1 Introduction
2 Dynamical biped walking model
Link |
\(l_i\,\hbox {(m)}\)
|
\(m_i\,\hbox {(kg)}\)
|
\(d_i\,\hbox {(Nms}/\hbox {rad})\)
|
---|---|---|---|
Head | 0.24 | 4.5 | 0.5 |
Upper body | 0.41 | 21.5 | 10.0 |
Middle body | 0.1 | 2.0 | 10.0 |
Lower body | 0.1 | 2.0 | 10.0 |
Upper arm | 0.31 | 2.3 | 0.03 |
Lower arm | 0.24 | 1.4 | 1.0 |
Hand | 0.18 | 0.4 | 2.0 |
Waist | 0.27 | 2.0 | 10.0 |
Upper leg | 0.38 | 7.3 | 10.0 |
Lower leg | 0.40 | 3.4 | 10.0 |
Foot | 0.07 | 1.3 | 10.0 |
Total weight (kg) | – | 64.2 | – |
Total height (m) | 1.7 | – | – |
3 Dynamic reconfiguration manipulability
4 Visual lifting approach
5 Stability analyses of biped walking by dynamical-evaluating index
Case | Walk or not | Number of steps (step) | Time (s) | Stride (m) | Average of DRMSI |
---|---|---|---|---|---|
\((1) {\varvec{K}}_\text {p}=\text {diag}[10, 190, 800]\)
| Fell down | 1 | 0.752 | 0.212 | 16,574 |
\((2) {\varvec{K}}_\text {p}=\text {diag}[20, 190, 800]\)
| Fell down | 1 | 0.752 | 0.212 | 16,574 |
\((3) {\varvec{K}}_\text {p}=\text {diag}[30, 190, 800]\)
| Fell down | 1 | 0.752 | 0.212 | 16,574 |
\((4) {\varvec{K}}_\text {p}=\text {diag}[10, 290, 800]\)
| Fell down | 4 | 2.876 | 0.285 | 25,716 |
\((5) {\varvec{K}}_\text {p}=\text {diag}[20, 290, 800]\)
| Fell down | 4 | 2.876 | 0.285 | 25,706 |
\((6) {\varvec{K}}_\text {p}=\text {diag}[30, 290, 800]\)
| Fell down | 4 | 2.876 | 0.285 | 25,715 |
\((7) {\varvec{K}}_\text {p}=\text {diag}[10, 390, 800]\)
| Fell down | 2 | 1.612 | 0.213 | 17,267 |
\((8) {\varvec{K}}_\text {p}=\text {diag}[20, 390, 800]\)
| Fell down | 2 | 1.614 | 0.213 | 17,254 |
\((9) {\varvec{K}}_\text {p}=\text {diag}[30, 390, 800]\)
| Fell down | 2 | 1.614 | 0.213 | 17,254 |
\((10) {\varvec{K}}_\text {p}=\text {diag}[10, 190, 900]\)
| Walked | 61 | 30.0 | 0.342 | 31,347 |
\((11) {\varvec{K}}_\text {p}=\text {diag}[20, 190, 900]\)
| Walked | 61 | 30.0 | 0.342 | 31,335 |
\((12) {\varvec{K}}_\text {p}=\text {diag}[30, 190, 900]\)
| Walked | 61 | 30.0 | 0.342 | 31,321 |
\((13) {\varvec{K}}_\text {p}=\text {diag}[10, 290, 900]\)
| Walked | 64 | 30.0 | 0.331 | 31,086 |
\((14) {\varvec{K}}_\text {p}=\text {diag}[20, 290, 900]\)
| Walked | 64 | 30.0 | 0.331 | 31,073 |
\((15) {\varvec{K}}_\text {p}=\text {diag}[30, 290, 900]\)
| Walked | 64 | 30.0 | 0.331 | 31,058 |
\((16) {\varvec{K}}_\text {p}=\text {diag}[10, 390, 900]\)
| Walked | 65 | 30.0 | 0.328 | 31,322 |
\((17) {\varvec{K}}_\text {p}=\text {diag}[20, 390, 900]\)
| Walked | 65 | 30.0 | 0.328 | 31,304 |
\((18) {\varvec{K}}_\text {p}=\text {diag}[30, 390, 900]\)
| Walked | 65 | 30.0 | 0.328 | 31,289 |
\((19) {\varvec{K}}_\text {p}=\text {diag}[10, 190, 1000]\)
| Walked | 42 | 30.0 | 0.409 | 33,550 |
\((20) {\varvec{K}}_\text {p}=\text {diag}[20, 190, 1000]\)
| Walked | 42 | 30.0 | 0.409 | 33,541 |
\((21) {\varvec{K}}_\text {p}=\text {diag}[30, 190, 1000]\)
| Walked | 42 | 30.0 | 0.409 | 33,551 |
\((22) {\varvec{K}}_\text {p}=\text {diag}[10, 290, 1000]\)
| Walked | 49 | 30.0 | 0.398 | 32,679 |
\((23) {\varvec{K}}_\text {p}=\text {diag}[20, 290, 1000]\)
| Walked | 49 | 30.0 | 0.398 | 32,671 |
\((24) {\varvec{K}}_\text {p}=\text {diag}[30, 290, 1000]\)
| Walked | 49 | 30.0 | 0.398 | 32,665 |
\((25) {\varvec{K}}_\text {p}=\text {diag}[10, 390, 1000]\)
| Walked | 56 | 30.0 | 0.382 | 31,896 |
\((26) {\varvec{K}}_\text {p}=\text {diag}[20, 390, 1000]\)
| Walked | 56 | 30.0 | 0.382 | 31,885 |
\((27) {\varvec{K}}_\text {p}=\text {diag}[30, 390, 1000]\)
| Walked | 56 | 30.0 | 0.382 | 31,874 |
\((28) {\varvec{K}}_\text {p}=\text {diag}[10, 190, 1100]\)
| Walked | 38 | 30.0 | 0.425 | 37,573 (maximum) |
\((29) {\varvec{K}}_\text {p}=\text {diag}[20, 190, 1100]\)
| Walked | 38 | 30.0 | 0.425 | 37,572 |
\((30) {\varvec{K}}_\text {p}=\text {diag}[30, 190, 1100]\)
| Walked | 38 | 30.0 | 0.425 | 37,571 |
\((31) {\varvec{K}}_\text {p}=\text {diag}[10, 290, 1100]\)
| Walked | 41 | 30.0 | 0.425 | 35,700 |
\((32) {\varvec{K}}_\text {p}=\text {diag}[20, 290, 1100]\)
| Walked | 41 | 30.0 | 0.425 | 35,698 |
\((33) {\varvec{K}}_\text {p}=\text {diag}[30, 290, 1100]\)
| Walked | 41 | 30.0 | 0.425 | 35,694 |
\((34) {\varvec{K}}_\text {p}=\text {diag}[10, 390, 1100]\)
| Walked | 45 | 30.0 | 0.420 | 34,613 |
\((35) {\varvec{K}}_\text {p}=\text {diag}[20, 390, 1100]\)
| Walked | 45 | 30.0 | 0.420 | 34,598 |
\((36) {\varvec{K}}_\text {p}=\text {diag}[30, 390, 1100]\)
| Walked | 45 | 30.0 | 0.420 | 34,622 |
\((37) {\varvec{K}}_\text {p}=\text {diag}[10, 190, 1200]\)
| Fell down | 1 | 1.194 | 0.100 | 11,163 (minimum) |
\((38) {\varvec{K}}_\text {p}=\text {diag}[20, 190, 1200]\)
| Fell down | 1 | 1.194 | 0.100 | 11,163 |
\((39) {\varvec{K}}_\text {p}=\text {diag}[30, 190, 1200]\)
| Fell down | 1 | 1.194 | 0.100 | 11,163 |
\((40) {\varvec{K}}_\text {p}=\text {diag}[10, 290, 1200]\)
| Fell down | 1 | 1.112 | 0.142 | 11,401 |
\((41) {\varvec{K}}_\text {p}=\text {diag}[20, 290, 1200]\)
| Fell down | 1 | 1.112 | 0.142 | 11,391 |
\((42) {\varvec{K}}_\text {p}=\text {diag}[30, 290, 1200]\)
| Fell down | 1 | 1.112 | 0.142 | 11,391 |
\((43) {\varvec{K}}_\text {p}=\text {diag}[10, 390, 1200]\)
| Walked | 39 | 30.0 | 0.451 | 37,487 |
\((44) {\varvec{K}}_\text {p}=\text {diag}[20, 390, 1200]\)
| Walked | 39 | 30.0 | 0.451 | 37,485 |
\((45) {\varvec{K}}_\text {p}=\text {diag}[30, 390, 1200]\)
| Walked | 39 | 30.0 | 0.451 | 37,490 |
\((46) {\varvec{K}}_\text {p}=\text {diag}[10, 190, 1300]\)
| Fell down | 1 | 1.262 | 0.068 | 11,506 |
\((47) {\varvec{K}}_\text {p}=\text {diag}[20, 190, 1300]\)
| Fell down | 1 | 1.262 | 0.068 | 11,506 |
\((48) {\varvec{K}}_\text {p}=\text {diag}[30, 190, 1300]\)
| Fell down | 1 | 1.262 | 0.068 | 11,506 |
\((49) {\varvec{K}}_\text {p}=\text {diag}[10, 290, 1300]\)
| Fell down | 1 | 1.180 | 0.099 | 11,191 |
\((50) {\varvec{K}}_\text {p}=\text {diag}[20, 290, 1300]\)
| Fell down | 1 | 1.180 | 0.099 | 11,191 |
\((51) {\varvec{K}}_\text {p}=\text {diag}[30, 290, 1300]\)
| Fell down | 1 | 1.180 | 0.099 | 11,191 |
\((52) {\varvec{K}}_\text {p}=\text {diag}[10, 390, 1300]\)
| Fell down | 1 | 1.106 | 0.139 | 11,514 |
\((53) {\varvec{K}}_\text {p}=\text {diag}[20, 390, 1300]\)
| Fell down | 1 | 1.106 | 0.139 | 11,514 |
\((54) {\varvec{K}}_\text {p}=\text {diag}[30, 390, 1300]\)
| Fell down | 1 | 1.106 | 0.139 | 11,514 |