Optimizing Trajectory and Dynamic Data Offloading Using a UAV Access Platform
1. Introduction
) platform can be optimized for data collection, basic data processing, and data offloading to the cloud within infrastructuredeficient environments. However, if the PoIs are arbitrarily distributed in 3D space such as the monitoring points in underconstruction projects, the maneuverability of the UAVs becomes challenging. UAVs that can be more agile by design are therefore better suited to reach arbitrary locations quickly and safely. Furthermore, such agile UAVs can carry different sensors such as multispectral cameras, nearinfrared cameras, etc. to collect the requisite data from the locations. Hence, instead of overloading the
$$with data collection and offloading tasks, it would be prudent to segregate the UAV functions to optimize them for specific tasks. In this paper, we introduce the Inspection UAVs (
$$) that are morphologically different from the
$$, as they are smaller and more flexible to maneuver at lower heights. The
$$act as a mobile visual sensing platform to collect visual data from different locations in the environment.
$$can be considered mobile sensors scattered throughout the environment. The
$$thus need to locate these dynamically moving
$$in order to collect data from them.
In this study, we address the challenges of deploying a heterogeneous multiUAV system comprising a single UAV access platform called the Access UAV (
$$) and multiple Inspection UAVs (
$$) for dynamic data collection in infrastructuredeficient environments. We propose a Distance and Access Latency Aware Trajectory (DLAT) of the
$$by considering the fair access schedules of the dynamically moving
$$. In addition, to address system instabilities due to queue backlogs, the proposed solution employs a Lyapunovbased online optimization approach. The overall problem has been formulated as minimizing the total energy consumption of the system. Furthermore, as the set of
$$and
$$operate independently without any central entity, their coordination is ensured through a messagebased estimation mechanism.
The contributions of this research are fourfold, which are summarised as follows:

An optimization model has been proposed for optimal trajectory planning of
$$
A
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U
A
V
to fairly access the dynamically moving
$$
I
_
U
A
V
s
in different time slots. The optimization model focuses on minimizing the distance travelled and generating a fair access schedule of
$$
I
_
U
A
V
s
.

From an applications point of view, this research focuses on trajectory optimization of the
$$
A
_
U
A
V
to consider the limited battery constraint and the distance from the location of battery replenishment unit at the site.

Further, a model based on the Lyapunov based online optimization framework is proposed to minimize the energy consumption and the queue backlog of
$$
A
_
U
A
V
and
$$
I
_
U
A
V
s
with limited storage capacity.

Finally, extensive numerical experiments are conducted to evaluate the efficiency and performance of the proposed framework against multiple baselines.
2. Related Work
). This problem brings another challenge of coordination among
$$and
$$in the absence of ubiquitous connectivity with a limited battery. The proposed solution in this study attempts to solve both problems.
3. System Model
) and a single UAV Access Platform (
$$).
$$s are smaller in size and more agile. They collect visual data from a set of k Point of Interests (PoIs) denoted as
$$. Because the framework considers infrastructureless environments, limited Access Points (APs) available for cloud connectivity. Further,
$$possess a limited connectivity range, making it difficult to transfer data directly to the cloud.
$$, which is larger in size and possesses higher computational capabilities, coordinates with the
$$to collect data. We assume that the
$$always maintains a constant height, thus its trajectory lies in a horizontal plane. Figure 1 shows a high level overview of the system under consideration with
$$tasked to collect data from the PoIs, whereas the
$$collects data from the dynamically moving
$$and relay it to the cloud. The notations used in this study are given in Table 1.
3.1. Communication Channel
and
$$(A2A channel) has a limited range and capacity. This work assumes that the achievable data transmission rate of the
$$$$
in a given time slot as
$$
. The communication channel between
$$and
$$involves both lineofsight (LoS) and nonlineofsight (NLoS) links as PoIs can be distributed vertically and longitudinally. Furthermore, the shadowing effect is also considered due to obstructions caused by buildings and other structures in the surroundings [28,29]. The path loss of a link is given as follows:
$$$$
where
$$is a shadowing factor that is indirectly proportional to the altitude of the PoI,
$$and
$$is the path loss exponent. The probability of LoS link,
$$, depends on the angle of elevation and environmental constraints (
$$and
$$) as given in Equation (2):
$$$$
The average pathloss is calculated as:
$$$$
and
$$provides connectivity to send collected data from PoIs to the cloud.
3.2. Data Gathering Process
Each PoI (
$$) is a tuple (
$$), where
$$specifies the amount of data (e.g., images) to be collected and
$$denotes the 3D coordinates of the PoI. The sequence of PoIs to be visited is provided to the
$$and the same is also shared with the
$$. During the traversal along the sequence of PoIs, if the buffer of any of the
$$overflows then that
$$waits at the same PoI until its data is offloaded.
communicates with a single
$$in a time slot. Let us denote the data gathered by each of the
$$in a time slot t by
$$
. Let
$$
be the queue of the
$$$$
and
$$
denotes the amount of data offloaded to the
$$by the
$$$$
in time slot t. The recursive equation to update the
$$
is as follows:
$$$$
be the queue of the
$$where
$$accepts the data from the selected
$$in the time slot t. The following equation updates
$$recursively:
$$$$
where
$$
is the amount of data offloaded to the cloud by the
$$in time slot t. Figure 2 shows the different functions performed by an
$$in a single timeslot. The decision function takes negligible time to decide on the next
$$for data gathering, followed by the transition function where
$$takes
$$time to move near the next possible location to connect with the chosen
$$. The search function (
$$) estimates the location of the selected
$$based on the queue and position estimation algorithm given in Algorithm 1. The bound on the maximum time required to estimate the position of
$$is discussed in Section 5.1. Finally, the data transmission function establishes the successful communication with the
$$(if it is not shadowed). The sequence of the functions mentioned above is repeated for every time slot. The next section describes the objective of the system and formulates it as an optimization problem.
Algorithm 1 Estimated position and queue length of
$$ 

5. Distance and Latency Aware Trajectory (DLAT) Optimization
Flexible and dynamic trajectory planning of
$$is crucial to applications where terrestrial communication infrastructure is missing. As already mentioned, the position of
$$s changes in every timeslot since they move through different PoIs to collect data. The
$$’s trajectory needs to be planned so that it can connect and access an
$$in a timeslot before the
$$’s queue overflows. Whenever an
$$’s queue gets full, it does not move to its next designated PoI. Instead, it sojourns at the same PoI until it can offload its data to the
$$and free up the queue space. In order to choose one of the
$$s to gather data, the
$$would require the realtime information about the queues of all
$$s in each timeslot. This information is not available a priori due to the dynamic nature of the system queues. We use a message passing based approach for estimating the queues of
$$s to make a selection. Further, the trajectory of the
$$must be optimized to consume minimal energy.
optimizes the tradeoff between the transition energy of
$$and the access latencies of all
$$s. In addition, this access latency based data offloading generates an access fair schedule for the
$$s to offload their data to the
$$. The access latency (
$$
) of the
$$$$
in the timeslot t is the difference between the time of its last access by the
$$and the current timeslot. The distance and latency aware trajectory optimization of
$$is formulated as:
$$$$
$$$$
$$$$
$$$$
$$$$
$$$$
$$$$
where the first constraint (23) signifies that the distance travelled within a timeslot is limited by the maximum velocity. Constraint (24) limits the time that has elapsed since the last access of
$$$$
to be less than
$$. The constraint in (25) selects the
$$which has data to offload whereas (26) enforces the selection of only one of the
$$s in a timeslot. The selected
$$transmission power should be bounded as given in (27).
5.1. Estimating Position and Queue Length
The exact position and queue length of
$$is not known to the
$$a priori. The
$$maintains the last access statistics of each
$$using status messages. The track of status messages received over time helps in computing the position (
$$) and queue length (
$$
) of
$$s in a timeslot. The status message comprises of the remaining queue size at the time of access and the data to be collected at the current PoI. Moreover, the precomputed trajectory of each
$$provides the set of PoIs to be visited by each
$$. Algorithm 1 describes the procedure to estimate the queue length of each
$$in every timeslot.
5.2. Estimation of Search Time Bound
$$
estimates the location of
$$in each time slot using the last access statistics. It could search the set of candidate locations to locate the precise location of selected
$$, which contributes to the search time. The bound on the search time depends on the data generation rate and the maximum buffer of
$$as derived below.
to locate the exact location of
$$with max buffer size
$$is given as:
$$$$
where ϱ is the maximum distance between two consecutive PoIs in the possible set of locations to be searched and
$$is the number of candidate locations for
$$and data generation process at each PoI follows the normal distribution
$$depends on the travel distance to cover the candidate PoI locations as given in Equation (30).
$$$$
$$$$
where
$$
is the set of locations visited when each location has minimum data
$$to be collected whereas
$$
is the set of locations when maximum data
$$is present at each location. As the memory of each
$$is bounded by
$$, it covers less number of locations for
$$as shown in Equation (31). Similarly, the data collected in both the scenarios will be same as the maximum memory size is fixed. The candidate locations are defined as the locations starting at
$$and ending at
$$. Intuitively, the number of candidate locations
$$
.
$$$$
From the above derivation, the locations in search trajectory are influenced by data rate and maximum limit of memory size for
$$. The upper and lower limit of normally distributed data is given as
$$and
$$respectively. Thus Equation (30) can be written as
$$$$
□
is the distance between consecutive PoIs which could be calculated from the precalculated trajectory of
$$based on shortest path.
6. Energy Aware Data Offloading
in each timeslot. The quadratic Lyapunov function, as given in Equation (36) associates a scalar measure to the queues of the system. Further, the stability of the system is maintained by a guaranteed mean rate stability of the evolving queues as given in Equations (34) and (35).
$$$$
$$$$
$$$$
where
$$
consists of all system queues at a time t and
$$is quadratic Lyapunov function of system queues. The Lyapunov drift corresponding to the above function is given as:
$$$$
The Lyapunov drift plus a penalty function is minimized to stabilize the queue backlog of the system is given as:
$$$$
where V is a positive constant that controls the tradeoff between Lyapunov drift and the expected system energy. A high value of parameter V signifies more weight on minimizing the energy of the system at the cost of high queue backlog. Therefore, V acts as a tradeoff parameter between system energy and queue backlog. An upper bound on
$$can be derived as follows, (for details see [10])
$$$$
where C is a deterministic constant.
$$$$
Hence, the original formulation P1 can be reduced to P3 which bounds the system’s drift to keep it stable.
$$$$
$$$$
$$$$
$$$$
$$$$
$$$$
and
$$are fixed in a given time slot t. The Lyapunov based online optimization is optimal for a stochastic system to derive the overall optimal solution [33].
6.1. Optimization of Transmission Energies of I_UAVs
. The variables
$$
, i.e., the position of
$$and the offloaded data
$$
of the selected
$$$$
are coupled in a particular timeslot. The fixed position of
$$decouples these variables. In the optimization model P 3.1, the transmission energy is optimized for a single timeslot (t) given the position of
$$:
$$$$
$$$$
$$$$
$$$$
The objective function in P 3.1 is a convex function. The first & second constraints are linear and the third constraint is upper bounded by a concave function. As a result, the stationary point of the objective function is found to be:
$$
.
6.2. Optimization of Transmission Energy of A_UAV
parameters for the amount of data offloaded to the cloud at time t. The updated optimization model is given as:
$$$$
$$$$
$$$$
$$$$
The model P 3.2 has a convex optimization objective subject to convex constraints to solve for the optimal transmission power of the
$$. The stationary point of the optimization model is
$$
.
Algorithm 2 Proposed Solution Approach 

7. Experimentation
with one
$$in all the simulation experiments. Each
$$is assigned to a cluster where
$$randomly choose a starting location within the cluster. The sequence of PoIs to be visited by each
$$is generated using the shortest path algorithm. Before proceeding to the next PoI, an
$$collects all the data (
$$
) from that PoI. In the data collection process, an
$$may sojourn at the same PoI across multiple timeslots until all the data (
$$
) of PoI is collected. For each PoI, the amount of data to be collected is modeled as a Gaussian distribution with a mean of 150 Kb and variance of 50 Kb. The
$$gets partial information about the data generated at each location so it could not accurately estimate the location of
$$in the next time slot; as a result, it has to search for candidate locations to access the selected
$$as discussed in Section 5.1. The tradeoff parameter V ranges from 10 to
$$. The length of each time slot
$$is 25 s divided into different sub slots as shown in Figure 2. The selection of
$$is assumed to take negligible time whereas transition may take up to 20 s. The search and transmit function takes total of 5 s. The maximum transmission power for
$$and
$$are 5 W and 2 W, respectively [25]. The other simulation parameters are listed in Table 2.
In order to validate the performance of our proposed approach, we compared our proposed approach with a set of baseline approaches on two broad categories of optimization parameters viz. Trajectory planning and Data offloading. We consider the following baseline approaches:

Distance Aware Trajectory planning (DAT): In this approach, the
$$
A
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V
selects to access an
$$
I
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U
A
V
based on the shortest distance from the current location in each time slot.

Round Robin based Trajectory planning (RR): In this approach, the
$$
A
_
U
A
V
accesses
$$
I
_
U
A
V
s
in sequential order in each time slot.

Maximum Transmission Power (MAX) data offloading: In each time slot, the
$$
A
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U
A
V
and the
$$
I
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A
V
operate at the maximum transmission power to offload data.
The proposed approaches are as follows:

Distance and Latency Aware Trajectory Optimization (DLAT): In this approach, the
$$
A
_
U
A
V
selects the
$$
I
_
U
A
V
based on the minimum distance, with maximum bits to offload and access latency constraint as given in the trajectory optimization problem.

Hybrid Approach for Trajectory Scheduling (HDLAT): In this approach, the
$$
A
_
U
A
V
selects the
$$
I
_
U
A
V
based on the minimum distance and access latency constraint as given in the trajectory optimization problem up to a certain threshold of battery, i.e., 75% of the total battery. Beyond the threshold, the scheduling algorithm switches to the DAT strategy (proposed approach).

Lyapunov Optimization for data offloading: In each time slot, the
$$
A
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V
and the
$$
I
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V
calculate the optimal value of transmission energy using the Lyapunov Optimization.
Experiments were conducted by taking a combination of one of the approaches from both the categories: (1) DAT + MAX, (2) DLAT + MAX, (3) RR + MAX, (4) HDLAT + MAX, (5) DAT + Lyapunov, (6) RR + Lyapunov (7) DLAT + Lyapunov (proposed approach) and (8) HDLAT + Lyapunov.
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