C.3 Problem Formulation

Problem Statement

C.3.1) Desired Behavior or Capability

In formulating a problem to attack for the remainder of the semester, we decided that the topics we discussed in our C1 and C2 assignments (serpentine locomotion and flight) were not directly applicable to the hexapod, legged robot that is RHex. However, one of the overarching issues that arose when delving into serpentine locomotion, where there are too many degrees of freedom to account for, was the issue of control, especially automated control and adaptability. While RHex does not have this problem with DOF, automated control is still a desired capability that has not yet been fully incorporated. [3] mentions that

“There is currently no well-established methodology for controlling the locomotion of robots with multiple degrees of freedom, in particular for non–steady-state locomotion in complex environments.”

See C1 for more annotation details. Indeed, disabling a leg adds additional degrees of freedom to RHex body's range of motion. Therefore, there are many analogies to serpentine locomotion.

We choose to focus on a very practical matter, observed in laboratory experiments - the loss of one leg before commencing of or during locomotion. Often times, RHex demonstrates dilapidated movements, and the running gait is terminated and started again. We aim to incorporate the capability of directed, controlled, and purposeful movement even in the absence of a leg. RHex would be able to compensate for the complete loss of function in one leg, restoring motion to a state comparable to full legged functions. The hypothesis section below will extrapolate on a few of the standards we will use to evaluate movement. Much like the idea of neural plasticity, where the human body can adapt to unexpected, obtrusive events, such as brain injury or loss of function in appendages, likely, we like to incorporate some artificial rendering of plasticity in RHex.

C.3.2) Present Unavailability

Indeed, RHex's adaptability to leg failure could be extrapolated to mechanisms of maneuver in unstructured environments, where one leg may have limited range of motion due to some obstacle in its path. Navigating in unstructured, unfamiliar terrains, where the unexpected occurs, [4] point out that

“Motion control is one of the most significant problems for emerging robotic applications dealing with locomotion in unstructured environments.”

In regards to research on fault-tolerable gaits, the fault being the breakdown of a leg, [5] performed studies on locked joint failure. While the concept of joints does not apply to RHex, the motivation for their study also provides insight on some of the gaps in the field. They quote:

"..the research on fault diagnosis and tolerance has been given little attention in the field of gait study for the past few decades."

Venturing further into the literature, we identified [2] (will be discussed in more detail in bibliography), a study on control of actuators in developing fault-tolerant motion. They too mention:

"The problem of fault recovery represents a vast, important domain in its own right that is still relatively unexplored in robotics.

[2] applied linear control theory, incorporating feedback and observers to control for motion when faulty events occur.

C.3.3) Desirability of Bioinspiration

Animal analogs have demonstrated uncanny ability to adapt to injuries and other sustained handicaps. [1] completed a study on how rats adapt to motor injuries after spinal cord injuries that compromise motion in one leg.

Indeed, mathematical models such as those presented by [2] provide a foundation for the implementation of certain desired capabilities. Ultimately, biology analogs contribute the most practical and applicable implementations, as they have already been so aptly used by animals like the rats studied in [1]. For instance, one of the observations is the following:

"First, in contrast with control animals, [injured rats demonstrated] ankle relative forward velocity peaked on the first third of the swing phase and decreased during the second third."

This provides insights on specific parameters to tune during the rotation of Rhex's legs. [((bibcite Collazos-Castro2006))] has authors with Scopus reported h-indexes of 4, 4, and 19, respectively. It was published in Journal of Neurotrama, with an ISI reported impact score of 4.255 and 5 year impact factor of 4.281, extending back to its 2006 publication date. It has been cited 12 types according to Scopus. Therefore, it is a quite credible biology source.

The Hypothesis

C.3.4) The Idea

Currently, RHex achieves stable gait with six functional legs through a Buehler Clock implementation, where there are two alternating tripod sets. As RHex begins to move, it is often the case that one leg loses complete range of motion, due to current overriding input or otherwise which compromises the stability in gait. The goal is to create functional, directed motion with minimal functionality (ie: when a leg or two is missing), adapting and expanding the Buehler Clock control so that it is no longer the simplified two tripod gait, but such that each leg operates on its own schedule. Modifying the control mechanisms for each leg, or set of legs is the next step towards this.

C.3.5) Refutability

We propose multiple design steps towards the ultimate goal of automated adaption to loss of a leg. First, we purposefully disable the use of one leg and test out parameters that drive stable forward motion. Next, we explore restorative gaits - we start RHex normally, with all legs, and then disable a leg halfway through, then implement some mechanism or algorithm to detect the failure and to compensate for it, recovering original function. The ultimate goal would be for RHex to operate normally, autonomously detect and recover from leg failure.

We propose several parameters to look at when evaluating the efficacy of our design protocol. We aim to achieve stable gait (stable center of mass, possibly recorded by an accelerometer), directed gait (position tracker, or ability to walk in straight path) and controlled gait (in terms of velocity, via Vicon, a motion capture system).

C.3.6) Necessary Means

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

1. an actuator to determine com
2. some tracking device to keep track of position
3. motion capture system
4. specific tuned parameter for controlling motion of each leg independently in the absence of one leg
5. mechanism to actively tune parameters when unexpected failure occurs

Annotated Bibliography

C.3.7) Major Source of Authority from the Robotics Literature

The paper [2] is an excellent example of recent research that addresses the problem that we hope to help solve. We have determined that this paper is a reliable source, since the third author, D. E. Koditschek, has an h-index of 21 according to Scopus. Also, all three authors are associated with the University of Pennsylvania. This paper has been cited twice, according to Google Scholar. The paper describes an approach to detecting the failure of a leg on the Rhex robot and adjusting the gait accordingly for the other five legs to allow it to continue moving. In this case, the robot attempts to regain stability by switching to a five-legged crawl gait.

The authors feel that neglecting this issue of recovering from disturbances would be a failure to take full advantage of the benefits that we gain from legged locomotion. They note that:

although the promise of redundancy against individual joint or limb failure ought to be one of the major advantages of legged mobility, with few exceptions [15–17] there is little legged robotics literature on gait adaptation in the face of compromised self-health.

This suggests that this capability is not only extremely useful, but is also "relatively unexplored"[2] as of the paper's publication in October of 2010.


The paper [2] cites 35 other papers. The two that we found to be the most important were [6] and [7].

The paper [6] more generally addresses the problem of generating and tuning gaits. We found this paper to be a reliable source because one of the authors, Daniel E. Koditschek, has an h-index of 21 according to Scopus. The authors here are associated with the University of Pennsylvania. This paper is an important precursor because the specific problem of designing gaits for a robot with a leg failure builds off the task of designing gaits in general. The paper [2] mentions this precursor in a discussion of previous investigations on adaptive legged locomotion.

The other close precursor, [7], discusses more specifically the problem of gait adaptation. We have found this paper to be reliable for the same reasons as the other close precursor. This one, however, has been cited 21 times according to Scopus. The paper goes into detail about a method of adapting gaits to new scenarios without hand tuning. This is extremely relevant to the [2] since a leg failure event necessitates quick adaptation.


The paper [2] has been cited twice according to Google Scholar. The closest successor here was [8]. This paper looks closely at how energy efficiency is affected by factors in the robots gait. This paper is extremely recent and has not been cited. We have determined that it is credible, however. One of the authors, Daniel E. Koditschek, has an h-index of 21 according to Scopus. The authors here are all associated with the University of Pennsylvania.

This and the other successor are not particularly relevant to our topic and do not reference the aspects of [2] that we are most interested in. They were the only two successors to choose from, which is the reason they are mentioned here.

C.3.8) Major Source of Authority from the Biology Literature

There have been several studies documenting the adaptability of animals to the loss of the use of a leg. These studies verifiably show us how an animal can adjust to a change in its physical structure and learn a new means of reasonably optimal locomotion within the constraints of the physical disability. It is this plasticity that we aim to replicate and explore with this experiment.

[9] tells us about the effects of varying degrees of paresis on the gaits of adult, male rats using pressure sensors to record gait measurements.

This paper is published in the Journal of Neuroscience Research which has an impact factor of 2.986 according to ISI Web of Knowledge Journal citation Reports which places it 104th out of 231 journals in the neuroscience category.

The paper tells us:

predictable data emerged such as decreased weight bearing in the affected limb(s) … compensatory changes in the gait cycle, particularly in forelimb dynamics were detected … documented longer stance time and shorter swing time of the right hindlimb during gait … Hindlimb paresis was accompanied by compensatory changes in forelimb movement as evidenced by shorter and more frequent forelimb strides … Such compensation emphasizes the dynamic interplay between forelimb and hindlimb function when the latter is markedly impaired.

Thus confirming that animals do alter their gait when injured.


[11] is a paper cited by this one. It is published in the Journal of Experimental Biology by a person affiliated with the Department of Organismic and Evolutionary Biology at Harvard University (was a Research Associate) and is now an Assistant Professor in the Dept. of Biological Sciences at Mount Holyoke College. This journal has an impact factor of 2.722 which ranks 19th out of 76 journals in the Biology category. The author Gary B. Gillis also has a scopus h index of 12. Thus the paper seems to be a credible source.


[10] is one of the papers citing this paper. It studies the effects of spinal injuries on the spatiotemporal awareness of dogs and thus the perturbations in their stride time, stance time, swing time, and stride length, and velocity. It was published in 2009, hence is a reasonably recent paper. The journal it comes from is the Journal of Neurotrauma which has an impact factor of 4.255 and ranks 50th out of 231 journals in the neuroscience category.


1. Collazos-Castro, J. E., López-Dolado, E., & Nieto-Sampedro, M. (2006). "Locomotor deficits and adaptive mechanisms after thoracic spinal cord contusion in the adult rat." Journal of Neurotrauma, 23(1), 1-17. Retrieved from www.scopus.com
2. Johnson, A.M., G.C. Haynes and D.E. Koditschek. "Disturbance Detection, Identification, and Recovery by Gait Transition in Legged Robots". 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems October 18-22, 2010, Taipei, Taiwan. pp. 5347-5353
3. Ijspeert, A. J. (2008). "Central pattern generators for locomotion control in animals and robots: A review". Neural Networks, 21(4), 642-653.
4. Sfakiotakis, M., & Tsakiris, D. P. (2007). "Neuromuscular control of reactive behaviors for undulatory robots". Neurocomputing, 70(10-12), 1907-1913.
5. Yang, J. -. (2005). "Gait synthesis for hexapod robots with a locked joint failure." Robotica, 23(6), 701-708. Retrieved from www.scopus.com
6. Weingarten, J. D., Groff, R. E., & Koditschek, D. E. “A framework for the coordination of legged robot gaits”. 2004 IEEE Conference on Robotics, Automation and Mechatronics. December 1, 2004. pp. 679-686.
7. Weingarten, J. D., Lopes, G. A. D., Buehler, M., Groff, R. E., & Koditschek, D. E. “Automated gait adaptation for legged robots”. 2004 IEEE International Conference on Robotics and Automation. April 26, 2004. New Orleans, LA. 2004(3) 2153-2158.
8. Haldun Komsuoglu, Anirudha Majumdar, Yasemin Ozkan Aydin, and Daniel E. Koditschek. “Characterization of Dynamic Behaviors in a Hexapod Robot”. International Symposium on Experimental Robotics, Delhi, India, December 2010.
9. Benjamin S. Boyd, Christian Puttlitz, Linda J. Noble-Haeusslein, Constance M. John, Alpa Trivedi, Kimberly S. Topp "Deviations in gait pattern in experimental models of hindlimb paresis shown by a novel pressure mapping system". Journal of Neuroscience Research, vol. 85 issue 10, pp. 2272-2283, August 2007.
10. Wanda J. Gordon-Evans, Richard B. Evans "Accuracy of Spatiotemporal Variables in Gait Analysis of Neurologic Dogs". Journal of Neurotrauma, vol. 26 issue 7, pp. 1055-1060, July 2009.
11. Gillis G.B., Biewener A.A. "Hindlimb muscle function in relation to speed and gait: In vivo patterns of strain and activation in a hip and knee extensor of the rat (Rattus norvegicus)". Journal of Experimental Biology, vol. 204 issue 15, pp. 2717-2731, Aug 2001.