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Figure from:Chapter 3 The Simplest 2-D Walker

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the walking map for the simplest walker. Analytic Stability Approximation Table 3.1: Summary of analytic results for the first two period-one fixed points of

Table 3 the walking map for the simplest walker. Analytic Stability Approximation Table 3.1: Summary of analytic results for the first two period-one fixed points of

Related Figures (16)

Figure 3.1: A typical passive walking step. The new stance leg (lighter line) has
Figure 3.1: A typical passive walking step. The new stance leg (lighter line) has
These are the equations of motion for a simple double pendulum. We wi whole mechanism) and about the hip (for the swing leg), respectively. study the special case where the foot is much smaller than the body, because of
These are the equations of motion for a simple double pendulum. We wi whole mechanism) and about the hip (for the swing leg), respectively. study the special case where the foot is much smaller than the body, because of
Equation 3.4 also reflects a change of names for the two legs. The swing leg
Equation 3.4 also reflects a change of names for the two legs. The swing leg
Figure 3.2: Leg angles versus time over one step at a long-period gait cycle. A
Figure 3.2: Leg angles versus time over one step at a long-period gait cycle. A
0.270837y7, where 6*is the stance angle at a fixed point. The inset box is showt proximately independent of y, for small y. Speeds thus scale with the stance angle This scaling result can also be argued as follows. The period of motion 7 is ap-
0.270837y7, where 6*is the stance angle at a fixed point. The inset box is showt proximately independent of y, for small y. Speeds thus scale with the stance angle This scaling result can also be argued as follows. The period of motion 7 is ap-
appears to adversely affect the accuracy of the analytic eigenvalue estimates. Figure 3.4: Comparison of analytic and numerical stability predictions for long
appears to adversely affect the accuracy of the analytic eigenvalue estimates. Figure 3.4: Comparison of analytic and numerical stability predictions for long
Figure 3.5: Several walker steps during a limping (period-two) gait. The walker’s
Figure 3.5: Several walker steps during a limping (period-two) gait. The walker’s
Figure 3.6: Period doubling of stable walking motions, inset from Figure 3.3. Un- discovered a stable period-three gait for this model at a slope of y © 0.0125. where stable gaits of higher order appear. Recently, Howell and Baillieul (1998,
Figure 3.6: Period doubling of stable walking motions, inset from Figure 3.3. Un- discovered a stable period-three gait for this model at a slope of y © 0.0125. where stable gaits of higher order appear. Recently, Howell and Baillieul (1998,
Figure 3.7: Poincaré section during chaotic walking motions, y = 0.0189. Usi
Figure 3.7: Poincaré section during chaotic walking motions, y = 0.0189. Usi
period gaits to be (to first order in 6): For comparison, eigenvalues of these matrices and eigenvalues found by numer- Using this procedure, we found approximate Jacobians for the long and short ical integration of the full non-linear equations are shown in Figure 3.4. Results to
period gaits to be (to first order in 6): For comparison, eigenvalues of these matrices and eigenvalues found by numer- Using this procedure, we found approximate Jacobians for the long and short ical integration of the full non-linear equations are shown in Figure 3.4. Results to
Figure 3.8: A plot of the function z(7)) showing locations of the zero-crossings.
Figure 3.8: A plot of the function z(7)) showing locations of the zero-crossings.
In Figure 3.10 we compare analytically-predicted step periods and numerical results. Figure 3.10: Analytically-predicted and numerically-evaluated step periods for short
In Figure 3.10 we compare analytically-predicted step periods and numerical results. Figure 3.10: Analytically-predicted and numerically-evaluated step periods for short