COSMOS project web site (still under construction)

]]>The CS LLC is an immersive educational experience aiming to enhance the recruitment and retention of women in CS. Students in the CS LLC live together as a community associated with Douglass Residential College(DRC). To our knowledge, it is the first living-learning community devoted exclusively to women in computer science.

]]>II-EN: Collaborative Research: Enhancing the Parasol Experimental Testbed for Sustainable Computing

Amount: $729,725

Joint with Ohio State (Co-PI: Stewart) and Stony Brook (Co-PIs: Gandhi and Liu)

Overview: The datacenters that are increasingly servicing our computing needs consume a vast amount of energy. Thus, the energy efficiency, energy-related costs, and overall sustainability of datacenters are critical concerns that are garnering considerable amount of research. Unfortunately, much of this research has been significantly hampered by the lack of an experimental testbed that is instrumented and isolated. The Parasol “green” micro-datacenter was designed and built to address this gap, and has served as an effective instrument to support research involving power/energy, cooling, and their coordination with and impact on resource management, scheduling, and system/application performance and dependability.

This project proposes to update and enhance Parasol’s infrastructure and computing systems as well as its software stack to make it an even more effective vehicle for research on sustainable computing. Specifically, we plan to populate the enhanced testbed, called Parasol-II, with current and next generation processor technologies, improve network connectivity and integrate software-defined networking (SDN) capabilities, increase solar energy generation capacity, add a low emission fuel cell power source, increase and diversify energy storage capacity, and improve the free-cooling system, as well as expand its capacity to meet the increased power consumption of the updated IT equipment. These enhancements are driven by the requirements of the research outlined in this proposal. At the same time, we will update and enhance Parasol’s current software stack for monitoring, programmatic control, and remote access. This will allow Parasol-II to be used by a significantly expanded set of researchers from Rutgers, Ohio State, and Stony Brook.

]]>Probabilistic roadmap planners utilize an offline phase to build up information about the configuration space (C-space) and solve many practical motion planning problems. Traditionally, many of these planners focus on feasibility and may return paths of low quality; considerably different from the optimal ones, where path quality can be measured in terms of length, clearance, or smoothness. Smoothing can be used to improve some of these measures and algorithms exist that produce roadmaps with paths that are deformable to optimal ones. Hybridization graphs combine multiple solutions into a higher quality one that uses the best portions of each input path. These techniques, however, can be expensive for the online resolution of a query, especially when multiple queries must be answered.

Alternatively, it is possible to construct larger, denser roadmaps that better sample the C-space by investing more preprocessing time. For instance, a planner that attempts to connect a new sample to every existing node in the roadmap will eventually provide optimal solutions, a property known as asymptotic optimality. Asymptotically optimal planners tend to work well in practice; however, current analysis only allows optimality guarantees in an asymptotic fashion. Since algorithms are terminated in finite time in practice, bounds on path quality after finite execution time is desirable. By leveraging probability theory, asymptotically optimal algorithms can be shown to be probably near-optimal in finite time. This guarantees that returned paths will be within a bound of optimal with a certain probability. In addition, path length can be estimated given the number of iterations an algorithm has been run. The following figure illustrates the predicted path length in orange, and 1000 paths extracted from a sampling-based planner.

While roadmaps with this property are desirable for their high path quality, their large size can be problematic. Large roadmaps impose significant costs during construction, storage, transmission and online query resolution, so they may not be feasible for some applications. The recently proposed k-PRM* algorithm minimizes the number of neighbors each new sample has to be connected to while still providing asymptotic optimality. Even so, the density of roadmaps produced by k-PRM* can be very high, resulting in slow online query resolution times, as shown in the following figure.

This project shows that a viable alternative is to compute roadmaps with asymptotically near-optimal guarantees. By relaxing the optimality guarantees, it is possible to construct roadmaps that are sparser, faster to build, and can answer queries more quickly while providing solution paths with near-optimal guarantees. Additionally, these roadmaps tend to return a solution in the same homotopic class as the optimum one, so smoothing brings path quality even closer to optimal in practice. These techniques are general enough to use on roadmaps in any configuration space such as the various robots and environments in SE(3) shown in the following image.

The Sequential Roadmap Spanner (SRS) technique uses the concept of graph spanners to provide smaller roadmaps with asymptotically near optimal solutions. Graph spanners are subgraphs which uphold the property that all paths through the spanner between two nodes of the graph are no longer than t times the length in the original graph, where t is called the ‘stretch factor’ of the spanner. The algorithm first runs an asymptotically optimal planner such as k-PRM* and then applies the spanner property to the resulting graph.

Computing the entire roadmap from k-PRM* can be very expensive in terms of memory, so this technique attempts to apply the spanner property during the construction of the roadmap. The Incremental Roadmap Spanner (IRS) technique applies a filter to the edges which would normally be added by k-PRM* by checking if the edge is required to uphold the spanner property for traveling from newly sampled configurations to the local neighborhood of the sample. The following image shows a result from this technique. A roadmap with 150 vertices and 2406 edges is reduced to 465 edges while preserving homotopy and adding only 7.3% to the mean path length over all shortest paths.

The SRS and IRS techniques use the results of graph spanners directly, and as such, they share a property with graph spanners, that is, that each node which would be added by k-PRM* is also added to the resulting roadmap. The SPArse Roadmap Spanner (SPARS) technique focuses on providing asymptotic near optimality while reducing the number of nodes added to the roadmap. The results are very sparse structures which not only maintain asymptotic near optimality as a property, but in practice return paths with very small amounts of degradation when compared to k-PRM*.

A Roadmap Spanner in an SE(3) environment constructed from the SPARS2 algorithm.

The method provides upper bounds on the length of paths through the resulting structure compared to the solutions returned by k-PRM*: returned_path_length = t*optimum_path_length + 3*D, where t and D are parameters of the algorithm. Furthermore, our analysis shows that the probability of adding nodes to the resulting data structure goes to zero as the iterations of the algorithms increase. This suggests that these structures may asymptotically converge to a finite-size while still providing solutions within a hard bound of optimal.

Path quality in both SE(2) and SE(3), along with number of answered queries (in SE(2)).

Experimental results show that the actual cost of paths returned by the resulting roadmap spanner is much smaller than the theoretical bounds drawn. Furthermore, choosing large values of t does not degrade paths returned by the framework dramatically. An interesting result indicates that at least in certain environments, the roadmap spanner framework is able to answer more queries than k-PRM* early in the execution of the algorithms.

Memory requirements of the approaches (offline and online) as well as termination condition tracking.

The memory usage for the roadmap spanner techniques during the preprocessing step is orders of magnitude smaller than k-PRM*. The resulting roadmap spanners vary on size depending on the specific algorithm used. The SPARS algorithm has a path quality/memory tradeoff compared to the SPARS2 variant. As shown, the SPARS2 algorithm uses less memory during offline pre-processing; however, the resulting roadmap which is used for online query resolution is generally much larger. Furthermore, the framework provides an automated stopping criterion, which checks the maximum number of consecutive failures. As the algorithms run, the maximum number of consecutive failures increases over time. This suggests that setting a threshold for maximum failures is a sufficient stopping criterion.

- Dobson, A., Bekris K E., Finite-Time Near-Optimality Properties of Sampling-Based Motion Planners. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2013, Tokyo Big Site, Japan.
- Dobson, A., Bekris K E., Improving Sparse Roadmap Spanners. International Conference on Robotics and Automation (ICRA) 2013, Karslruhe, Germany.
- Dobson, A., Krontiris, A., Bekris K E., Sparse Roadmap Spanners. Workshop on the Algorithmic Foundations of Robotics (WAFR) 2012, MIT, Cambridge, Massachusetts, USA.
- Marble, J., Bekris K E., Asymptotically Near-Optimal Planning with Probabilistic Roadmap Spanners. IEEE Transactions on Robotics (TRO) 2013.
- Marble, J., Bekris K E., Asymptotically Near-Optimal is Good Enough for Motion Planning. International Symposium on Robotics Research (ISRR) 2011, Flagstaff, Arizona, USA.
- Marble, J., Bekris K E., Computing Spanners of Asymptotically Optimal Probabilistic Roadmaps. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2011, San Francisco, California, USA.

This work has been supported by NSF CNS 0932423. Any opinions and findings expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsor.

- Andrew Dobson
- James Marble
- Kostas Bekris

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