Time and Energy Optimal Path Planning in General Flows

Abstract

Abstract-Autonomous surface and underwater vehicles (ASVs and AUVs) are increasingly being used for persistent monitoring of ocean phenomena. Typically, these vehicles are deployed for long periods of time and must operate with limited energy budgets. As a result, there is increased interest in recent years on developing energy efficient motion plans for these vehicles that leverage the dynamics of the surrounding flow field. In this paper, we present a graph search based method to plan time and energy optimal paths in a flow field where the kinematic actuation constraints on the vehicles are captured in our cost functions. We also use tools from topological path planning to generate optimal paths in different homotopy classes, which facilitates simultaneous exploration of the environment. The proposed strategy is validated using analytical flow models for large scale ocean circulation and in experiments using an indoor laboratory testbed capable of creating flows with ocean-like features. We also present a Riemannian metric based approximation for these cost functions which provides an alternative method for computing time and energy optimal paths. The Riemannian approximation results in smoother trajectories in contrast to the graph based approach while requiring less computational time. I. INTRODUCTIONTo better understand oceanic processes, researchers are employing autonomous underwater and surface vehicles (AUVs and ASVs) for long-term surveillance of the dynamics of plankton assemblages [5], temperature and salinity profiles [19,29,27], and the onset of harmful algae blooms [6,9]. In these and similar environmental monitoring applications in the ocean, AUVs and ASVs are often deployed over long periods while operating with limited energy budgets. As such, there is increased interest in recent years on developing more energy efficient motion and trajectory plans for AUVs and ASVs.In recent years, researchers have demonstrated how AUV/ASV motion planning and adaptive sampling strategies can be improved by incorporating either historical or current ocean flow data [24,26,25]. In [24,26], Smith et al. rely on regional ocean model systems (ROMS) to predict the dynamics of an evolving ocean front and uses the resulting predictions to generate waypoints for the AUV to enable it to track the feature of interest. The approach was then integrated with an unscented Kalman filter to better estimate the vehicle's deadreckoning error along a given path in [25]. Path planning for an AUV tasked with an adaptive sampling task was achieved in [8] by employing Lagrangian drifters to drift along a "patch" of water of interest. Rather than rely on ROMS data, Das et al. effectively achieves real-time sampling of the ocean currents in the region of interest using the drifters. Wu et al. solves the inverse problem in [30] where differences in actual and

Non-Gaussian Estimation of a Potential Flow by an Actuated Lagrangian Sensor Steered to Separating Boundaries by Augmented Observability

“…We extend augmented observability to the nonlinear setting for system (12) by utilizing the empirical observability Gramian of Krener and Ide [22], yielding the empirical augmented observability Gramian…”

“…Prior research has planned time-optimal and energy-optimal paths for continuously self-propelled vehicles [10]- [12].…”

Down the CLiFF: Flow-Aware Trajectory Planning Under Motion Pattern Uncertainty

“…Kularatne et al [4] use a graph-search based optimization technique to plan energy-efficient paths over vector fields. Another approach for planning over unimodal fields is the Vector Field RRT algorithm proposed by Ko et al [5].…”

Kinodynamic motion planning on Gaussian mixture fields

“…Past approaches have considered motion planning over regular (unimodal) vector fields: Kularatne et al [11] present a graph-based approach that generates time optimal and energy efficient motion plans for autonomous surface and underwater vehicles in time-varying flow fields. The kinematic constraints of the vehicles are accounted for in the cost function.…”

“…Unlike [11,14,12,9] we use a more powerful probabilistic representation than vector fields named Circular Linear Flow Field (CLiFF) map [10]. It associates a Gaussian mixture model to each location whose components encode multiple weighted flow directions.…”