C.2) Source Annotation

Important Note

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

For the sake of continuity, I have chosen to push ahead collecting information and writing a review relating to the theme initiated in my previous C.1 assignment:

“How can animals improve their locomotion patterns to succeed stably over very high speeds and very complex and varied terrain? What would it take to get a robot with such a capability?”

In some real sense this is "cheating" since I am surely a domain expert in this area, and unlike the students in the class, I will be coming to the literature with a long history of work and thought and a great familiarity with the surrounding literature. Nevertheless, I have tried to proceed in a formulaic manner (that does not utilize in any way my privileged background) whose steps and reasoning I have done my best to document as a model for the students.

Instructor's Sample Assignment Solution

Reactive Running

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

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.

Existing Technology

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."

Potential Biological Solution

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 [9] that all animals interact with the ground as if they were a pogo-stick - an inverted pendulum swinging or bouncing along [10]. 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.

Value of Sources

Examples of blind keyword searches with mixed outcome are provided by the PubMed and the Biosis searches reported in my C.1 solution. For example, the article on fish-inspired underwater vehicle control electronics had nothing to do with the intended focus on agile running and is likely a consequence of the insufficiently specific search term, “bioinspired robot locomotion”, which would need to be refined as a next step of this research. Similarly, insect-inspired adhesive with application to climbing robots is distant from the intended focus on agile running.

In contrast the article turned up by the Biosis keywords (“robot” AND “locomotion” AND “run$”) concerning a general neural controller for quadrapedal locomotion looked like a great potential source. Unfortunately, it is not entirely clear from the abstract and only begins to become clear from the introduction and the conclusion that the paper has no mathematical results, and no physical implementation, but rather presents an elaborated simulation study. Roboticists who have any experience at all with moving simulated controllers into physical plants will cast a very skeptical eye on the likely benefits of such simulation-only studies.

Open Problems

The authors of the primary robotics reference [1] find that the performance of the bioinspired robot [3] worsens as the machine is required to traverse badly broken terrain at high speed. In their discussion, they admit that the analytical perspective will take a long time to catch up to explaining even how the machine performs at all - much less how its performance might be improved. Thus, there is good motivation to explore bioinspired solutions.

In their discussion, the authors of the primary biology reference [5] adopt the "template" hypothesis of [4], reasoning that controlling a complex body as if it were a simple pogo-stick might greatly reduce the complexity of the system to a few controllable limb parameters. They note from [1] that such simple mechanisms can achieve stable running with many different gaits, and hypothesize that the bird's posture dependent joint compliance strategy may afford rapid control of posture and velocity when running over rough terrain. Their results suggest that a combination of feedforward and feedback styles of joint control organized by proximity to body center (feedback influences increasing with greater distance from body and closer proximity to the direct environment) may help achieve the appropriate selection of gait in response to badly broken terrain with its treacherously large, unanticipated height variations.

These observations suggest a number of exciting open question. First, empirically, we might build a new variation on the singly actuated legs of the RHex machine [3] that might afford additional, active variation of stiffness beyond those presently mechanically fixed selections and experimentally explore the possible benefits in traversal of treacherous terrain. Specifically, we might attempt to implement the "graded" feedback influence by locating leg sensors on the ends of the legs and stiffening or relaxing the variable springs as a function of foot load. Finally, we might attempt to show mathematically how systematic stiffening or relaxation of a pogo-stick spring, independent of its recirculation speed, might achieve stability over ground of suddenly varying height.


Robotics Paper

Paper [1] (whose likely importance was documented in my solution to the first assignment ) reviews an integrated approach to the study of muscular, skeletal, and neural mechanics associated with arthropod runners. It is intended as a non-technical tutorial introduction to the mathematical expression of various hypotheses about animal running that have been rendered concretely in the robot RHex. It stresses the interplay of materials properties and algorithmic design in achieving behavior, as well as the mix of animal, mathematical and physical models in generating hypotheses that probe their inter-relationships.


The authors cite [6] prominently, as responsible for the fundamental idea of a "preflex" - tuned muscles acting through skeletal postures. This is not a refereed journal or conference paper, but, rather, an apparently unrefereed chapter in a book - nevertheless a Google Scholar search reveals it has been cited 71 times. They also insert the (partial) self-citation to the highly cited RHex paper [3] (which has been cited 391 times according to a Google Scholar search) as an exemplar of the process of bioinspired engineering.


A Scopus search on this paper's title yields 35 subsequent successors (i.e., papers that cite it). Of these the most highly cited in turn is the (partial) self-citing survey article on neuromechanics [7] which itself registers 68 subsequent citations according to Scopus. The second most highly cited successor is [8] with 29 successors as registered by Scopus.

Biology Paper

Important Note: The reasons for picking this paper may not be clear as initial version of this solution is from 2009. Number of citations and h-impact all have up-to-date values.

Reference [5] (whose quality I did not establish in my response to C.1 and, hence, I must assess now) is likely to have made an important contribution to the literature because:

  • for a relatively recent article it enjoys a sizable body of citing papers (a Google Scholar search showed 8 successors as of Jan. 26, 2011) ;
  • it appeared in a high impact biology journal (J. Exp. Biol. ranks in the top 20 of all biology journals according to it's ISI impact factor of 2.722)
  • its authors are associated with a highly reputable US University (…well… maybe not quite so reputable as Penn :) but probably most would agree that Harvard comes reasonably close …) ; the senior author has an impressive Scopus h-index; 26

This paper addresses the problem of how animals - specifically, a bipedal bird - stabilize their gait when running over bad terrain. They find evidence that muscles acting on joints close to the body are controlled in a more feedforward manner while, in contrast, control at joints located further away from the body are more sensitive to variations in the loading during a stride. The key notion is that recovery from perturbations is enhanced by these distant joints switching over from controlled behavior that resembles a mechanical "damper" during flight to behavior that exhibits more "springlike" properties during stance.


The authors cite a paper from 1977 [9] which has been cited by other articles 555 times according to a Google Scholar search presenting some of the earliest evidence that many different running animals use similar basic mechanisms for steady state movement. They also cite a more recent paper [10] which itself has been cited 302 times according to Scopus reiterating the same point, supporting the authors' contention that it is still unclear whether such simple similar mechanisms are used in more general non-steady conditions.


This article has been cited by a recent survey paper about "neuromechanics" [11] which has itself already been cited 25 times according to a Scopus. It has also been cited very recently by a paper [12] in one of the top robotics journals (e.g. by relative impact factor) exploring the the effect of joint level compliance on running stability.


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. I. E. Brown, G. E. Loeb, "A Reductionist Approach to Creating and Using Neuromusculoskeletal Models", Biomechanics and Neural Control of Posture and Movement, pp. 148. Springer, 2000.
7. P. Holmes, R. J. Full, D. Koditschek, J. Guckenheimer, "The Dynamics of Legged Locomotion: Models, Analyses, and Challenges", SIAM Review, vol. 48, no. 2, pp. 207-304, 2006.
8. D. I. Goldman, T. S. Chen, D. M. Dudek and R. J. Full, "Dynamics Of Rapid Vertical Climbing In Cockroaches Reveals A Template", Journal of Experimental Biology, vol. 209(15), pp. 2990-3000, 2006.
9. 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.
10. 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.
11. K. Nishikawa, A. A. Biewener, P. Aerts, A. N. Ahn, H. J. Chiel, M. A. Daley, T. L. Daniel, "Neuromechanics: An Integrative Approach for Understanding Motor Control", Integrative and Comparative Biology, vol. 47, no. 1, pp. 16-54, 2007.
12. J. Rummel, A. Seyfarth, "Stable Running with Segmented Legs", The International Journal of Robotics Research, vol. 27, no. 8, pp. 919-934, 2008