C.2 Source Annotation

Gait Transitions

Motivation to Develop Gait Transitions in Robots

Among wild animals, the diversity of terrains and environments has promoted, by means of evolution, development in animals of myriad behaviors which help the animals survive and, ideally, thrive in such environments. Among the many capabilities of animals, their ability to locomote is of paramount importance, as it enables them to flee predators, chase prey, find water or shelter, and to otherwise interact with their surroundings. While a robot in the same environment as an animal does not necessarily have to avoid predators or find resources the same way that an animal does, a robot's efficacy in a particular environment is frequently judged based upon its ability to match (and ideally, supersede) an animal's ability to locomote in the same environment.

In the wild, a single animal will frequently make use of several modes of locomotion. For example, a squirrel must be able to both run, climb, and jump. While running may be called a single behavior, a squirrel will likely change its posture, leg speed, limb orientation, etc. based upon whether it is running over a tree branch, flat grass, sloped grass, flat dirt, sloped dirt, etc. Handling such diversity of challenges is not unique to squirrels but instead is virtually a prerequisite for navigating any complex environment. In recent years, roboticists have made a push toward using robots in real-world environments rather than simply in a laboratory, and there has been a corresponding push in developing a repertoire of behaviors which enables the effective traversal of such terrains. However, the ability to change between behaviors (or even detecting that there must be a change and then selecting a new behavior to activate) is one which still needs attention. While some robots have implemented several modes of locomotion, such as the RiSE platform which can both walk on flat ground and climb vertical surfaces, transitioning between these modes frequently requires user input or else is done in a way which does not even come close to real-world unpredictability.

Having the ability to juxtapose robots and animals lends itself to creativity but also to comparison. While creativity has lead roboticists to new ways to mimic animal locomotion, comparison makes clear the fact that robots have not reached the locomotive capacity of animals. The ability to transition between different gaits represents a step towards allowing robots to handle unpredictable, rapidly changing environments autonomously and without human intervention so as to more accurately capture in an artifact of engineering the designs crafted by evolution.

Applications of Gait Transitions

A robot which is able to transition effectively between modes of locomotion could have endless applications. The morphology of a particular platform obviously restricts its capabilities (there is no panacea for the problem of robot locomotion), though a single platform capable of effecting changes in its own locomotion patterns could certainly see real-world use. One possibility in this domain is using robots as transport vehicles for the military. At present, there is a great need to transport supplies efficiently over long distances which are frequently spread across barren, desert areas. A robot capable of traversing rocky and broken terrain, sandy terrain, hills, and mountains could be used to fulfill such transport needs of the military. Walking on rocky, uneven terrain requires a walking or running gait which can handle obstacles while remaining stable. Moving over sandy terrain presents a different set of challenges as granular media can behave like fluids or solids, thus requiring a different set of behaviors apt to handle forces behaving in this manner. Hill-climbing requires a further set of behaviors which move efficiently over rocky or sandy slopes while still maintaining stability to prevent rolling over. Traversing mountainous areas can, in addition to requiring a very robust walking or running gait, require a robot to climb. Climbing Further complicates the task of transport as the robot must have a means of adhering to a surface in addition to moving over it efficiently. The addition of external weather forces such as rain or wind further complicate all of these tasks. If such a robot were to be of any use doing all of these things, it would need to be able to not only do all of them effectively, but to transition between them effectively. Notwithstanding the design challenges presented by this proposed military application, there remains the problem of switching between these behaviors effectively.

While gait transitions are certainly a subtle problem, they remain an important one for applications such as the aforementioned one. A transition from running to climbing must be smooth and stable; a stumbling robot making such a transition could fall over backwards and damage itself. A bad transition from running on rocky ground to running on sand will cause the robot to waste energy and sink into the sand, causing it to potentially be stuck. If a robot must leap to clear a short chasm, it must do so effectively for a single leg which moves at the improper time could easily cause the robot to fail to reach its target. Transitions between gaits are a potential source of failure and must therefore be treated with care.

Capabilities of Existing Technology

Returning to [1] from C.1, we see that the authors discuss three separate approaches to biologically-inspired animal locomotion. The first of these methods is one in which there is not a suite of previously tuned behaviors which the robot changes between, but rather is just a means of having the robot move by reacting to its environment:

Biologists reverse-engineered the neuronal bases of locomotion,while their applied counterparts created robots that used networks of simple reflexes and coordination schemes to locomote. These policies result in networks of simple computational elements from which gait-like behaviors emerge. There is no concept of “changing between gaits”, as all motions are produced by the reactive policies.

The second approach mentioned is the opposite of the above approach and instead seeks to plan exactly the time at and manner in which each foot strikes the ground:

The opposite approach has been deliberate and careful planning of every footfall a robot makes. These methods require very accurate sensor information, accurate modeling of the constraints related to locomotion, and computational power to perform the planning, all of which are difficult to achieve on a mobile platform.

The third approach, which is the one undertaken by the authors of this paper, instead exists at some point in between the two aforementioned methods. This methods seeks to develop several different gaits and then switch between them at runtime based on the environment the robot is in:

An alternative approach is to explicitly store individual gaits, each designed for a specific purpose. In the absence of sensor information, intuitive feedforward motion patterns can be rapidly developed and are often quite successful at various tasks… With a large set of possible gaits, the challenging task becomes understanding how to transition between them, while still adhering to the basic principals of legged locomotion.

Thus we see that the present state of technology in robotic gait transitions has not yet even settled down to a single approach, but rather appears to still be probing a continuum of strategies which range from locomoting by planning every footfall to locomoting only by responding to the surrounding environment.

If we assume that the authors believe their approach to be best (which should be a reasonable assumption), we see that there is still plenty of work to be done. In their conclusion, they write:

Future directions for this research branch out in a variety of ways. Our newfound understanding of gaits is allowing us to consider a continuum of gaits, rather than isolated gaits. Using this continuous representation, we intend to apply control by evolving a gait over time, performing local feedback by moving throughout a local neighborhood of gaits. We are also interested in techniques of leg coordination, to encode gaits and gait transitions in a continuous framework. Lastly, we intend to study the potential of applying this work to quadrapedal robots, in addition to continuing our work with hexapods.

This indicates that while roboticists have already begun chipping away at the problem of making appropriate gait transitions in legged robotic platforms, past work has largely been incremental, focusing on a small set of gaits on one or two robotic platforms. This paper lays out clearly the need for effective gait transitions in robots and shows that there is still plenty of work to be done.

Potential Biological Solutions

Using [2], we can return to biologically-inspired literature. The very first sentence of the abstract of this paper highlights some of the controversy regarding exactly why it is that horses change gaits when they do:

Two studies have focused on potential triggers for the trot-gallop transition in the horse. One study concluded that the transition was triggered by metabolic economy. The second study found that it was not metabolic factors but, rather, peak musculoskeletal forces that determine gait transition speeds.

The authors of this paper seek to resolve this controversy by devising an experiment of their own. Theory suggests that the ground reaction forces seen by moving horses should be constant whether the horse is moving on an incline or on flat ground. Thus the experimenters here ran horses on flat ground and on a 10% incline in order to observe the speed at which they changed gaits from a trot to a gallop. If the horses changed gaits at the same speeds, then it appears that ground reaction forces are the cause for gait transitions because the ground reaction forces were (assumed to be) constant in both instances. Alternatively, if the horses in this experiment change gaits at different speeds, their cause for changing would appear to be metabolic economy because running on an incline requires more energy. The authors of this paper found that horses changed from a trot gait to a gallop gait at significantly lower speeds on the incline, thus suggesting that metabolic economy is in fact the deciding factor in determining when to change gaits.

While this paper supports the theory that "metabolic economy" is the cause of gait transitions, this paper does not appear to single-handedly bring this disagreement to an end. Further, even if this paper's hypothesis is correct for horses, it is not necessarily so for the rest of the animal kingdom; thus there may be two options for robots to determine when and why to change gaits.

The first mentioned cause for gait transitions is metabolic economy; frequently, the appropriate robotic analogue for metabolism is battery power. Thus metabolic economy may be incorporated in robotics by always using the most efficient gait. This requires real-time measurements of power consumption, which require a fairly modest level of computational and sensing power. One advantage of this method is that power measurements are relatively easy to incorporate into robotic systems (as there is often circuitry that monitors battery activity). One disadvantage is that this method will only provide a centralized notion of what the robot is doing and does not necessarily provide the user with any knowledge of the leg-by-leg performance of the robot.

The second mentioned cause for gait transitions is musculoskeletal forces. This idea may not have a direct analogue in the world of robots, though a reasonable approximation could be ground reaction forces per leg. One immediate disadvantage of doing this is that there is significant sensing and computational power required to find the force on each leg of a robot. One clear advantage of this method is that the user has a much clearer idea of what each leg is doing as these computations are doing.

Value of Sources

One paper from the robotics literature that seemed very promising was [3]. I interpreted the title, perhaps naively, as representing a robot which could adapt to its environment by transitioning gaits. This paper is from a reputable, IEEE sponsored conference with credible authors, so it is undoubtedly a valuable paper. However, this paper is concerned with creating gaits for robots rather than the methods by which robots transition gaits. This paper is somewhat relevant in that for gait transitions to be necessary, there must be gaits to transition between, though this paper turned out to not be directly relevant.

Another paper from the robotics literature that seemed valuable at first glance is [12]. This paper discusses transitioning from walking to climbing in a robot by mimicking the method of doing so employed by geckos. This represents a very clear instance of biologically-inspired robotics and presents an approach very different from [1]. However, in reading the abstract of this paper, I found that their results were exclusively simulation-based. While simulations are certainly valuable, I opted not to use this paper on the basis that the authors had not actually proven that their bio-inspired methods had any value to robots roaming the real world.

A third paper from the robotics literature that I was initially considering using is [13]. The abstract of this paper mentions that future robots are expected to navigate rough terrain as well as potentially hazardous environments. The abstract goes on to discuss the fact that stability of locomotion is key to these robots' success and that the stability of gait transitions is of particular importance. This paper seemed very fitting for this assignment, though in looking at the authors' credentials, I found that they were BSE students at a University. While having one undergraduate on a paper is not abnormal, all three of these authors were BSE students; as a result, I felt inclined to look elsewhere for other sources as the credentials of these authors were just not strong enough to warrant this paper's use.

Open Problems

Open Problems in Robotics

In [1], the authors begin with a discussion of various methods making robots locomote. In discussing the various methods for doing this, the authors mention their approach, saying:

[our]approach is to explicitly store individual gaits, each designed for a specific purpose. In the absence of sensor information, intuitive feedforward motion patterns can be rapidly developed and are often quite successful at various tasks.

Immediately, it seems that the authors of this paper can turn to biology to understand how animals incorporate sensory feedback when the transition gaits figure out what feedback animals use (i.e., visual cues such as seeing a terrain change, forces per leg while using a particular gait, energy use of a gait, etc.) and how certain data which are fed back are then used to decide when to switch gaits and what gait to switch to. In the conclusion of this paper, the authors appear to be thinking along these lines when they remark that:

Our newfound understanding of gaits is allowing us to consider a continuum of gaits, rather than isolated gaits. Using this continuous representation, we intend to apply control by evolving a gait over time, performing local feedback by moving throughout a local neighborhood of gaits.

This draws on bio-inspiration in that it incorporates feedback into the controller responsible for changing gaits, just as animals do, and also in that the authors intend to consider gaits as a continuum, a consideration for which there is evidence in biology [7]. In addition, this notion of considering more gaits is another open problem; these authors consider two types of gaits on the RHex platform, and three families of gaits on the RiSE platform. An open problem which supports the authors' notion of a continuum of gaits is to consider a wider range of gaits on these platforms in order to better match the continuum of gaits that the authors of this paper derive from biological inspiration. Yet another open problem is adapting these strategies for gait transitions to other platforms. The authors appear, too, to be thinking along these lines when they close their paper by saying:

[l]astly, we intend to study the potential of applying this work to quadrapedal robots.

This presents an open problem which is perfect for bio-inspiration as there is a great deal of biological research into how quadrupeds locomote and change gaits [7], [2], [8], [10].

Open Problems in Biology

In the discussion section of [2], the authors reiterate that in the past, there have been several studies into whether horses change gaits based upon musculoskeletal forces they experience, or based upon metabolic economy. This study concludes that horses change gaits based upon metabolic economy; this is in direct conflict with a previous study, as the authors say:

[t]he discrepancy between the present study and Farley and Taylor's is puzzling … [t]hese small differences [omitted for brevity; see citation below for full quote] in our methods were ones we could identify, but it seems unlikely that they can account for the very different results.

Thus the authors seem to suggest that the very subject of this paper, the trot-gallop transition in horses, is still an open problem in biology as they do not attempt to draw any absolute conclusions. Within the realm of gait changes, there is still question as to whether gait transitions from faster to slower gaits are caused by different factors than gait transitions from slower to faster gaits, as evidenced in the discussion:

different triggers may be required to explain the transition from trotting to galloping when speed is increasing and the transition from galloping to trotting when speed is decreasing

Thus we see that there are several open problems. On top of reconciling past data and determining exactly what causes gait transitions, extending this research to a wider range of speeds is also an open problem. These problems (and their solutions) will likely be of interest to roboticists as these problems may present new, undiscovered methods of changing gaits which could be used in robots to further facilitate efficient locomotion in robotics.

Annotated Bibliography

Robotics Paper

For a discussion of the relevance and quality of [1], please refer back to my Communications 1 assignment.

In [1], the authors present gait transitions in two hexapedal, biologically-inspired robotic platforms, RHex and RiSE. Their approach to the problem of gait transitions is to endow their robots with specific gaits which are tuned for performing a single type of locomotion (i.e., stair climbing, climbing a wall sideways, etc.) and then switching between these discrete gaits based upon the requirements of the environment. The authors explore a walk-to-stair climbing gait transition in RHex and transitions among tripod, tetrapod, and pentapod gaits in RiSE.

Predecessor Literature

The authors of this paper cite [5] several times throughout their paper. Google Scholar shows that this paper has been cited 64 times. There are a few papers cited by my seed paper which have more citations, though I feel that the subject of this paper is more relevant than other papers with more citations. This paper is relevant because it explores the stair climbing behavior in RHex, which is a key part of [1]. In [1], the authors experiment with gait transitions between walking and stair climbing with RHex, creating a clear context for [1] because we are able to see how gaits were developed for RHex and how the need for gait transitions was addressed thereafter.

My second predecessor paper is [11]. This paper has 94 citations in Google Scholar and presents a different approach to locomotion than the authors of this paper use and is from the year before my seed paper, meaning that this paper gives a good sense of the state of robot locomotion leading up to my seed paper. This paper is relevant to [1], despite using a different technique on a different platform, because it represents that [1] came at a time when changing locomotion patterns in response to the robot's environment was an important topic across a wide array of platforms.

Note on Predecessor Source Selection

While the assignment asks us to examine the papers cited by our "seed" paper which themselves have the most citations, I talked to Doug McGee about the papers I wanted to use and he pointed out that they were fairly old papers and may not represent the state of the art at the time of my seed paper or allow me to put my seed paper into the appropriate context. Taking that into account, I revised my choices to instead use the sources above.

In addition, while the previous assignment wanted papers which were 5 or fewer years old, that was not necessarily possible for this part of this assignment; as my "seed" paper is from 2006 sources which it cites will reasonably more than 5 years old.

Successor Literature

My first successor paper is [15]. Google Scholar shows that this paper came out in 2008, but already has 38 citations, making it the most cited successor paper to [1]. This paper is relevant because it further explores locomotion on the robotic RiSE platform and mentions in particular (in its abstract) that the authors are considering locomotion on both flat ground and on a vertical surface. This paper is a very good successor paper as it further expands the gait transitions of the RiSE robot beyond those discussed in [1].

My second successor paper is [14]. This paper was released only 4 months ago, so it does not yet have any citations. However, it is a good successor paper because it considers gait transitions in ways beyond those explored in [1]; in particular, [14] considers a platform which can switch between both legged and wheeled methods of locomotion. Within the legged capabilities of their platform, the authors discuss a means of minimizing energy use, which is also related to earlier biology research. I feel that this is a good successor paper because it presents a robot which can not only transition among legged gaits, but which can also change its means of locomotion entirely.

Biology Paper

For a discussion of the relevance and quality of [2], please refer back to my Communications 1 assignment.

In [2], the authors are concerned with what causes horses to transition from a trot gait to a gallop gait; they focus on whether the impetus for change lies in the musculoskeletal forces experienced by the horse, or whether it is the result of metabolic considerations. This study runs horses in two environments which have the same musculoskeletal forces, but different metabolic factors and concludes that gait transitions are the result of metabolic efficiency. This conflicts with earlier studies on the same matter; the authors admit to being puzzled by this discrepancy in the discussion section, meaning that there is potential for further study in this matter.

Predecessor Literature

My first predecessor paper is [6]. This paper is shown by Google Scholar to have 38 citations, meaning it has the second most among predecessors to [7]. This paper is relevant to [7] because it considers mechanical and metabolic details of gaits in ostriches, which are bipeds, while [7] studies the same aspects of gaits but instead on horses, which are quadrupeds.

My second predecessor paper is [9]. This paper is shown by Google Scholar to have 64 citations, the most among predecessors to [1]. This paper is relevant to [7] because it seeks use math and physics to model dynamic legged motion. [7] considers a similar approach, though focuses exclusively upon horses in their modeling.

Successor Literature

The first successor paper I have chosen is [8]. While this paper is very recent and is listed by Google Scholar as have no citations, I believe that the venue of this paper makes it worthwhile. ISI Web of Science tracks 129 zoology journals and puts the venue of this paper, the Journal of Zoology, at 34th out of 129 (when ranked by impact factor), with an impact factor of 1.545. In addition, the Journal of Zoology ranks 8th out of 129 zoology journals when ranked based upon total citations, meaning that this paper is likely to garner more citations as time passes. This paper relates the [7] because this paper explores which parameters control the gait of alpacas and seeks to understand why alpacas trot and pace. This paper is relevant because it seeks to model biological gaits like [7], though does so in an animal that appears to be thus far un(der)explored.

The second successor I have chosen is [10]. While this paper has only one citation on Google Scholar, I believe that this is due to its relative youth. The venue for this paper is the Journal of the Royal Society Interface, which is somewhat new, though the stated aim of this journal is

promoting research at the interface between the physical and life sciences

which is very relevant here. This paper is relevant because it further explores horse gaits by considering what initiates the transition to the transverse gallop in horses. This paper also considers what initiates the transition to the rotary gallop in cheetahs. This paper builds on [7] because it further considers horse gaits, though also explores cheetah gaits and puts an emphasis on why gait transitions take place in each animal.

1. G. Clark Haynes and Alfred A. Rizzi, "Gaits and Gait Transitions for Legged Robots", Proceedings of the 2006 IEEE International Conference on Robotics and Automation
2. Wickler SJ, Hoyt DF, Cogger EA, Myers G., "The energetics of the trot-gallop transition", Journal of Experimental Biology, May 2003
3. Joel D. Weingarten, Gabriel A. D. Lopes, Martin Buehler, Richard E. Groff, Daniel E. Koditschek,
"Automated Gait Adaptation for Legged Robots", IEEE International Conference on Robotics Automation (ICRA), April 2004
4. Ohung Kwon and Jong Hyeon Park, "Gait Transitions for Walking and Running of Biped Robots", IEEE International Conference on Robotics Automation (ICRA), September 2003
5. Moore, E.Z.; Campbell, D.; Grimminger, F.; Buehler, M., "Reliable stair climbing in the simple hexapod 'RHex'", IEEE International Conference on Robotics and Automation (ICRA), May 2002
6. Jonas Rubenson, Denham B Heliams, David G Lloyd, and Paul A Fournier, "Gait selection in the ostrich: mechanical and metabolic characteristics of walking and running with and without an aerial phase", Proceedings of the Royal Society B, May 2004
7. Robilliard JJ, Pfau T, Wilson AM., "Gait characterisation and classification in horses", Journal of Experimental Biology, January 2007
8. T. Pfau, E. Hinton, C. Whitehead, A. Wiktorowicz-Conroy, J. R. Hutchinson, "Temporal gait parameters in the alpaca and the evolution of pacing and trotting locomotion in the Camelidae", The Journal of Zoology, January 2011
9. Philip Holmes, Robert J. Full, Daniel E. Koditschek, John Guckenheimer, "The Dynamics of Legged Locomotion: Models, Analyses, and Challenges", Society for Industrial and Applied Mathematics, May 2006
10. John E.A. Bertram and Anne Gutmann, "Motions of the running horse and cheetah revisited: fundamental mechanics of the transverse and rotary gallop", Journal of the Royal Society Interface, June 2009
11. Chestnutt, J., Lau, M., Cheung, G., Kuffner, J., Hodgins, J., Kanade, T., "Footstep Planning for the Honda ASIMO Humanoid", Proceedings of the 2005 IEEE International Conference on Robotics and Automation (ICRA), April 2005
12. Wang Jing, Liu Ying, Li Xiaohu, Meng Cai, "Gait planning of the gecko-like robot transition to wall", Proceedings of the 2010 International Conference on Electrical and Control Engineering, June 2010
13. Masakado, Seiji, Ishii, Takayuki, Ishii, Kazuo, "A gait-transition method for a quadruped walking robot", Proceedings of the 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), July 2005
14. Tokuji Okada, Wagner Tanaka Botelho, Toshimi Shimizu, "Motion Analysis with Experimental Verification of the Hybrid Robot PEOPLER-II for Reversible Switch between Walk and Roll on Demand", The International Journal of Robotics Research, August 2010
15. M. J. Spenko, G. C. Haynes, J. A. Saunders, M. R. Cutkosky, A. A. Rizzi, R. J. Full, D. E. Koditschek, "Biologically inspired climbing with a hexapedal robot", Journal of Field Robotics, May 2008