford Technical
Solutions (Oxfordshire, UK) RT3002 inertial and GPS navigation
system. The RT3002 incorporates a NovAtel (Calgary, Alberta, Canada)
OEM4 GPS receiver fitted with RT-2 software, an Aero-Antenna
(Chatsworth, California) AT2775-12 L1/L2 antenna, Honeywell
(Plymouth, Minnesota) QA650 accelerometers, and BAE Systems
(Bristol, UK) RRS01-0100 angular rate sensors, coupled with a
Burr-Brown analog–digital converter and 40MHz floating point digital
signal processor from Texas Instruments (Dallas, Texas).

http://www.gpsworld.com/gpsworld/article/articleDetail.jsp?id=63212

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