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Haldun Komsuoglu





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Toward a Formal Framework for Open-Loop Stabilization of Rhythmic Tasks

Ph.D. Thesis, University of Michigan, September 2004

Komsuoglu, H.
Department of Electrical Engineering and Computer Science, University of Michigan

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The wheel has been the primary means of terrestrial transportation since its invention in 4000 B.C. The popularity of wheeled vehicles can be attributed to the ease of their control, which requires no or very little sensory feedback in most scenarios. Unfortunately, the operational domain of wheeled vehicles is severely limited in natural settings where the conditions favorable to wheeled locomotion are seldom met. On the other hand, legged animals exhibit extraordinary locomotion performance over highly unstructured and unstable surfaces that no wheeled vehicle can even approach. Legs are also highly versatile tools that can serve for purposes other than locomotion, such as manipulation of external ob jects. However, in the field of robotics, these desirable features of legged systems have been overshadowed by the difficulty of construction and control of legged platforms which remains a ma jor obstacle to producing physically viable legged systems. Combining the ease of control of wheeled approaches with the performance of legs may likely lead to a quantum leap in our ability to move in terrestrial settings. Recent collaborations between engineers and biologists have led to the identification of a family of biologically-inspired control principles for legged locomotion. It was shown that the passive mechanical musculoskeletal system plays a crucial part in the control of legged locomotion. In fact, in some extreme cases the active control takes the form of a purely feed-forward excitation of this passive mechanical system. RHex — a highly dexterous autonomous hexapod robot — has demonstrated that task-level open-loop control can in fact give rise to exceptional performance over rough surfaces and may be the key to the eventual development of real world products.
From an engineering point of view, open-loop controllers are very desirable solutions due to their significantly simpler structure which does not require sensors or related infrastructure. In essence, the ability to control legged locomotion by feed-forward controllers brings ease of control — a feature typically attributed to wheeled vehicles — into the field of legged robotics. Unfortunately, to this date the design of open-loop controllers is still a “black art” in which the intuition of the researcher acts as the only design tool. This thesis marks the beginning of a formal framework to design and verify open-loop controllers for dynamical legged locomotion. To this end we consider a very simple open-loop controlled dynamical model — a clock driven 1-DOF hopper — to investigate the basic principles of open-loop control with the overarching goal of identifying sufficient (and hopefully necessary) conditions for stable locomotion. We present an analysis which allows us to study arbitrary excitation patterns. We discuss a computational algorithm for the design of open-loop controllers based on these analytic results. Furthermore, we introduce a family of hierarchical stride-to-stride adaptation laws that take advantage of this open-loop setup. Our numerical studies suggest that some key ideas discovered in this simple illustrative model indeed extend to a wide family of physically relevant setups.
BibTeX entry
  author = {Komsuoglu, H.},
  title = {Toward a Formal Framework for Open-Loop Stabilization of Rhythmic Tasks},
  school = {University of Michigan},
  year = {2004},
  type = {Ph.D.},
  address = {Ann Arbor},
  month = {October}

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