Safe Hopping

Papers in progress based on Brian Howley's thesis and presentation materials:

• Safe Hopper draft 2 Jan 07 (16 pp)
• see BrianDefense? for materials from Brian Howley's defense.
• Should attach a .zip file of the latest version of the paper in tex format.

1. Text is generally good & clear.
2. It is too long. The IEEE and ASME transactions limits are ~10 pages.
3. We need to add some references to previous work on single-legged hoppers and the state of the analysis that exists for them regarding stability, etc. We also need a bit of introductory text to motivate single-legged hopping as a topic worth studying. Single-legged hoppers embody many of the stability and energy efficiency issues found in multi-legged locomotion, but with fewer degrees of freedom and a more tractable analysis. There is also the concept that animals with 2, 4, 6 or more legs follow a "template" (Full and Koditschek 1999) such as the spring-loaded inverted pendulum. Most of the needed references can be pulled from Chapter 2 of Brian's thesis. That is, we are studying the single legged hopper for the same reasons that Raibert, Koditschek Komsuoglu and Koditscheck, and Buehler, Ringrose, Berkelmeier, Cham, Mombauer (sp?) and others have studied it.
4. I think, in contrast, that the general dynamically stable legged robots review could be condensed a bit.
5. So maybe the extension to planar running gets put into a second paper... It could even be submitted at the same time as the first and could reference it extensively.

MattSpenko? - 02 Jan 2007: Comments on the 02Jan Draft.

A couple thoughts

Introduction Paragraph 5. So if the robot wins the game keeps going. If the environment wins the game is over. Perhaps that's obvious, but it might clarify things if you can state that you are essentially finding ways to keep the game going.

If you need more space you might be able to combine figures 1 and 2.

Hopper Dynamics, paragraph 4. I thought the extra notation on describing disturbances (d, theta_d) was extraneous.

Hopper Dynamics, paragraph 6. I was not very clear on why allowing u to vary between u_min and u_max caused thrashing, or exactly what thrashing is. Also in fig. 3 you state that liftoff takes place when either u = 0 or u_max, but in the text it is either u_min or u_max.

Hopper Safety and Control Synthesis Approach, intro and section A. I have to admit I got pretty lost during this section, but I may just need to re-read it a few times. However, I was wondering if this section was really necessary. Obviously it is critical in the sense that it describes the approach that you are taking, but it seems to me that it is mostly a restatement of Tomlin's paper. Would it be possible to just refer to her work and leave it up to the interested reader?

Figure 6. Obviously there is a lot of information here, but it took me a while to really understand it. I thought of a couple of things that might make it easier to understand. 1) is there any way to shade in the descent, ascent, and contact areas? 2) You refer to different symbols in the text. for example you refer to the star. I wasn't exactly clear if this was the five point or six point star. One possibility is that you change it to read A) max leg compress -> star, so that you have a letter that you can refer to in the text (A), a description of the point, and then an arrow that points to the star. Also is it possible to remove any of the symbols that aren't referred to in the text?

Figure 9. I would change the y-axis to read "Ruggedness" or "Ruggedness - Step Height." I had to reread the paper a bit to figure that out. You could also cut one of the subplots and go with three across. I think that three would still show the trends and the format would fit nicely into a double column width. The thrust values of 2,3,and 4 are more clear to me than 1, which I find confusing since things are so close together. Also, how does the figure look with all of the y-axes with the same values. It would emphasize the fact that ruggedness increases with increasing u_max.

Ruggedness, paragraph 6. In mobile robotics, I have found that a "hole" is commonly referred to as a "negative obstacle" and most people refer to ditches, holes, etc as obstacles so I was a little confused when you refer to the "step-down" as compression limited and the step-up as obstacle limited. I think of them both as obstacles. A minor point, but it might be easier to just refer to them as step-up and step-down limit curves.

In agreement with Mark, I would cut section 6. You could possibly just add a short paragraph of it in future work or even a second paper (would that make three papers?).

Mark, thanks for comments. Agree text is too long - wasn't aware of page limits till you pointed them out. Also agree that planar running can be sacraficed - I thought I'd add that at the last minute but its bigger than I wanted.