4.3 Method and results

4.3.1 The interface

The graphic display was from a rider's eye point of view, showing a dark riding area, criss-crossed by white lines at 10m intervals, and surrounded by four uniform walls 1m high, each of a different shade. The area between the top of the wall and the horizon was green and above the horizon blue. This meant that when the SUV was not leaning over, a reasonable amount of green could be seen, but as it leaned further over, less and less was visible. As well as this static scenery, visual feedback of the position of the handlebars and front wheel was given, again based on the way which would be expected on a real bicycle.

At first, the display was drawn as if the rider's head and eyes stayed fixed relative to the SUV, so that the horizon tilted on the screen when the vehicle rolled. Later, following comments from users, this was changed to make the horizon remain horizontal, with the parts of the vehicle drawn tilted instead. Though this seemed a little less disconcerting, there was no clear difference in difficulty of the task.

The steering of the SUV invited a number of solutions. The standard keyboard or mouse could be used, but this would not be very realistic, and it was thought that this could lead to the task taking longer to learn than if more realistic controls were used. It was hoped that using handlebars would help to associate people's bicycle riding skill with the task. The author made some wooden handlebars, designed to match approximately the dimensions and angles of the top section of mountain bike handlebars. To provide a signal, a potentiometer was built in to the stem. A battery connected to this gave an analogue voltage linearly dependent on the handlebar angle. This was connected to an A-to-D converter card on the Iris workstation at Charing Cross Tower (YARD).

The SUV's speed was set at a constant 5m/s, and there were no controls provided for speeding up or slowing down. It was thought that providing such controls would add even more difficulty to the task.

Controlling the SUV when the simulation was running at a lifelike speed proved to be very difficult indeed. Therefore a facility for slowing down the simulation was introduced. Slowing the vehicle down would not have worked, since it becomes much more difficult to control at low speeds. So slowing down simulation time itself was enabled. By pressing any of the numeral keys on the keyboard, the time would be slowed down by that factor, and the simulation could run as if in `slow motion', making the simulation more easily controllable. As an added help in difficulty, it was arranged that when the left mousebutton was pressed, the action would stop until the middle mousebutton was pressed. This was to allow a rider to think about setting the handlebars to a sensible value at leisure.

4.3.2 Collection of data

As the simulation program ran, data was collected into a large array, and at the end, stored into a file whose name was constructed from the time, to ensure uniqueness. These files contained the values, at each time step, of the state vector variables, in their internal form, not immediately readable as an ascii file would be. This amounted to 28 bytes per time step, and since there were 50 time steps per (simulation) second, these files were reasonably large even for short runs. The record files did, however, successfully allow replaying of the runs. During replays, the user had the option of seeing a simple representation of the scene viewed from above, as well as the rider's-eye view which was given during the runs.

Several records files were made. However, the author was the only person of those who tried to control the simulation, who developed any degree of reliability. Other volunteers generally did not spend sufficient time at the task to progress beyond the stage of losing control within a few seconds of starting, even at speeds such as five times slower than real (which was given as the default). In the course of some hours of practice (during program development and testing), the author learnt to control the simulation running at half proper speed, and just one run at this speed was initially selected for detailed analysis. This run comprised 8900 time steps, which represents 178 seconds of simulation time, or 356 seconds of real time, and it ended without falling.

4.3.3 Processing of data

Of the state variables (see above, § 4.1.1), x, y, and phi are not primarily relevant to the task of keeping from falling over, and v is constant. It is the remaining three variables that would be expected to determine the larger part of balancing control actions: theta, the angle of roll; omega, the rate of roll; and alpha, the handlebar angle itself. What is not clear is how to represent the control actions.

4.3.3.1 Control as handlebar angle setting

A first possibility to consider is that the rider's actions consist in choosing an appropriate value for the handlebar angle in any given conditions.

The time units are seconds of simulation time, each equivalent to two seconds of real time in this run. The angular unit is the radian. ``ANGLE'' is alpha, ``ROLL'' is theta. Figure 4.1: Handlebar angle and SUV roll against time for the initial part of the analysed run

Figure 4.1 shows that there is some connection between the roll angle of the SUV and the handlebar angle. Examining the simulation equations (§ 4.1.1) reveals part of the reason. The roll acceleration omega dot is zero when

and since

the relationship between alpha and theta is

The values used in the simulation, ks = 0.854, v = 5.0 and g = 9.81, leave us with

Statistical analysis of the data was carried out on one in twenty of the data points (455 out of 8900), and one of the results of this was to find a best fit model for alpha in terms of theta and omega. Ignoring the very small constant term, this gave

A further method was developed specially for the analysis of this data, and was termed `subduction', after Mill's fourth `canon'. (``Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.'' [90]) The principle was to find a factor connecting two variables by using a very simple measure of the extent of the match between two corresponding strings of data. The degree of match was evaluated on the basis of how often both quantities appeared at the same time on the same side of their mean value. This also had the feature that the two strings of data could first be given a time offset relative to each other, to see what time offset would give the best match. The factor connecting the variables was that which, when that factor of the independent variable was subtracted from the dependent variable, gave a minimum value to the matching function. The method is not further described here, since it was not highly developed or evaluated.

The subduction method gave

as the best description of the connections present in the analysed run. A zero offset was found to give the best initial match. Thus a simple model of correlation between the rate of roll and the handlebar angle explains part of the experimental data.

4.3.3.2 Control as setting the rate of handlebar movement

Another reasonable hypothesis is that the control action is manifested in the rate at which the handlebar angle is changed. Since the handlebar angle is tied to the roll angle, it is reasonable to expect at least some connection between their respective rates of change. The rate of roll (omega) is immediately apparent on the display, and intuitively it seems to be one of the chief quantities determining the rider's actions. However, one problem is that changes in the time-delay factor mean that the same (simulation time) rate of roll appears as a rate that depends on that time-delay factor. Thus, when the time-delay is greatest, with the simulation time much slower than control time, the visual feedback of rate of roll is least apparent.

The time units are seconds of simulation time, each equivalent to two seconds of real time in this run. The angular unit is the radian per second. ``DANGLE'' is alpha dot, ``DROLL'' is omega. Figure 4.2: Handlebar angle and SUV roll rates of change against time for the initial part of the analysed run

Examination of Figure 4.2 shows a very sharply fluctuating pattern for the rate of change of angle. This is in part due to the quantised nature of the handlebar angle measurement, where the size of one increment is about 0.004 radian, or roughly one third of a degree. The method of calculation meant that the rates of change of handlebar angle were multiples of this amount divided by two time steps (0.04s), i.e., approximately multiples of 0.1 radian/s. This can be seen in the figure.

This graph clearly does not reflect accurately the rider's actions, because of the limitations of the recording equipment. Moreover, it is unclear what would actually reflect the rider's actions. If the graph were smoothed, that would give a better approximation to the angular speed of the handlebars. When the graph is heavily smoothed, its shape gets much closer to the shape of the ``DROLL'' graph, but since this is anyway implied by a correlation between angle and roll, it does not reveal anything more about the nature of the actions.

Some exploratory statistical analysis was performed on ``DANGLE''. This was not taken far, and no results are given here, for reasons that will be covered in the discussion.

4.3.4 Comparison with hand-written control rules

Another approach to modelling human control of the SUV is to attempt to construct (by whatever means) control rules that have similarities with human control, either analytical similarities or similar results. We have already seen above (§ 4.1) how qualitative rules can be constructed. Further rules were constructed with the human data in mind, from intuitive ingenuity based on knowledge of the problem.

One such rule works in two stages. If omega, the rate of roll, is too large, the handlebars are shifted in the direction that will reduce the magnitude of omega. If omega is within a reasonably small region close to zero, the handlebar angle is set to a multiple of the roll angle similar to that obtained above from the experimental data. To enable steady turning, the handlebar angle calculation can be divided into two parts. The first part of the angle is simply that needed to hold the SUV in equilibrium at the current value of roll, that is, 0.46theta. The other part, corresponding to the difference between the 0.46 and the 0.53 or 0.59 factors above, can be set at any of a range of values around 0.1 times the difference between the current roll and the desired roll. Suitable choice of parameters allow this strategy to give anything from highly unstable performance to very smooth, stable performance.

What this hand-written strategy does not deal with, however, are the psycho-motor factors influencing and limiting the human's performance, and the noise. Because of this, among other things, it would not be justified to put this forward as a model of human performance. Also, in the process of writing the rules, there are assumptions made that have no foundation in the empirical data.