This paper addresses the problem of sampling-based motion planning for a parallel robot called the Variable Topology Truss (VTT). VTTs have edge modules, each with an active prismatic joint and passive joint ends. The robot configuration is defined by the edge lengths and node joint assignments. Reconfiguration motions are of two types: geometrical (changing of edge lengths) and topological (changing node connectivity through Split and Merge actions). The main challenge is that the search space is much larger than the reachable space. This is because motions are subject to the following constraints: the VTT has to be rigid, its nodes must be of degree three for controllability, and 18 members are the minimum. The authors propose an extension of [12] where the search space is reduced by computing first the reachable C-Space for a single node and this space is decomposed into convex polygons. Here, the same method is used, but instead of dealing with a single node, pairs of nodes are considered to compute the reachable C-Space. This significantly accelerates the time to solve the problem in comparison to [12]. Also, the topology reconfiguration presented enables the algorithm to deal with harder problems. The problem addressed in this paper is relevant to the community, the approach presented is generally sound and the paper is well organized. The way the search space reduction is achieved is insightful, and although the extension to [12] only considers pairs of nodes the speedup achieved is significant. Moreover, the topology I recommend the authors to be more clear on the following aspects of their work: - In the introduction, make a clear list of contributions and, in particular, explicitly state the similitudes and differences with respect to [12]. - try to find a way to better present Figure 6. A close-up to the nodes in the middle could help, also explain better why they are different. - please improve section IV.B, it is currently a bit hard to parse. - in the experiments, emphasize better what is possible now with the topological reconfiguration presented that the approach in [12] was not able to handle. Also, please do a thorough proof read of the paper since there are several scattered typos.

The paper presents a method for motion planning for reconfigurable truss structures where nodes can connect and disconnect (this idea is interesting and related to RSS). Sampling based motion planning sampling and collision checking is defined in terms of the shape of the current truss to speed the algorithm. This is a great idea, however it was first presented in [18], the current paper extends this idea to multiple nodes, which is a fair contribution. Results are generated for simulated problems using OMPL. This shows proof of concept, but nothing more. The idea is relevant, the paper is easy to understand. The experiments that are performed are in simulation. This is not inherently bad, but given the ease of performing simulations, it is expected that the new approach should be both: (1) compared to the existing state of the art. (2) repeated trials performed and statistics presented. 1) There are many interesting ideas shown in the paper, but how they improve the state of the art is not well explained. Comparison to existing methods would improve the paper. For example showing how each of the improvements presented in the paper affects runtime and number of samples required for a solution, on average, for different problems. 2) Given that RRT uses randomness, it would have been nice to see how the proposed improvements affect the runtime by exploring tests for all combinations of: {naive, smart} x {collision checking, point sampling} and then values reported for the mean time and number of samples required to find a solution. Right now, there is no evidence that the algorithm can be expected to perform well in general, only that one or two problem instances exists for which the algorithms worked well one time. 3) Related work exists that was not cited: Komendera, Erik, and Nikolaus Correll. "Precise assembly of 3D truss structures using MLE-based error prediction and correction." The International Journal of Robotics Research 34.13 (2015): 1622-1644. More discussion of the difficulty of extending the methods of [18] to the current manuscript is also necessary to justify that the new manuscript is sufficiently novel with respect to the existing state of the art. For example, how is extending collision checking of a single node to multiple nodes challenging or how are special aspects of the problem leveraged to do this well? What breakthroughs were necessary to achieve this result?

The paper is extremely well written and it was very exciting to read about such great work when presented with as much clarity as in this paper. My major comments are related to section 6 (Test Scenarios): 1) If possible, could the authors address the problem of figuring out which nodes need to be moved (and how), if only the start and goal node configurations are known, without an accompanying one-to-one correspondence of start and goal for each node? In section 6.A the authors assume knowledge about the start and goal configuration of the 4 nodes that need to be moved. If instead they were given unlabeled start and goal configurations of the VTT, could their method be used to solve the planning problem? 2) What is the effect, on computational times and overall success rates, of randomly selecting the node groupings for geometry reconfiguration? For a reconfiguration problem that involves a sizable number of nodes, there can be a very large number of such groupings and randomly selecting could need a lot of time before a successful grouping is found. Other comments are mostly concerned with getting a better understanding of the test: 1) In Section 1 (and elsewhere), the authors point to prior work to say a VTT needs 18 members for topology reconfiguration. It would be helpful if they could provide intuition about why this is so in text or with a figure. 2) In Section 3, the concept of the state of every member A^v(q^v) was a little tricky to understand. Am I correct in understanding that given a q^v, you could have different sets of member states (lengths) that achieve the same q^v? I was thinking of A^v(q^v) as a vector of lengths of the edge members connected to node v. Is that so? 3) Minor typo in Section 4.A before equation (3) - inconsistency in notation between \mathcal{O} and \hat{\mathcal{O}}. 4) In the same section, when two nodes v^i and v^j are connected by an edge member, are their respective obstacle spaces still computed by ignoring the members of the other as Figure 6 suggests? How is the edge joining the two nodes handled in this case? 5) In Section 6.B, the authors present three invariants they try to maintain during path planning for a group of nodes. With regards to claim about the last two invariants being hard to compute, if the motions of the two nodes are known, could they not compute the volume swept by an edge member across those motions and check for intersections between comparable triangles in spacetime (comparable in terms of the initial and final times of the motion)? 6) In Section 5.A I did not understand the claim about each polygon in C^v_{obs} being connected to only two enclosed subspaces. 7) If I could suggest one major change (addition) to the paper, it would be that a pictorial representation of the graph from Section 5.B be included. I think this paper presents great work in a fantastic way and I strongly recommend this paper for acceptance.