## The role of motion dynamics in the design, control and stability of bipedal and quadrupedal robots (2002)

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Citations: | 13 - 3 self |

### BibTeX

@INPROCEEDINGS{Hardt02therole,

author = {Michael Hardt and Oskar Von Stryk},

title = {The role of motion dynamics in the design, control and stability of bipedal and quadrupedal robots},

booktitle = {},

year = {2002},

pages = {206--223},

publisher = {Springer}

}

### Years of Citing Articles

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### Abstract

Abstract. Fundamental principles and recent methods for investigating the nonlinear dynamics of legged robot motions with respect to control, stability and design are discussed. One of them is the still challenging problem of producing dynamically stable gaits. The generation of fast walking or running motions require methods and algorithms adept at handling the nonlinear dynamical effects and stability issues which arise. Reduced, recursive multibody algorithms, a numerical optimal control package, and new stability and energy performance indices are presented which are well-suited for this purpose. Difficulties and open problems are discussed along with numerical investigations into the proposed gait generation scheme. Our analysis considers both biped and quadrupedal gaits with particular reference to the problems arising in soccer-playing tasks encountered at the RoboCup where our team, the Darmstadt Dribbling Dackels, participates as part of the German Team in the Sony Legged Robot League.

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8 |
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Citation Context ...ically enter different discrete states with each new contact state which (discontinuously) switch the dynamical model. The numerical solution of hybrid optimal control problems is in its early stages =-=[3, 33]-=-, yet when the discrete trajectory (contact events) is previously specified, current numerical solution techniques have been shown to work well [5, 16]. Specifying the order of contact events for a bi... |

6 |
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Citation Context ...which can be advantageous for increasing robustness and reducing power 2sconsumption. Nonetheless, 3-D bipeds and quadrupeds have been constructed which perform dynamically stable walking and running =-=[18, 34, 37]-=-. Though due to excessive power consumption they were either not autonomous or required a substantial battery supply for only a short operational period. In Sect. 3, alternative stability as well as e... |

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Citation Context ...which can be advantageous for increasing robustness and reducing power 2sconsumption. Nonetheless, 3-D bipeds and quadrupeds have been constructed which perform dynamically stable walking and running =-=[18, 34, 37]-=-. Though due to excessive power consumption they were either not autonomous or required a substantial battery supply for only a short operational period. In Sect. 3, alternative stability as well as e... |

3 |
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Citation Context ...gs d t , discontinuous states at collision times k of the legs with the ground, tS¥ switching dynamics, and actuation limits. This method of generating optimal reference trajectories was also used in =-=[7, 16, 17]-=-. It may be applied to much higher dimensional systems than finite-element approaches as used for example in [4], and the numerical package is more general than that for example used in [5]. 4.2 Numer... |

3 |
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Citation Context ... configurations where the ZMP provides little useful information. The FRI can also be extended to the quadrupedal case though other similar measures specialized to quadrupeds have been introduced. In =-=[24]-=-, the angular momentum about the support edges was used to define a postural stability index. Like the FRI, this method provides both directional information and a reference stability quantity that ca... |

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Citation Context ... stability refers to the dynamical system definition of stability for limit cycles in periodic gaits. Numerical methods for classifying or acquiring stable gait trajectories are presented in [21] and =-=[26]-=- respectively. Due 7 G 2 i ηi mi ¢sto the nonconvexity of the problem and the high dimensional nonlinear dynamics, direct optimization methods cannot be readily applied to the full-dimensional dynamic... |

2 |
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Citation Context ...2.2. Dynamical Stability of Legged Robot Motion. There exists a wide spectrum of previously presented approaches for generating dynamically stable motions in bipeds and quadrupeds. Analytical methods =-=[14, 19, 22]-=- usually rely on simplified models and are not yet at a stage where the many influencing dynamical effects previously mentioned can be considered. More complete 3-D modeling approaches [20, 27] for bi... |

2 |
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Citation Context ...c Algorithms Many methods exist for evaluating multibody robot dynamics. Symbolic methods construct efficient, closed form dynamics for the specific multibody systems through symbolic simplifications =-=[28]-=-. This approach is not well-suited though to legged systems due to the switching characteristic of the dynamics in different contact states, varying 1 � �¡���������� ¡ § £¢��������������£¢ ���������¡�... |

1 |
O.: DIRCOL: A direct collocation method for the numerical solution of optimal control problems
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(Show Context)
Citation Context ...n, we explore in this work a numerical optimization approach which minimize performance or stability objectives in the gait generation problem. Numerical optimization tools have advanced sufficiently =-=[2, 11, 32]-=- such that all the above-mentioned modeling and stability constraints can be incorporated into the problem formulation together with a relatively complete dynamical model so as to obtain truly realist... |