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63

4.The chaotic walk (see Figure 4.6) has significantly larger error with respect to the


desired RV values, Qd
, as compared to stable limit cycles (note the scale of the graph).

The visual appearance of this walk is noticeably more clumsy than the other walks.

  1. Generally speaking, the forward component of Qstabilizes more quickly than the

lateral component and exhibits smaller variation in steady-state (e.g. Figure 4.4).

6.Q
i*can oscillate from step to step. This is noteworthy since the overall motion should


ideally have nearly identical characteristics from one step to the next.


Other Observations

4. 1. 1

The walks generated using the up-vector display a number of notable characteristics.

First, while

step length is not a regulated variable, virtually all of the walks travel a uniform distance from one

step to the next. Figure 4.7 shows the step lengths over the course of a typical walk.

This result

is encouraging since an irregular walk would be much less appealing and a suitable remedy is not

immediately obvious. This also serves as evidence that the unobservable state variables approach

a limit cycle as desired.


Another characteristic of the resulting motions is that not all of the walks follow a straight line.

This can be seen clearly in the hip plots of Figure 4.3.

Without any form of directional control,

most of the walks follow a curved path. The chaotic walk corresponding to the Qd= [.35,0] trial

of Figure 4.3 (d) follows a less regular path, weaving back and forth over the course of the trial.

As we shall see in the next chapter, this can be solved by explicitly controlling the biped's

direction with an additional feedback loop.


An adverse effect apparent in some of the walks is a tendency to place each stance foot directly in

line with the previous in the lateral dimension as if walking a tightrope.

In a few cases, this even

results in the biped crossing legs slightly each step, with one leg passing through the other since

such interpenetrations are not prohibited in our simulations.

While the tightrope walkingis

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