A big challenge in environmental monitoring is the spatiotemporal variation of the phenomena to be observed. To enable persistent sensing and estimation in such a setting, it is beneficial to have a time-varying underlying environmental model. Here we present a planning and learning method that enables an autonomous marine vehicle to perform persistent ocean monitoring tasks by learning and refining an environmental model. To alleviate the computational bottleneck caused by large-scale data accumulated, we propose a framework that iterates between a planning component aimed at collecting the most information-rich data, and a sparse Gaussian Process learning component where the environmental model and hyperparameters are learned online by taking advantage of only a subset of data that provides the greatest contribution. Our simulations with ground-truth ocean data shows that the proposed method is both accurate and efficient.
Planning and environment monitoring are two big and well studied topics. Here we briefly review the works that are related to the informative planning and the model prediction with sparse GPs. Representative informative planning approaches include, for example, algorithms based on a recursive-greedy style @cite_7 @cite_12 where the informativeness is generalized as submodular functions and a sequential-allocation mechanism is designed in order to obtain subsequent waypoints. This recursive-greedy framework has been extended later by incorporating obstacle avoidance @cite_23 and diminishing returns @cite_1 . In addition, a differential entropy based framework @cite_20 @cite_0 was proposed where a batch of waypoints can be obtained through dynamic programming. We recently proposed a similar informative planning method based on the dynamic programming structure in order to compute the informative waypoints @cite_10 . This method is further extended here as an adaptive path planning component by incorporating the online learning and re-planning mechanisms. There are also many methods optimizing over complex deterministic and static information (e.g., see @cite_24 @cite_13 ).
@cite_13 @cite_7 @cite_1 @cite_0 @cite_24 @cite_23 @cite_10 @cite_12 @cite_20
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This paper investigates data-adaptive path planning schemes for wireless networks of mobile sensor platforms. We focus on applications of environmental monitoring, in which the goal is to reconstruct a spatial map of environmental factors of interest. Traditional sampling theory deals with data collection processes that are completely independent of the target map to be estimated, aside from possible a priori specifications reflective of assumed properties of the target. We refer to such processes as passive learning methods. Alternatively, one can envision sequential, adaptive data collection procedures that use information gleaned from previous observations to guide the process. We refer to such feedback-driven processes as active learning methods. Active learning is naturally suited to mobile path planning, in which previous samples are used to guide the motion of the mobiles for further sampling. This paper presents some of the most encouraging theoretical results to date that support the effectiveness of active over passive learning, and focuses on new results regarding the capabilities of active learning methods for mobile sensing. Tradeoffs between latency, path lengths, and accuracy are carefully assessed using our theory. Adaptive path planning methods are developed to guide mobiles in order to focus attention in interesting regions of the sensing domain, thus conducting spatial surveys much more rapidly while maintaining the accuracy of the estimated map. The theory and methods are illustrated in the application of water current mapping in a freshwater lake. Many robotic path planning applications, such as search and rescue, involve uncertain environments with complex dynamics that can be only partially observed. When selecting the best subset of observation locations subject to constrained resources (such as limited time or battery capacity) it is an important problem to trade off exploration (gathering information about the environment) and exploitation (using the current knowledge about the environment most effectively) for efficiently observing these environments. Even the nonadaptive setting, where paths are planned before observations are made, is NP-hard, and has been subject to much research. In this paper, we present a novel approach to adaptive informative path planning that addresses this exploration-exploitation tradeoff. Our approach is nonmyopic, i.e. it plans ahead for possible observations that can be made in the future. We quantify the benefit of exploration through the adaptivity gap'' between an adaptive and a nonadaptive algorithm in terms of the uncertainty in the environment. Exploiting the submodularity (a diminishing returns property) and locality properties of the objective function, we develop an algorithm that performs provably near-optimally in settings where the adaptivity gap is small. In case of large gap, we use an objective function that simultaneously optimizes paths for exploration and exploitation. We also provide an algorithm to extend any single robot algorithm for adaptive informative path planning to the multi-robot setting while approximately preserving the theoretical guarantee of the single robot algorithm. We extensively evaluate our approach on a domain and a scientific monitoring problem using a real robotic system. A new framework which adopts a rapidly-exploring random tree (RRT) path planner with a Gaussian process (GP) occupancy map is developed for the navigation and exploration of an unknown but cluttered environment. The GP map outputs the probability of occupancy given any selected query point in the continuous space and thus makes it possible to explore the full space when used in conjunction with a continuous path planner. Furthermore, the GP map-generated path is embedded with the probability of collision along the path which lends itself to obstacle avoidance. Finally, the GP map-building algorithm is extended to include an exploration mission considering the differential constraints of a rotary unmanned aerial vehicle and the limitation arising from the environment. Using mutual information as an information-theoretic measure, an informative path which reduces the uncertainty of the environment is generated. Simulation results show that GP map combined with RRT planner can achieve the 3D navigation and e... One central issue in practically deploying network coding is the adaptive and economic allocation of network resource. We cast this as an optimization, where the net-utility-the difference between a utility derived from the attainable multicast throughput and the total cost of resource provisioning-is maximized. By employing the MAX of flows characterization of the admissible rate region for multicasting, this paper gives a novel reformulation of the optimization problem, which has a separable structure. The Lagrangian relaxation method is applied to decompose the problem into subproblems involving one destination each. Our specific formulation of the primal problem results in two key properties. First, the resulting subproblem after decomposition amounts to the problem of finding a shortest path from the source to each destination. Second, assuming the net-utility function is strictly concave, our proposed method enables a near-optimal primal variable to be uniquely recovered from a near-optimal dual variable. A numerical robustness analysis of the primal recovery method is also conducted. For ill-conditioned problems that arise, for instance, when the cost functions are linear, we propose to use the proximal method, which solves a sequence of well-conditioned problems obtained from the original problem by adding quadratic regularization terms. Furthermore, the simulation results confirm the numerical robustness of the proposed algorithms. Finally, the proximal method and the dual subgradient method can be naturally extended to provide an effective solution for applications with multiple multicast sessions