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

Figure 3.14 - Right hip pitch and roll perturbations .................................................... 42

Figure 3.15 - Typical effect of stance hip perturbations................................................ 43

Figure 3.16 - Balance RV components vs linearly scaled hip pitch perturbation.................... 44

Figure 3.17 - Balance RV components vs linearly scaled hip roll perturbation ..................... 45

Figure 3.18 - Direction of change of forward RV components with hip pitch ...................... 46

Figure 3.19 - Estimate of desired lateral RV components.............................................. 48

Figure 3.20- Balancing process for each step ........................................................... 48

Figure 3.21 - Unobserved state problem................................................................. 49

Figure 3.22 - Model construction and extrapolation.................................................... 49

Figure 3.23 - 2D sampling strategies..................................................................... 51

Figure 3.24 - Sampling point pitfalls in discrete model construction................................. 53

Figure 3.25 - Torso servo parameters.................................................................... 54

Figure 3.26 - Pelvis-based up vector balance indicator ................................................ 55

Figure 3.27 - Falling with torso servoing enabled...................................................... 55

Figure 4.1 - A sequence of steps from a walking limit cycle .......................................... 57

Figure 4.2 - Continuous-time up-vector RV component phase diagrams............................ 58

Figure 4.3 - Nominal up-vector RV target range and plan-views..................................... 60

Figure 4.4 - Discrete RV values for L-F sampling, Qd= [.2,0] ...................................... 62

Figure 4.5 - Discrete RV values for SP sampling, Qd= [.3,0] ....................................... 62

Figure 4.6 - Discrete RV values for L-F sampling, Qd= [.35,0]..................................... 62

Figure 4.7 - Step length vs step number ................................................................. 64

Figure 4.8 - Continuous-time swing-COM RV phase diagrams ...................................... 65

Figure 4.9 - Swing-COM RV target range and hip plots............................................... 67

Figure 4.10 - Discrete RV values for L-F sampling, Qd= [0.05,0].................................. 68

Figure 4.11 - Discrete RV values for SP sampling, Qd= [0.0,0] .................................... 68

Figure 4.12 - Step length vs step number, SP sampling............................................... 69

Figure 4.13 - Discrete RV values for SP sampling, Qd= [0.0,±0.03] .............................. 69

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