Part B | 21.1
482 Part B Autonomous Ocean Vehicles, Subsystems and Control
paths for swarms of ocean vehicles and the second is
the use of models to predict the sensing expected to be
most useful. Prediction of optimal paths for ocean vehicles is referred to here as path planning. This search
for optimality often focuses on time-optimal or energyoptimal paths. The prediction of optimal sensing strategies is referred to as adaptive sampling. We note that in
both cases, the prediction of paths can itself be improved
adaptively in the sense that observations collected along
the path can be utilized to update the predictions. Such
updates can be completed onboard vehicles in the form
of onboard routing or by central/hierarchical computational entities for high-level routing.
Recent autonomous marine activities have started
a revolution that was possibly first imagined by Henry
Stommel in his now famous article, The Slocum mission [21.1]. Today, the number of autonomous platforms used in semi-coordinated sea operations can be
larger than 10, and this number is increasing. This new
paradigm in ocean science and operations motivates the
need to carry out interdisciplinary research in the science of autonomy. This chapter reviews some recent
fundamental results and research directions in timeoptimal path planning and optimal adaptive sampling,
setting a basis for a large number of vehicles forming
heterogeneous and collaborative underwater swarms
that are smart, i. e., knowledgeable about the predicted
environment and their uncertainties, and about the predicted effects of autonomous sensing on future operations. The methodologies are generic and applicable
to any swarm that moves and senses dynamic environmental fields. However, the focus of this chapter is
underwater path planning and adaptive sampling with
a range of vehicles such as AUVs, gliders, ships, or remote sensing platforms.
When compared to related control and robotics
problems of large dimensions, the differences with the
present focus on ocean applications are that:
Naval platforms are heterogeneous and their data
are gappy but multivariate.
Marine fields can strongly affect vehicles’ operations, are dynamic on multiple-scales, and have very
large dimensions, but are predictable to some degree.
The measurements to be collected affect these future predictions.
Therefore, there are feedbacks between optimal planning, sampling and predicting, in time and space, and
across variables. The field of ocean autonomy thus
uses guidance from ocean flow and acoustic propagation modeling, information theory, dynamical system
theory, uncertainty prediction, decision-making under
uncertainty, machine learning, bio-inspired algorithms,
and distributed computing. In all cases, our focus here is
to predict global dynamic swarm patterns and perform
high-level optimization. This is not the detailed fullyresolved control of a single robot. In our focus, a global
objective function defines the optimal dynamic and collaborative autonomy. In general, objective functions
depend on the predicted environment, on the predicted
values and positions of the expected measurements, and
on the feedbacks between measurements and predicted
dynamics.
In what follows, we focus on the science of
autonomy results obtained by our multidisciplinary
simulation, estimation, and assimilation systems
(MSEAS) group and recent collaborators. We first
outline and present a subset of our results on timeoptimal path planning for swarms of ocean vehicles
(Sect. 21.1). This is followed by an overview of some
of our results in adaptive sampling (Sect. 21.2). Our
objective is to outline overall schemes and approaches,
and to illustrate their applications in idealized and
realistic ocean conditions. For detailed descriptions of
the algorithms and methodologies we developed and
utilized, we refer to references cited in each of these
sections. For general reviews on oceanic path planning,
we refer to [21.2] and [21.3], and for general reviews
on oceanic adaptive sampling, to [21.4–8], and [21.9].
Brief conclusions and outlook are given in Sect. 21.3.
21.1 Time-Optimal Path Planning for Swarms of Ocean Vehicles
Our new level-set based method for time-optimal path
planning of vehicle swarms in time-varying uncertain
velocity fields (ocean currents) was developed and described in [21.2, 3, 10–14]. To forecast the time-optimal
trajectories of large numbers of robotic vehicles navigating in strong and dynamic flows, our approach first
evolves the reachable sets from the starting points.
A reachable set is the set of points that can be visited by
a vehicle at a given time. The boundary of such a set is
called the reachability front. Our approach keeps track
of the reachability front at all times, so that we can
determine when the front first reaches the end point.
A path traced by a point on the reachability front that
first reaches the end point is an optimal path that we
wish to compute.
We obtained a modified level set (21.1) for
o , the
scalar field that governs the evolution of reachability
fronts [21.3, 10, 11, 14], linking it to the Hamilton–
482 Part B Autonomous Ocean Vehicles, Subsystems and Control
paths for swarms of ocean vehicles and the second is
the use of models to predict the sensing expected to be
most useful. Prediction of optimal paths for ocean vehicles is referred to here as path planning. This search
for optimality often focuses on time-optimal or energyoptimal paths. The prediction of optimal sensing strategies is referred to as adaptive sampling. We note that in
both cases, the prediction of paths can itself be improved
adaptively in the sense that observations collected along
the path can be utilized to update the predictions. Such
updates can be completed onboard vehicles in the form
of onboard routing or by central/hierarchical computational entities for high-level routing.
Recent autonomous marine activities have started
a revolution that was possibly first imagined by Henry
Stommel in his now famous article, The Slocum mission [21.1]. Today, the number of autonomous platforms used in semi-coordinated sea operations can be
larger than 10, and this number is increasing. This new
paradigm in ocean science and operations motivates the
need to carry out interdisciplinary research in the science of autonomy. This chapter reviews some recent
fundamental results and research directions in timeoptimal path planning and optimal adaptive sampling,
setting a basis for a large number of vehicles forming
heterogeneous and collaborative underwater swarms
that are smart, i. e., knowledgeable about the predicted
environment and their uncertainties, and about the predicted effects of autonomous sensing on future operations. The methodologies are generic and applicable
to any swarm that moves and senses dynamic environmental fields. However, the focus of this chapter is
underwater path planning and adaptive sampling with
a range of vehicles such as AUVs, gliders, ships, or remote sensing platforms.
When compared to related control and robotics
problems of large dimensions, the differences with the
present focus on ocean applications are that:
Naval platforms are heterogeneous and their data
are gappy but multivariate.
Marine fields can strongly affect vehicles’ operations, are dynamic on multiple-scales, and have very
large dimensions, but are predictable to some degree.
The measurements to be collected affect these future predictions.
Therefore, there are feedbacks between optimal planning, sampling and predicting, in time and space, and
across variables. The field of ocean autonomy thus
uses guidance from ocean flow and acoustic propagation modeling, information theory, dynamical system
theory, uncertainty prediction, decision-making under
uncertainty, machine learning, bio-inspired algorithms,
and distributed computing. In all cases, our focus here is
to predict global dynamic swarm patterns and perform
high-level optimization. This is not the detailed fullyresolved control of a single robot. In our focus, a global
objective function defines the optimal dynamic and collaborative autonomy. In general, objective functions
depend on the predicted environment, on the predicted
values and positions of the expected measurements, and
on the feedbacks between measurements and predicted
dynamics.
In what follows, we focus on the science of
autonomy results obtained by our multidisciplinary
simulation, estimation, and assimilation systems
(MSEAS) group and recent collaborators. We first
outline and present a subset of our results on timeoptimal path planning for swarms of ocean vehicles
(Sect. 21.1). This is followed by an overview of some
of our results in adaptive sampling (Sect. 21.2). Our
objective is to outline overall schemes and approaches,
and to illustrate their applications in idealized and
realistic ocean conditions. For detailed descriptions of
the algorithms and methodologies we developed and
utilized, we refer to references cited in each of these
sections. For general reviews on oceanic path planning,
we refer to [21.2] and [21.3], and for general reviews
on oceanic adaptive sampling, to [21.4–8], and [21.9].
Brief conclusions and outlook are given in Sect. 21.3.
21.1 Time-Optimal Path Planning for Swarms of Ocean Vehicles
Our new level-set based method for time-optimal path
planning of vehicle swarms in time-varying uncertain
velocity fields (ocean currents) was developed and described in [21.2, 3, 10–14]. To forecast the time-optimal
trajectories of large numbers of robotic vehicles navigating in strong and dynamic flows, our approach first
evolves the reachable sets from the starting points.
A reachable set is the set of points that can be visited by
a vehicle at a given time. The boundary of such a set is
called the reachability front. Our approach keeps track
of the reachability front at all times, so that we can
determine when the front first reaches the end point.
A path traced by a point on the reachability front that
first reaches the end point is an optimal path that we
wish to compute.
We obtained a modified level set (21.1) for
o , the
scalar field that governs the evolution of reachability
fronts [21.3, 10, 11, 14], linking it to the Hamilton–