Many applications of path planning in time-varying flow fields, particularly in areas such as marine robotics and ship routing, can be modelled as instances of the time-varying shortest path (TDSP) problem. Although there are no known polynomial-time solutions to TDSP in general, our recent work has identified a tractable case where the flow is modelled as piecewise constant. Extending this method to allow for computational reuse in larger multi-query problems, however, requires additional thought. This paper shows that the piecewise-linear form of the cost function employed in previously work can be used to build an analogy of a shortest path tree, thereby enabling optimal concatenation of sub-problem solutions in the absence of an optimal substructure, and without uniform time discretisation. We present a framework for multi-query TDSP that finds an optimal path that passes through a defined sequence of waypoints and is computationally efficient. Performance comparison is provided in simulation that shows large (up to 100x) speedup compared to a naive approach. This result is significant for applications such as ship routing, where route evaluation is a desirable capability.

We consider the coordinated escort problem, where a decentralised team of supporting robots implicitly assist the mission of higher-value principal robots. The defining challenge is how to evaluate the effect of supporting robots' actions on the principal robots' mission. To capture this effect, we define two novel auxiliary reward functions for supporting robots called satisfaction improvement and satisfaction entropy, which computes the improvement in probability of mission success, or the uncertainty thereof. Given these reward functions, we coordinate the entire team of principal and supporting robots using decentralised cross entropy method (Dec-CEM), a new extension of CEM to multi-agent systems based on the product distribution approximation. In a simulated object avoidance scenario, our planning framework demonstrates up to two-fold improvement in task satisfaction against conventional decoupled information gathering. The significance of our results is to introduce a new family of algorithmic problems that will enable important new practical applications of heterogeneous multi-robot systems.

We propose an algorithm for solving the time-dependent shortest path problem in flow fields where the FIFO (first-in-first-out) assumption is violated. This problem variant is important for autonomous vehicles in the ocean, for example, that cannot arbitrarily hover in a fixed position and that are strongly influenced by time-varying ocean currents. Although polynomial-time solutions are available for discrete-time problems, the continuous-time non-FIFO case is NP-hard with no known relevant special cases. Our main result is to show that this problem can be solved in polynomial time if the edge travel time functions are piecewise-constant, agreeing with existing worst-case bounds for FIFO problems with restricted slopes. We present a minimum-time algorithm for graphs that allows for paths with finite-length cycles, and then embed this algorithm within an asymptotically optimal sampling-based framework to find time-optimal paths in flows. The algorithm relies on an efficient data structure to represent and manipulate piecewise-constant functions and is straightforward to implement. We illustrate the behaviour of the algorithm in an example based on a common ocean vortex model.

As the future of autonomous underwater vehicle (AUV) deployments tends to multi-vehicle systems, new approaches in coordination and control are needed. In this work, we consider the problem of simultaneous survey and inspection where one vehicle dynamically discovers objects while another vehicle must inspect as many of the objects as possible over the course of the mission. This requires a fully autonomous inspection vehicle, and to this end, we present a planning approach which couples sampling-based motion planning with timed roadmap constraints as well as a real-time execution framework. The methods presented address the underlying challenges that arise during simultaneous survey and inspection using AUVs, namely those of communication constraints, safety of navigation constraints, and dynamically discovered tasks. Additionally, we present field results for the simultaneous survey and inspection mission using teamed AUVs.

We present a method to estimate two-dimensional, time-invariant oceanic flow fields based on data from both ensemble forecasts and online measurements. Our method produces a realistic estimate in a computationally efficient manner suitable for use in marine robotics for path planning and related applications. We use kernel methods and singular value decomposition to find a compact model of the ensemble data that is represented as a linear combination of basis flow fields and that preserves the spatial correlations present in the data. Online measurements of ocean current, taken for example by marine robots, can then be incorporated using recursive Bayesian estimation. We provide computational analysis, performance comparisons with related methods, and demonstration with real-world ensemble data to show the computational efficiency and validity of our method. Possible applications in addition to path planning include active perception for model improvement through deliberate choice of measurement locations.

We present a path planning framework for marine robots subject to uncertain ocean currents that exploits data from ensemble forecasting, which is a technique for current prediction used in oceanography. Ensemble forecasts represent a distribution of predicted currents as a set of flow fields that are considered to be equally likely. We show that the typical approach of computing the vector-wise mean and variance over this set can yield meaningless results, and propose an alternative approach that considers each flow field in the ensemble simultaneously. Our framework finds a sequence of vehicle controls that minimises the root-mean-square error distance (RMSE) over the full set of ensemble-induced trajectories. The key to achieving computational efficiency in this approach is our use of Monte Carlo tree search (MCTS) with a specialised heuristic that improves convergence rate while preserving asymptotic optimality and the anytime property. We demonstrate our results using real ensemble forecasts provided by the Australian Bureau of Meteorology, and provide comparisons with the deterministic mean-based approach where we observe RMSE reductions of 92% and 43% in two example scenarios. Further, we argue that the framework can be used in a plan-as-you-go manner where ensemble forecasts change over time. These results help to introduce ensemble forecasts as a viable source of data to improve path planning in marine robotics.

Estimating ocean flow fields in 3D is a critical step in enabling the reliable operation of underwater gliders and other small, low-powered autonomous marine vehicles. Existing methods produce depth-averaged 2D layers arranged at discrete vertical intervals, but this type of estimation can lead to severe navigation errors. Based on the observation that real-world ocean currents exhibit relatively low vertical velocity components, we propose an accurate 3D estimator that extends our previous work in estimating 2D flow fields as a linear combination of basis flows. The proposed algorithm uses data from ensemble forecasting to build a set of 3D basis flows, and then iteratively updates basis coefficients using point measurements of underwater currents. We report results from experiments using actual ensemble forecasts and synthetic measurements to compare the performance of our method to the direct 3D extension of the previous work. These results show that our method produces estimates with dramatically lower error metrics, with and without measurement noise.

We present an efficient approach for finding shortest paths in flow fields that vary as a sequence of flow predictions over time. This approach is applicable to motion planning for slow marine robots that are subject to dynamic ocean currents. Although the problem is NP-hard in general form, we incorporate recent results from the theory of finding shortest paths in time-dependent graphs to construct a polynomial-time algorithm that finds continuous trajectories in time-dependent flow fields. The algorithm has a hierarchical structure where a graph is constructed with time-varying edge costs that are derived from sets of continuous trajectories in the underlying flow field. We show that the continuous algorithm retains the time complexity and path quality properties of the discrete graph solution, and demonstrate its application to surface and underwater vehicles including a traversal along the East Australian Current with an autonomous marine vehicle. Results show that the algorithm performs efficiently in practice and can find paths that adapt to changing ocean currents. These results are significant to marine robotics because they allow for efficient use of time-varying ocean predictions for motion planning.

Motion planning for vehicles under the influence of flow fields can benefit from the idea of streamline-based planning, which exploits ideas from fluid dynamics to achieve computational efficiency. Important to such planners is an efficient means of computing the travel distance and direction between two points in free space, but this is difficult to achieve in strong incompressible flows such as ocean currents. We propose two useful distance functions in analytical form that combine Euclidean distance with values of the stream function associated with a flow field, and with an estimation of the strength of the opposing flow between two points. Further, we propose steering heuristics that are useful for steering towards a sampled point. We evaluate these ideas by integrating them with RRT*and comparing the algorithm's performance with state-of-the-art methods in an artificial flow field and in actual ocean prediction data in the region of the dominant East Australian Current between Sydney and Brisbane. Results demonstrate the method's computational efficiency and ability to find high-quality paths outperforming state-of-the-art methods, and show promise for practical use with autonomous marine robots.

Underwater robots are subject to position drift due to the effect of ocean currents and the lack of accurate localisation while submerged. We are interested in exploiting such position drift to estimate the ocean current in the surrounding area, thereby assisting navigation and planning. We present a Gaussian process (GP)-based expectation-maximisation (EM) algorithm that estimates the underlying ocean current using sparse GPS data obtained on the surface and dead-reckoned position estimates. We first develop a specialised GP regression scheme that exploits the incompressibility of ocean currents to counteract the underdetermined nature of the problem. We then use the proposed regression scheme in an EM algorithm that estimates the best-fitting ocean current in between each GPS fix. The proposed algorithm is validated in simulation and on a real dataset, and is shown to be capable of reconstructing the underlying ocean current field. We expect to use this algorithm to close the loop between planning and estimation for underwater navigation in unknown ocean currents.

Motion planning for underwater vehicles must consider the effect of ocean currents. We present an efficient method to compute reachability and cost between sample points in sampling-based motion planning that supports long-range planning over hundreds of kilometres in complicated flows. The idea is to search a reduced space of control inputs that consists of stream functions whose level sets, or streamlines, optimally connect two given points. Such stream functions are generated by superimposing a control input onto the underlying current flow. A streamline represents the resulting path that a vehicle would follow as it is carried along by the current given that control input. We provide rigorous analysis that shows how our method avoids exhaustive search of the control space, and demonstrate simulated examples in complicated flows including a traversal along the east coast of Australia, using actual current predictions, between Sydney and Brisbane.

Autonomous underwater gliders frequently execute extensive missions with high levels of uncertainty due to limitations of sensing, control and oceanic forecasting. Glider path planning seeks an optimal path with respect to conflicting objectives, such as travel cost and safety, that must be explicitly balanced subject to these uncertainties. In this paper, we derive a set of recursive equations for state probability and expected travel cost conditional on safety, and use them to implement a new stochastic variant of FMT* in the context of two types of objective functions that allow a glider to reach a destination region with minimum cost or maximum probability of arrival given a safety threshold. We demonstrate the framework using three simulated examples that illustrate how user-prescribed safety constraints affect the results.