Figure 4.14 - Variation of stance-COM RV with stance hip pitch .................................... 70

Figure 4.15 - Up vector RV range and hip plots withtorso servoing enabled...................... 72

Figure 4.16 - Continuous-time up vector component phase diagram with torso servoing......... 73

Figure 4.17 - Robo-bird base PCG for running ........................................................ 74

Figure 4.18 - A running robo-bird........................................................................ 74

Figure 5.1 - Speed control using composite RV ........................................................ 79

Figure 5.2 - Forward velocity (m/s) versus time for velocity feedback .............................. 80

Figure 5.3 - Steady-state velocity vs ^Qbiasd
.............................................................. 80

Figure 5.4 - Acceleration and deceleration............................................................... 80

Figure 5.5 - Turning perturbations for human model with ball-and-socket hips.................... 83

Figure 5.6 - Typical operation of a right turn perturbation............................................. 84

Figure 5.7 - Hip plots for the most successful turning perturbation trials ........................... 85

Figure 5.8 - Hip plots for less successful turning perturbation trials................................. 86

Figure 5.9 - Turning perturbation with torso servoing applied........................................ 86

Figure 5.10 - Point-following............................................................................. 88

Figure 5.11 - Path following .............................................................................. 88

Figure 5.12 - Stride rate perturbation for human model with ball-and-socket hips ................. 89

Figure 5.13 - Results of applying different stride rate perturbation scalings ........................ 90

Figure 5.14 - Average speed for varying stride rates................................................... 91

Figure 5.15 - Bent-knee perturbation for a human model.............................................. 92

Figure 5.16 - Bent-knee walking with a parameter scaling of 1.0 .................................... 92

Figure 5.17 - Bent-over walking perturbation........................................................... 92

Figure 5.18 - Bent-over walking.......................................................................... 93

Figure 5.19 - Composite bent-knee, bent-over and bent-neck perturbation ......................... 94

Figure 5.20 - Ducking...................................................................................... 94

Figure A-1 - States of a 1 degree-of-freedom swinging pendulum plotted vs time................109

Figure A-2 - State-space trajectory of a simple swinging pendulum ................................109

ix