Assignment #4

Provide a short discussion of each of the assigned papers (listed under Course Materials). Below are questions to think about (you should discuss at least some of these but you don't have to address them all):

RRT-Connect
Optional section: 4 (but try to understand what is being proved)

• Why don't we just use A* search?
• How is the simple one-directional RRT different (and preferable to) a "random walk" in the configuration space?
• What happens in this algorithm if a collision-free path does not exist?
• There is no explicit "heuristic" in this search, why does it work well (it does)?
• The authors mention "path smoothing", what is that and why is it important in this context?

Logic-Geometric Programming
The paper formulates Task and Motion Planning (TAMP) as optimizing a logic-geometric program in which geometric reasoning is encoded within the constraints of the program.

• Another approach in TAMP uses samplers to generate geometric parameters such as grasp poses, placement poses, and motion plans (e.g., using RRT). What are the advantages and disadvantages of optimization-based vs sampling-based methods?
• Briefly explain how the three levels of approximation in the solver (Section 4) interact with each other. What would happen if Level 1 was removed? Would it be possible to remove Level 3?
• How is the optimization objective defined In this paper? Do you think this is a natural way to specify goals for robots?

Diffusion Policy
(feel free to skim the results section and related work)
This paper presents a perspective on diffusion models as modeling the gradient of an energy function.
If you haven’t seen diffusion models before, you may want to review other introductions to them. I wrote up a nontechnical treatment here.

• Classic policies output a single action to take at each timestep. Diffusion policies, in contrast, output a sequence of actions to take (of length T_p), then take T_a actions along this sequence. What is the advantage of doing this? What are some disadvantages?
• The paper says that diffusion models can get around the problem of multi-modal predictions. This means they can handle the case where there are two good trajectories you can take, and they lead in different directions. How does a diffusion policy model both? How does it decide which to take?

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