1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135

43

Foreach

particular RV at the end of a single step for a range of applied perturbation scalings.

curve, a different initial state is used. The initial state for step nwas generated by first simulating

n-1 steps with the open-loop base PCG. By the fourth step, the figure is falling noticeably.

IMAGE Imgs/thesis.final.w658.gif

IMAGE Imgs/thesis.final.w661.gif

IMAGE Imgs/thesis.final.w659.gif

IMAGE Imgs/thesis.final.w660.gif

(a)

(b)

Figure 3.15 - Typical effect of stance hip perturbations when dynamics are considered
(a) right stance hip roll
(b) right stance hip pitch


The graphs illustrate that hip pitch varies nearly linearly with Qfwdfor all three choices of RV.

Similarly, hip roll is nearly linear with respect to Qlat. These relationships provide evidence which

supports our assumption that the discrete system can be modelled using a linear model. Despite the

fact that the perturbations themselves are mutually independent, their effect on the RVs is not

cleanly decoupled. Thus, they do not provide truly independent control over each RV dimension

as desired.

In general, however, the magnitudes of the undesired variations are not excessively

large relative to the accessible range of RV values in the desired control dimensions.

Completely

independent control of the RVs would imply a diagonal discrete system Jacobian.

The relatively

small effects of each perturbation on other's control dimension mean that the off-diagonal elements

of the discrete system Jacobian will be small compared to the diagonal elements.

[CONVERTED BY MYRMIDON]