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We develop a path-planning algorithm to guide autonomous
amphibious vehicles (AAVs) for flood rescue support missions.
Specifically, we develop an algorithm to control multiple AAVs to
reach/rescue multiple victims (also called targets) in a flood
scenario in 2D, where the flood water flows across the scene and
the targets move (drifted by the flood water) along the flood
stream. A target is said to be rescued if an AAV lies within a
circular region of a certain radius around the target. The goal is
to control the AAVs such that each target gets rescued while
optimizing a certain performance objective. The algorithm design
is based on the theory of

Various guidance algorithms for autonomous amphibious vehicles (AAVs) are being designed and tested to fight today’s global warming disasters such as flooding, typhoon, and hurricane [

Flood scenario.

Guidance control methods [

The AAV guidance problem is specified as follows.

In this study, we assume that there are multiple mobile targets (flood victims) located in a river, being drifted down by the flood water, as shown in Figure

There are multiple autonomous amphibious vehicles (AAVs) located on the shore, as shown in Figure

The elevation map of the region is known a priori. The landscape for this problem is shown in Figure

Typically a river flows slowly near the coastlines (where the river is shallow) and flows quickly far from the coastlines (i.e., toward the center of the river where the river is deep). In this paper, we assume that the river flows from the north toward the south in a v-shaped channel as shown in Figure

The sensors onboard an AAV generate noisy observations of target locations and the depth of the river directly beneath the vehicle, that is, the sensors generate the observations of the depth of the river only when the AAV is in the river.

A target is said to be rescued if there is an AAV within a circular region of radius

We cast the AAV guidance problem into the framework of a

Let

The vehicle and the track states are assumed to be fully observable. The river and the target states are only partially observable. The observation of the river state at an AAV is given by

The actions include the controllable aspects of the system. In this problem, the actions include the decisions on the assignment of AAVs to targets, and kinematic control commands for AAVs. Let

The state-transition law specifies the next-state distribution given the current state and the action. The transition function for the vehicle state is given by

The cost function represents the cost of performing an action at the current state. The cost function is given by

The belief state

The goal is to find the action sequence

The computational requirements of obtaining the optimal assignments of AAVs to targets (

The belief states corresponding to the river state and the target state are given by

Here, we adopt an approach called “receding horizon control,” according to which we optimize the action sequence for

The kinematic equations of an AAV vary depending on whether the AAV is in the river or on the land. When the AAV is in the river, we take into account the speed of the river to write the kinematic equations. The steering and thrust generation of the vehicle are modeled based on the work done by the authors of [

This subsection provides the definition of

Free body diagram of an AAV.

This subsection provides the definition of

We implement the NBO method in MATLAB, and we use the command

In the simulations, an AAV is represented by a rectangle, and the line connecting the rectangles represents the trajectory of the AAV. We define a performance metric called

Simulation of Scenario I with NBO approach,

Simulation of Scenario I with greedy approach,

Simulation of Scenario II with NBO approach,

Simulation of Scenario II with the greedy approach,

Simulation of Scenario III with NBO approach,

Simulation of Scenario III with the greedy approach,

We compare the performance of the NBO approach with that of the greedy approach through Monte-Carlo simulations. We simulate the above scenarios with the NBO and the greedy approaches separately for 50 Monte-Carlo runs. In each scenario, we compute the

Performance comparison for Scenario I: NBO approach versus greedy approach.

Performance comparison for Scenario II: NBO approach versus greedy approach.

Performance comparison for Scenario III: NBO approach versus greedy approach.

The algorithm (NBO) runtime to compute the control commands for three AAVs (in Scenario III) in any time step in MATLAB is approximately 4 seconds on a lab computer (Intel Core i7-860 Quad-Core Processor with 8 MB Cache and 2.80 GHz speed). This runtime can be greatly reduced on a better processor and by further optimizing the code. Since the algorithm runtime is not prohibitive, it can be used in real time (i.e., for practical purposes).

We designed a guidance algorithm for autonomous amphibious vehicles (AAVs) to rescue moving targets in a 2D flood scenario, where the flood water flows across the scene, and the targets move in the flood water. We designed this algorithm based on the theory of

This work was supported in part by the Fulbright Foundation. The authors would also like to acknowledge Colorado State University’s support via the Libraries Open Access Research and Scholarship Fund (OARS).