C.3) Problem Formulation

Important Note

Similar to instructor's solution for C.2, this solution was put together in Spring 2009. Although there have been some updates and modifications, its core does not necessarily align with instructor's recent solution for C.1.

Instructor's Notes

Once again, to conserve effort, I will play the role of "having been "lucky" to have chosen a "group" project topic that matches the topics I investigated in the Source Acquisition and Source Annotation assignments, so that much of this page is copied from the latter page. Of course, the entire the Hypothesis section is new, but note as well that I was forced to re-read the chief biological reference [5] and determine the specific details of the bird's hypothesized control pattern in order to be able to propose a precise experimental protocol in the Refutability Section.

A Note on Reuse: Copying Vs. Citing

Notice that I have chosen to reuse my original C.2 solution textual material by directly copying whereas, in contrast, I have simply left a citation to my previous annotations in the form of a url to the relevant portion of the C.2 page. This reflects my judgement that "typical" readers would be better served to not have to switch back and forth between two different pages when they are reading this page for the first time. In contrast, the casual reader will not have too much initial interest in annotations, so it has seemed better to leave them uncopied in place.

A Note on Self-Plagiarism

Everyone knows that plagiarism (the copying of others' work without proper attribution) is a cardinal misdeed in the realm of science and, indeed, any activity related to cultivating human knowledge. It is worth noting in passing that self-plagiarism (the copying of one's own work in a manner that does not document the original source) is no less reprehensible. There is a very useful Wikipedia discussion of self-plagiarism contained within the general article on plagiarism that offers up an interesting list of relevant references as well. Please note that I have made certain to alert the reader in my previous paragraph to the wholesale copying of paragraphs. I have also taken the precaution of placing the specific attributions in each subsection as well so there could be no appearance of self-plagiarism.

Instructor's Sample Assignment Solution

Problem: The Nature of Reactive Running

What is Reactive Running? (copied from Koditschek: C.2)

Reactive running denotes the ability of a legged body traveling with significant momentum to recover in midstride from some severe, unexpected perturbation delivered by the traversed ground. Today's robots have finally begun to get out of the lab and into the real world. When they get there, they encounter fields punctured by craggy rockbeds, streams lined by steep, irregular stone and gravel banks, trails littered with stumps, branches and organic debris, deserts with oceans of sand, mountain passes coated with ice, and every imaginable mixture. Animals, benefitting from hundreds of million years of design iteration, traverse these natural landscapes with ease. Although many are specialized to achieve truly spectacular performance in one or another specific environment, they are naturally at home almost anywhere. It is almost unimaginable that any random animal placed in any random natural setting would not be able at least awkwardly to scramble away from a predator or toward prey. Yet, of course, very few robots can negotiate natural terrain at all, and the very best state of the art machines are quickly immobilized when their environments depart significantly from their designers' expectations. Reactive running represents one of the many missing capabilities that might improve legged robot performance in the face of the inevitable, severe, unanticipated perturbations they will suffer in natural terrain.

Uses of Reactive Running (copied from Koditschek: C.2)

Today's robot's missions fail for want of adequate mobility. The Mars rover, Spirit got stuck in loose sand, nearly aborting its historic mission. Lives tragically lost in the Sago mine disaster might have been saved had the mine disposal robot not gotten bogged down after moving just 21 metres into the tunnel. Mobility failures were cited as one of the primary limitations of robots introduced into the 9/11 Ground Zero rescue effort. In all these varied situations, speed of locomotion was of the essence, and a greater ability to negotiate loose, rocky, and broken ground could have made a crucial difference for outcomes of significant human interest. Surely a reactive running capability would have been relevant - and possibly decisive in some of these and many other high impact application settings.

Present Unavailability (copied from Koditschek: C.2)

Toward the end of the introduction of the primary robotics reference [1], the authors mention a hypothetical architecture (whose origins they attribute to their earlier work [2]) for connecting up a purely mechanical arrangement for locomotion control with an "internal" set of oscillators evocative of a nervous system. This results in a tunable family of couplings:

"…spanning on the one hand a range between pure feedback and pure feedforward control options, and, on the other, a range between completely centralized and completely decentralized computational options."

and they point out in the conclusion that the advanced hexapod, RHex [3], initially used coordination algorithms with a centralized feedforward character inspired by the hypothesis of a specific kind of dynamical model (that they term a "template" and credit to [4]). This simple architecture then increased in complexity with the introduction of more sophisticated sensory devices and a larger number of "clocks." In general, they point out:

"…there is no aspect of locomotion capability presently to be found on RHex or any other extant robot that can begin to compare to any legged animal."

In particular, they observe toward the end of the discussion of new experiments with RHex that the robot encounters problems with fast maneuvers over badly broken terrains, admitting:

"The only gaits we presently have developed that are capable of ascending rocky slopes at average inclinations greater than not, vert, similar15° are very slow, centralized, open loop, quasi-static ‘creepers’ that attempt blindly to secure footholds and handholds, advance the body slowly enough to leave them intact, and then reposition trusting the body's ‘grip’ on the terrain to hold the ground already gained."

Desirability of Bioinspiration

In the primary biological reference [5] the authors point out that relatively little is known about how animals achieve dynamic stability when running over bad terrain. It has been known for decades [6] that all animals interact with the ground as if they were a pogo-stick - an inverted pendulum swinging or bouncing along [7]. But since purely spring-mass systems are conservative, changes in total energy cannot be achieved without some more active measures.

The General Nature of the Chief Discovery (copied from Koditschek: C.2)

In the primary biological reference [5] the authors point out that relatively little is known about how animals achieve dynamic stability when running over bad terrain. It has been known for decades [6] that all animals interact with the ground as if they were a pogo-stick - an inverted pendulum swinging or bouncing along [7]. But since purely spring-mass systems are conservative, changes in total energy cannot be achieved without some more active measures.

The authors investigated how a small (bipedal) bird would negotiate an unanticipated drop in the terrain height while running. They found variation in the type of control the muscles asserted at the bird's joints organized by the relative distance away from the center of the body. Specifically, muscles actuating the hip and knee joints were found to be controlled in a primarily feedforward manner and were insensitive to changes in the environment impacting the bird's gait. In contrast, at the ankle and toe joints proved to be quite sensitive to the altered load and rapidly changing consequent bodily sensations. They switched between more spring-like or more lossy depending upon the posture at ground contact. Contrarily, the overall limb touchdown and liftoff motion and velocity patterns, determined largely by the hip, did not exhibit much change before and after the pertrurbation was applied. In this manner, the authors proposed that phase relationships between the legs that determine coordination and gait timing might remain invariant even as the posture and energy management during contact are adapted significantly to the radically changing environment.

The Specific, Relevant Details of the Chief Discovery

In order to pursue a robot-experimental implementation of this idea in the Refutability Section, below, it is necessary to describe the specific nature of the limb tuning pattern in some detail. A corrected version of Fig. 9 in [5] indicates that when the bird's knee is extended then the distal joints act as dampers and the limb does net negative work. In contrast, when the knee is flexed then the distal joints act as springs and the net limb work is positive.

The Hypothesis

The primary biological reference [5] makes very concrete and specific claims about the mechanical function of the bird's reflex controller. If implemented in a robot, these same mechanical adjustments ought to provide enhanced performance over similarly broken ground.

The Idea

The Section on Present Unavailability introduced the notion of a bioinspired control architecture implemented on the RHex robot [3] that could be used for coupling mechanical systems with models of neural oscillators.

"spanning on the one hand a range between pure feedback and pure feedforward control options, and, on the other, a range between completely centralized and completely decentralized computational options" [2]

Moreover, RHex was shown [1] to exhibit roughly the same pogo-stick-like "template" [4] that the present source of bioinspiration [5] finds to be characteristic of the birds as well. Although RHex had only one actuated degree of freedom (in its hip) for each leg, it might be possible to add another active mechanism onto the leg of a Junior that could tune the compliance and damping of the lower length - the "distal" end in the language of the primary biological reference [5]. The Junior representation of a "flexed knee" pose could be interpreted as a leg that had touched down with initial ground contact relatively high up on the C-leg; an "extended knee" pose could be interpreted as a leg that had touched down near the very distal end of the C-leg. These analogies would provide a ready test of the control methodology hypothesized in that article.

Refutability

Given a Junior with mechanically tunable legs, one could run a series of experiments over progressively more broken terrain and explore the role of compliance and damping in the distal" degrees of freedom in helping to stabilize the gait. A direct experimental test would compare performance over various terrain conditions under three different types of settings. First, as a control, one would run a well-tuned version of the original RHex gait. A second and third version of the neural oscillator architecture would interpret position of the ground contact (along the arc up and down the leg) as determining the "posture" along the lines just proposed. The second version, following in analogy to the hypothesized biological control strategy, would call out a stiffer, more damped setting of the limb when touchdown occurs closer to the toe, while commanding a more compliant and less damped setting of the limb when touchdown occurs higher up along the limb. The third version, contradicting the hypothesized strategy, would reverse the effect by commanding more compliance and less damping when touchdown occurs at the toe. If gait performance were more enhanced by the second controller relative to the first and third then the hypothesis would be strengthened. In contrast, if gait performance were more enhanced by the third, or there were only slight differences between the three, then the hypothesis would be weakened.

Necessary Means

In order to pursue this project with Junior hardware, one would require

  1. a contact sensor along the Junior's C-leg to determine where ground contact has occurred at what point in the stride
  2. a means of actively tuning the stiffness and damping properties of the C-leg
  3. a method for driving the stiffness/damping tuning actuator according to the readings of the contact sensor

References

1. D. E. Koditschek, R. J. Full, M. Buehler, "Mechanical aspects of Legged Locomotion", Arthropod Structure and Development, vol. 33, no. 3, pp. 251-272, 2004.
2. E. Klavins, H. Komsuoglu, J. Robert, D. E. Koditschek, "The Role of Reflexes versus Central Pattern Generators in Dynamical Legged Locomotion", MIT Press, pp. 351-382, Cambridge, MA, 2002.
3. U. Saranli, M. Buehler, D. E. Koditschek, "RHex: A Simple and Highly Mobile Hexapod Robot", The International Journal of Robotics Research, vol. 20, no. 7, pp. 616, 2001.
4. R. J. Full, D. E. Koditschek, "Templates and Anchors: Neuromechanical Hypotheses of Legged Locomotion on Land", Journal of Experimental Biology, vol. 202, pp. 3325-3332, 1999.
5. M.A. Daley, G. Felix, A.A. Biewener, "Running Stability is Enhanced by a Proximo-Distal Gradient in Joint Neuromechanical Control", Journal of Experimental Biology, vol. 210, no. 3, pp. 383-394, 2007.
6. G. A. Cavagna, N. C. Heglund, C. R. Taylor, "Mechanical Work in Terrestrial Locomotion: Two Basic Mechanisms for Minimizing Energy Expenditure", American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, vol. 233, no. 5, pp. 243-261, 1977.
7. M. H. Dickinson, C. T. Farley, R. J. Full, M. A. R Koehl, R. Kram, S. Lehman, "How Animals Move: An Integrative View", Science, vol. 288, no. 5463, pp. 100-106, 2000.