A novel path planning proposal based on the combination of deterministic sampling and harmonic functions

The sampling-based approach is currently the most successful and yet more promising approach to path planning problems. Sampling-based methods are demonstrated to be probabilistic complete, being their performance reliant on the generation of samples. To obtain a good set of samples, this paper proposes a new sampling paradigm based on deterministic sampling paradigm based on a deterministic sampling sequence guided by an harmonic potential function computed on a hierarchical cell decomposition of C-space. In the proposed method, known as Kautham sampler, samples are not isolated configurations but parts of a whole. As samples are generated they are dynamically grouped into cells that capture the C-space structure. This allows the use of harmonic functions to share information and guide further sampling towards more promising regions of C-space. Finally, using the samples obtained, a roadmap is easily built taking advantage of the known neighbourhood relationships

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

PRM-RL: Long-range Robotic Navigation Tasks by Combining Reinforcement Learning and Sampling-based Planning

We present PRM-RL, a hierarchical method for long-range navigation task completion that combines sampling based path planning with reinforcement learning (RL). The RL agents learn short-range, point-to-point navigation policies that capture robot dynamics and task constraints without knowledge of the large-scale topology. Next, the sampling-based planners provide roadmaps which connect robot configurations that can be successfully navigated by the RL agent. The same RL agents are used to control the robot under the direction of the planning, enabling long-range navigation. We use the Probabilistic Roadmaps (PRMs) for the sampling-based planner. The RL agents are constructed using feature-based and deep neural net policies in continuous state and action spaces. We evaluate PRM-RL, both in simulation and on-robot, on two navigation tasks with non-trivial robot dynamics: end-to-end differential drive indoor navigation in office environments, and aerial cargo delivery in urban environments with load displacement constraints. Our results show improvement in task completion over both RL agents on their own and traditional sampling-based planners. In the indoor navigation task, PRM-RL successfully completes up to 215 m long trajectories under noisy sensor conditions, and the aerial cargo delivery completes flights over 1000 m without violating the task constraints in an environment 63 million times larger than used in training.Comment: 9 pages, 7 figure

The Critical Radius in Sampling-based Motion Planning

We develop a new analysis of sampling-based motion planning in Euclidean space with uniform random sampling, which significantly improves upon the celebrated result of Karaman and Frazzoli (2011) and subsequent work. Particularly, we prove the existence of a critical connection radius proportional to ${\Theta(n^{-1/d})}$ for $n$ samples and ${d}$ dimensions: Below this value the planner is guaranteed to fail (similarly shown by the aforementioned work, ibid.). More importantly, for larger radius values the planner is asymptotically (near-)optimal. Furthermore, our analysis yields an explicit lower bound of ${1-O( n^{-1})}$ on the probability of success. A practical implication of our work is that asymptotic (near-)optimality is achieved when each sample is connected to only ${\Theta(1)}$ neighbors. This is in stark contrast to previous work which requires ${\Theta(\log n)}$ connections, that are induced by a radius of order ${\left(\frac{\log n}{n}\right)^{1/d}}$. Our analysis is not restricted to PRM and applies to a variety of PRM-based planners, including RRG, FMT* and BTT. Continuum percolation plays an important role in our proofs. Lastly, we develop similar theory for all the aforementioned planners when constructed with deterministic samples, which are then sparsified in a randomized fashion. We believe that this new model, and its analysis, is interesting in its own right