Work minimization accounts for footfall phasing in slow quadrupedal gaits

Quadrupeds, like most bipeds, tend to walk with an even left/right footfall timing. However, the phasing between hind and forelimbs shows considerable variation. Here, we account for this variation by modeling and explaining the influence of hind-fore limb phasing on mechanical work requirements. These mechanics account for the different strategies used by: (1) slow animals (a group including crocodile, tortoise, hippopotamus and some babies); (2) normal medium to large mammals; and (3) (with an appropriate minus sign) sloths undertaking suspended locomotion across a range of speeds. While the unusual hind-fore phasing of primates does not match global work minimizing predictions, it does approach an only slightly more costly local minimum. Phases predicted to be particularly costly have not been reported in nature

Frequency-Aware Model Predictive Control

Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion infeasible on the real system. Model errors can be a result of model simplifications, but also naturally arise when deploying the robot in unstructured and nondeterministic environments. Predominantly, compliant contacts and actuator dynamics lead to bandwidth limitations. While classical control methods provide tools to synthesize controllers that are robust to a class of model errors, such a notion is missing in modern trajectory optimization, which is solved in the time domain. We propose frequency-shaped cost functions to achieve robust solutions in the context of optimal control for legged robots. Through simulation and hardware experiments we show that motion plans can be made compatible with bandwidth limits set by actuators and contact dynamics. The smoothness of the model predictive solutions can be continuously tuned without compromising the feasibility of the problem. Experiments with the quadrupedal robot ANYmal, which is driven by highly-compliant series elastic actuators, showed significantly improved tracking performance of the planned motion, torque, and force trajectories and enabled the machine to walk robustly on terrain with unmodeled compliance

Üner Tan Syndrome: Review and Emergence of Human Quadrupedalism in Self-Organization,\ud Attractors and Evolutionary Perspectives\ud

The first man reported in the world literature exhibiting habitual quadrupedal locomotion was discovered by a British traveler and writer on the famous Baghdat road near Havsa/Samsun on the middle Black-Sea coast of Turkey (Childs, 1917). Interestingly, no single case with human quadrupedalism was reported in the scientific literature after Child's first description in 1917 until the first report on the Uner Tan syndrome (UTS: quadrupedalism, mental retardation, and impaired speech or no speech)in 2005 (Tan, 2005, 2006). Between 2005 and 2010, 10 families exhibiting the syndrome were discovered in Turkey with 33 cases: 14 women (42.4%) and 19 men (57.6%). Including a few cases from other countries, there were 25 men (64.1%)and 14 women (35.9%). The number of men significantly exceeded the number of women (p < .05). Genetics alone did not seem to be informative for the origins of many syndromes, including the Uner Tan syndrome. From the viewpoint of dynamical systems theory, there may not be a single factor including the neural and/or genetic codes that predetermines the emergence of the human quadrupedalism.Rather, it may involve a self-organization process, consisting of many decentralized and local interactions among neuronal, genetic, and environmental subsystems. The most remarkable characteristic of the UTS, the diagonal-sequence quadrupedalism is well developed in primates. The evolutionarily advantage of this gait is not known. However, there seems to be an evolutionarily advantage of this type of locomotion for primate evolution, with regard to the emergence of complex neural circuits with related highly complex structures. Namely, only primates with diagonal-sequence quadrupedal locomotion followed an evolution favoring larger brains, highly developed cognitive abilities with hand skills, and language, with erect posture and bipedal locomotion, creating the unity of human being. It was suggested that UTS may be considered a further example for Darwinian diseases, which may be associated with an evolutionary understanding of the disorders using evolutionary principles, such as the natural selection. On the other hand, the human quadrupedalism was proposed to be a phenotypic example of evolution of reverse, i.e., the reacquisition by derived populations of the same character states as those of ancestor populations. It was also suggested that the emergence of the human quadrupedalism may be related to self-organizing processes occurring in complex systems, which select or attract one preferred behavioral state or locomotor trait out of many possible attractor states. Concerning the locomotor patterns, the dynamical systems in brain and body of the developing child may prefer some kind of locomotion, according to interactions of the internal components and the environmental conditions, without a direct role of any causative factor(s), such as genetic or neural codes, consistent with the concept of self-organization, suggesting no single element may have a causal priority