The Dynamics of Legged Locomotion: Models, Analyses, and Challenges; Holmes, Full, Koditschek, Guckenheimer

This was the 100 pager, which i managed in one sitting, at the expense of section 5 (the meat) and lots of biophysics (boring). It was better than I was expecting, lots of leads and good insight.

This is a very impressive review consolidating work in modeling, analysis, robotics, biophysics and neuroethology. They cover a ridiculous array of methods and models, drawing from everywhere. It isn't quite my one stop reference shop, but it will provide many useful leads, and after I look closer at section 5, some tools too. The bias is towards running insects.

• Section 1 is introduction
• Section 2 reviews earlier work on locomotion and movement modeling, relevant machanical, biomechanical, neurobiologaical and robotics background.
• Section 3 summarizes experimental work on running and walking animcals
• Section 4 introduces analytic methods to be employed in section 5
• Section 5 solves some problems and provides procedures for answering some tricky questions.
• Section 6 has lots of great conclusions and directions

Comments

"Ultimate goal is to produce a "behaving insect"" That is without any reference to Brooks that I can determine.

Acknowledging role of engineer's optimization and reduction

Contrast "Completely actuated and sensed machines..whose stability can be established and tuned analytically...[requiring] a very high deegree of control authority" with "The analytically messier, "low-affordance" ... autonomous, dynamically stable ... preflexively stabilized...[with] centralized/decentralized feedforward/feedback lovomotion control architectures". Further: "a gulf remains between the performance we can elicit empirically and what mathmatical analyses or numberical simulations can explain." Brings up the interesting personal question. Is my role to work towards filling the gap? Right now, I think my goal will be to find tools that make researchers comfortable leaving the other ones behind.a

simulations are allowing empirical results to be trustworthy enough to replace theoretical results, in many cases.

A worried question: "Are coordination patterns unique within species?" Even if the answer is yes, the procedure each species followed to find the pattern is the same. The problem of designing distributed systems is making them design themselves.

There was a subtle point that seemed important that I didn't understand (and can't find). Animal limbs have many many degrees of freedom, which is a pain for analysis, so they must have methods for constraining the space of conformations. Mention was made that the constraint is goal based? I have to determine the possibilities of that for myself. Oh, here is the mention:

"collapse of dimension: the emergence of a low-dimensional attractive incariant submanifold in a much larger state space. This dynamical collapse appears to be associated with a posture principle: the restiction of motion to a low-dimensional subspace within a high-dimensional joint space. A kinematic posture principle has been discovered in mammalian walking[citation], as demonstrated by planar sovarianation of limb elebation angles which persists in the face of large variations in steady state loading conditions[citation]"

Collapse of dimension is a great concept and section 5 may provide a tool useful to me. What is the 'posture principle' and can I abstract it or generalize it? I don't know what submanifolds are. 'dynamical collapse'? I wonder if randy has anything to say about that.

My notes on this quote say "many constraints" and "patterns". As for the first, the quote validates the intuition behind something I wrote elsewhere, about needing a procedure by which we can engineer how modules locally constrain each other in the same way that we can engineer how a central module constrains its parts in a central architecture. Regarding "patterns", it may be that the best way to collapse the search space will be to create behavior patterns like in Brook's Attila or Hannibal. Related to this is collapsing the search space by making irreducible modules like in conventional engineering and cockroach legs, where each leg can influence the other, but the actual motion of a leg is largely locally controlled.

"We also believe that the rapid runing regime pushes animals close to limits of feasible neuromuscular activity and hence constrains the space of activations and dynamical forces available, much as in the case of static force production [citations], making it more likely that lower-dimensional behavior will emerge" Great quote! Important insight! I just don't know in what way.

Also: "A model that leaves nothing out is not a model" hear hear!

"growing consensus with the animal neuromotor community that control is organized in a distributed modular hierarchy" Distributed implies (only) local communication. Modular implies modules, or functional black boxes. hierarchy implies multiple scales and modules that control action at scales below them. It also, by my definitions, contrasts with the word distributed (though ther aren't necessarily mutually exclusive in this context). What are their definitions? Well, there is a chart on p230 with a 'decentralized centralized' axis and a 'feed-forward feedback' axis. Modules are assumed. It is possible that for them decentralized and distributed are synonymous and centralized and heirarchical are synonymous.

To Read

• Hutchinson
• autopoesis, Manchuera? Bolera?
• Look into RHex