# Resource Optimization in MEC-Assisted Multirobot Cooperation Systems

Authors: Lanxin Qiu; Yi Zhang; Yanbo Wang; Yineng Shen; Jiantao Yuan; Rui Yin
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

With prevalent utilization ofmultirobot cooperation (MRC) systems, people pay more attention to improve the system performance. Among them, the energy consumption and implementation latency of MRC systems are major concerns, and mobile edge computing (MEC) provides a potential way to solve these problems. Therefore, how to leverage MEC to get the balance between computing and communication consumption in MRC systems needs to be investigated urgently. In this paper, a MRC system deployed to accomplish multiple time-critical tasks by MEC technology is studied. The proposed MRC system includes a powerful master robot (MR) and several slave robots (SRs). As a scheduler, MR is responsible for allocating tasks to SRs and has more computing power. SRs are robots with sensors that interact with the environment. In this paper, we propose a strategy for task allocation and resource management in MRC systems. The results show that the proposed scheme can effectively reduce the total energy consumption in SRs.


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## Body

## 1. Introduction

At present, there are many practical applications of multirobot systems, such as floor mopping robots, rescue robots after nature disasters, surgery by surgical robots, and manufacture by mechanical arms [1]. Obviously, multirobot collaboration can greatly improve efficiency compared to a single robot. Therefore, a very hot research direction is the MRC system [2]. However, in a MRC system, the difficulty in accomplishing the lantency-sensitive and computation-intensive tasks comes from diverse computation, communication and sensing capacities of the individual robots, and the limited battery budget [3]. On the one hand, multirobots need cooperate to accomplish the time-critical jobs. On the other hand, efficient cooperation between multirobot is definitely inseparable from efficient communication. Fortunately, MEC technology has emerged as a promising solution to enable the task offloading via wireless communication, which perfectly fits the MRC system structure.As driven by the explosive growth on data traffic,artificial intelligence (AI) has revolutionized science and social life. However, AI also brought tremendous computation workloads [4]. Inevitably, robots also undertake more and more AI tasks in various applications, which imposes a certain computational burden on robot with limited size. To ease these burdens, many research have been done to accelerate computing efforts in the following three areas [2]: different types of robots, control architectures, and communication technologies.In order to solve the above problems, both the field of robotics and the field of communication are making contributions. In robotics, the solution is to collaborate by adding more robots to overcome the resource constraints of a single robot. Firstly, in [5], the author introduces the controlled mobility to enable the sparse sensing, which can be exploited for energy-efficient and nonredundant sensing in MRC networks. Secondly, through efficient wireless communication technology, robots can share data and working status. In [6], the authors come up an ad hoc based MRC system in which p-persistent real-time ALOHA is used as the channel competation strategy. By doin this, they achieve ultrareliability and ultralow latency communication. Furthermore, some researchers have noticed that with the development of wireless communication technology, it is a feasible way to deploy the computing tasks of robots to the cloud [7]. For instance, in [8], the authors utilize a distributed framework to build a visual SLAM robotic system, where cloud servers are responsible for map optimization and storing information to reduce computational workload. Furthermore, UAV is a segment of robotics research that has received great attention, and in [9], a joint offloading and trajectory design scheme that minimizes the sum of maximum delay is proposed in a MEC-based UAV system.As an emerging computation offloading and wireless communication combination technology, MEC deploys cloud-like functions closer to the edge of networks to reduce latency. MEC trades off computational offloading and wireless communication, which plays an important role in reducing energy consumption and computing latency [10]. MEC has also been extensively used in many areas including vehicle to vehicle (V2V) [11], unmanned aerial vehicle (UAV) [12], and augmented reality [13]. In [14], an air-ground integrated multiaccess edge computing system has been investigated. The interaction among mobile users has been modelled as a stochastic game, which is transformed into a single-agent Markov decision process at each user. Then, an online deep reinforement learning scheme has been proposed to approximate the Q-factor and postdecision Q-factor, respectively, which is used to find the optimal solution at each user. In [15], computation offloading in beyond the fifth generation networks has been studied, where the combination of the wireless communications and multiaccess edge computing is considered. Multiagent Markov decision process has been applied to model the computation offloading problem, where a distributed learning framework is developed. Authors in [16] have extended the MEC technology to the unlicensed bands, where a context-aware communication approach is to efficiently integrate licensed and unlicensed spectrums by MEC technologies.Based on above investigation, we can observe that MEC is suitable for computation task offloading in MRC systems. In [17], the authors propose an energy-efficient task offloading scheme for multiple devices for TDMA and OFDMA systems. Moreover, in [18], an algorithm based on Alternating Direction Method of Multipliers (ADMM) is proposed to maximize the revenue of MEC system operator (MSO), which is comprehensive considering offloading, resource allocation, and content caching strategies. To overcome network congestion and long latency in cloud computing, a multilevel resource management algorithm is designed in [19], in which cloud and edge servers cooperate to complete tasks. In the scenario of multiserver serving multiuser, [20, 21] have proposed centralized and distributed methods to derive the optimal task offloading strategies, respectively. In [22], we have propose a MEC-based MRC system and an algorithm to offload task and allocate the resource which focus on fairness and robustness. In [23], we have developed the optimal resource scheduling scheme to ensure that the task can be accomplished in time. Therefore, in our previous work [22, 23], there have two different models, where the optimal model guarantees the performance, and the fairness model guarantees that the SR is always “online.” However, how to achieve the optimality and fairness is still an urgent problem to be solved.This paper is devoted to proposing a resource allocation scheme applied to an MRC system, which minimizes the total energy consumption of SRs under a task implementation latency constraint. First, we consider a complicated realistic scenario where the SRs are in charge of the sensing and data collection and a MR is responsible for the task offloading and wireless communication resource management. Accordingly, a task implementation strategy in MEC-based MRC system is proposed, in which we divide each task into three parts. Then, an optimal and fair resource scheduling scheme is proposed to minimize the energy consumption of SR. The results show that the proposed scheme can effectively reduce the total energy consumption in SR.


## 2. System Model

In the paper, a time-critical task implementation process is proposed for MRC systems, and an MEC-based resource allocation scheme is studied. As shown in Figure1, a MR M cooperates with K SRs, which denoted by a set of S=s1,s2,⋯,sK. In addition, a powerful base station will handle some computing tasks for MR. The MR has more powerful computing ability than SRs, but SR has the ability to interact with the environment. Then, we let the MR lead multiple SRs on latency-sensitive computationally intensive tasks, such as AI applications and path planning.Figure 1
Multirobot cooperation system model.As shown in Figure2, the proposed task implementation process is divided to three stages. The first stage is called the sensing stage where each SR collects data required by the task under a duration of Tss. The second is named as SR offloading stage. The SRs will process a certain amount of data locally and the rest of data will be offloaded to the MR with a time limitation Tsco. In the MR offloading stage, which is the third stage, the MR also preform computation and offloading trade-offs to meet the latency TMco.Figure 2
The time division structure and energy flow for system model.On the one hand, the MR needs to decide the amount of data each SR needs to collect, the transmit power of each SR, and the amount of data offloaded from each SR. The MR makes decisions based on the channel status of the SR and the remaining battery power, so the SR will feed back these information to the MR through the control channel at the beginning to ensure reliable communication. The MR then feeds back the decision to each SR via the control channel. Similarly, at the beginning of the third stage, the MR first measures and estimates the channel state information between the MR and the BS.On the other hand, general working robots cannot be very large, so their battery and computing device capabilities are also limited. So we assume that SR has much less battery capacity and computing power than MR, and most of the energy of SR will be spent on sensing and collecting data in the first stage. In order to maintain the functionality of the MRC system for as long as possible, the power consumption of the SR should be minimized and balanced. To achieve this goal, the mathematical model of the system will be described in detail in the following subsections.


### 2.1. Data Collection Model

Firstly, MR will allocate different sensing timetkss to each SR based on the information provided by the SR, which is a variable. The amount of collected data bits at the k-th SR is denoted as
(1)dk=pksstkssHk,where Hk represents the energy consumption used to sense one bit [24], and pkss is a constant which denote as the sensing power consumption at the kth SR.


### 2.2. Computation-Offloading Model

Figure2 also shows the direction of data flow and energy consumption in the MRC system. Let dkol denotes the offloaded data bits from the kth SR to the MR, and dM=∑k∈Sdkol as the total received data from SRs.Then, (dk−dkol) bits are the data that need to be processed locally. Moreover, let Wk represents the computation capability of the kth SR, which is the number of central processing unit (CPU) cycles executed per second, and WM as the computation capacity of the MR. Moreever, Ck as the number of CPU cycles is required at the kth SR to calculate 1-bit data, and CM as the number of CPU cycles is required for computing 1-bit of data at the MR. To guarantee the latency constraint, the time spent on local computing should be less than a threshold Tsco.


### 2.3. Communication Model

Consider the TDMA system. According to Shannon formula, the transmission data rate from thek-th SR to the MR is given by
(2)rk=Bklog21+pktrhkNk,where Bk is the channel bandwidth allocated to the kth SR, pktr is the transmission power consumed at SR k, hk denotes the mean channel gain on the wireless channel between SR k and the MR, and Nk is the Gaussian channel noise, which is fixed. It is noteworthy that the channels between the SRs and MR experience both large fading due to the path loss and shadowing and fast fading due to the reflection and diffraction. Based on Equation (2), the time spent on offloading data from the kth SR to the MR can be written as
(3)tkol=dkolrk.Similarly, when the MR offloads the data to the BS, the transmission rate is given by(4)rM=BMlog21+pMtrhMNM,where BM is the bandwidth allocated to the MR, pMtr is transmission power allocation at the MR, hM is the mean channel gain between the MR and the BS, and NM is the noise power, which is fixed. According to Equation (4), the time spent on the transmission at the MR is given by tMol=DMol/rM.


### 2.4. Energy Consumption Model

As shown in Figure2, energy needs to be consumed in the three stages of the system. It is worth noting that we assume that the BS has sufficient computing and communication capabilities and energy. In this paper, we focus on the energy consumption of SRs, hence the computation time spent on the feedback from the BS and the energy cost at the BS is neglected.First, According to Section2.1, the energy consumption on sensing is given by Ekss=pksstkss.Next, the energy consumption on local computation at thekth SR is given by
(5)Ekco=dk−dkolCkpkco,where pkco is the power consumption per CPU computing cycle at the kth SR. Similarly, when the MR executes the computation locally, the energy consumption is EMco=dM−dMolCMpMco, where pMco is the power consumption per CPU cycle of computing at the MR.Finally, for convenience, we define a functionfx=Nk2x/B−1, and according to Equation (3), the energy consumed on data transmission at the kth SR and the MR is given by Ektr=pktrtkol=tkol/hkfdkol/tkol and EMtr=pMtrtMol=tMol/hMfDMol/tMol, respectively.Based on the above analysis, the total energy consumption at thekth SR and the MR during the task implementation is given by Ek=Ekss+Ekco+Ektr and EM=EMco+EMtr, respectively.


## 2.1. Data Collection Model

Firstly, MR will allocate different sensing timetkss to each SR based on the information provided by the SR, which is a variable. The amount of collected data bits at the k-th SR is denoted as
(1)dk=pksstkssHk,where Hk represents the energy consumption used to sense one bit [24], and pkss is a constant which denote as the sensing power consumption at the kth SR.


## 2.2. Computation-Offloading Model

Figure2 also shows the direction of data flow and energy consumption in the MRC system. Let dkol denotes the offloaded data bits from the kth SR to the MR, and dM=∑k∈Sdkol as the total received data from SRs.Then, (dk−dkol) bits are the data that need to be processed locally. Moreover, let Wk represents the computation capability of the kth SR, which is the number of central processing unit (CPU) cycles executed per second, and WM as the computation capacity of the MR. Moreever, Ck as the number of CPU cycles is required at the kth SR to calculate 1-bit data, and CM as the number of CPU cycles is required for computing 1-bit of data at the MR. To guarantee the latency constraint, the time spent on local computing should be less than a threshold Tsco.


## 2.3. Communication Model

Consider the TDMA system. According to Shannon formula, the transmission data rate from thek-th SR to the MR is given by
(2)rk=Bklog21+pktrhkNk,where Bk is the channel bandwidth allocated to the kth SR, pktr is the transmission power consumed at SR k, hk denotes the mean channel gain on the wireless channel between SR k and the MR, and Nk is the Gaussian channel noise, which is fixed. It is noteworthy that the channels between the SRs and MR experience both large fading due to the path loss and shadowing and fast fading due to the reflection and diffraction. Based on Equation (2), the time spent on offloading data from the kth SR to the MR can be written as
(3)tkol=dkolrk.Similarly, when the MR offloads the data to the BS, the transmission rate is given by(4)rM=BMlog21+pMtrhMNM,where BM is the bandwidth allocated to the MR, pMtr is transmission power allocation at the MR, hM is the mean channel gain between the MR and the BS, and NM is the noise power, which is fixed. According to Equation (4), the time spent on the transmission at the MR is given by tMol=DMol/rM.


## 2.4. Energy Consumption Model

As shown in Figure2, energy needs to be consumed in the three stages of the system. It is worth noting that we assume that the BS has sufficient computing and communication capabilities and energy. In this paper, we focus on the energy consumption of SRs, hence the computation time spent on the feedback from the BS and the energy cost at the BS is neglected.First, According to Section2.1, the energy consumption on sensing is given by Ekss=pksstkss.Next, the energy consumption on local computation at thekth SR is given by
(5)Ekco=dk−dkolCkpkco,where pkco is the power consumption per CPU computing cycle at the kth SR. Similarly, when the MR executes the computation locally, the energy consumption is EMco=dM−dMolCMpMco, where pMco is the power consumption per CPU cycle of computing at the MR.Finally, for convenience, we define a functionfx=Nk2x/B−1, and according to Equation (3), the energy consumed on data transmission at the kth SR and the MR is given by Ektr=pktrtkol=tkol/hkfdkol/tkol and EMtr=pMtrtMol=tMol/hMfDMol/tMol, respectively.Based on the above analysis, the total energy consumption at thekth SR and the MR during the task implementation is given by Ek=Ekss+Ekco+Ektr and EM=EMco+EMtr, respectively.


## 3. Problem Formulation

The aim of the proposed MEC-based resource allocation scheme in MRC system is to accomplish time-critical tasks while maintaining the function of the system as long as possible. Then, the key problem is how to management sensing data and offload data in each SRs and MR. Furthermore, we define a weighted factorαk associated with the kth SR, which can be expressed as αk=minEkRe/EkRe,k∈S. The factor takes into account the fairness among all SRs. Accordingly, the optimization problem (P1) for the SRs is formulated as
(6)mintKss,dKol,tKol∑k=1KαkEk(7a)s.t.∑k=1Kdk≥D(7b)dk−dkolWk≤Tsco,k∈S(7c)EkRe−Ek≥0,k∈S(7d)Tss≥tkss≥0,k∈S(7e)Tsco≥tkol≥0,k∈S(7f)dk≥0,k∈S(7g)dkol≥0,k∈Swhere EkRe denotes the remaining battery energy at the kth SR, tKs is the sensing time vector of SRs which denoted as tKss=tissi=1K, dKol is the allocated offloading data vector of SRs which represented as dKol=dioli=1K, and tKol is the time vector spent on data offloading with tKol=tioli=1K.In problem (P1), the objective function is set to a min-max problem to improve fairness among SRs. Constraint (7a) is to guarantee the SRs collect the required number of data, (7b) ensures that each SR has an upper limit that spend on the local computing. Similarly, (7d) and (7e) represent the time constraints for the first and second stages, respectively. (7c) is to guarantee that the total power consumption at the kth SR is less than its remaining power.Next, in the third stage, it needs to decide how much data should be offloaded to the BS to minimize the energy consumption. Accordingly, the problem (P2) is written as(8)mintMol,dMolEM(9a)s.t.EMRe−EM≥0(9b)TMco≥tMol≥0(9c)dM−dMolWM≤TMco(9d)dM≥dMol≥0where (9a) is to guarantee that the total power consumption at the MR is less than its remaining battery power, (9b) represents the time constraints for the third stages, (9c) ensures that the time MR spend on the local computation should be less than TMco, and (9d) is to guarantee that the offloaded data bits are less than the total received data bits from SRs.


## 4. Proposed Algorithm

Through the analysis of the (P1), we find the energy consumption of SRs is coupled with constraints (7a) and (7c), which makes it complicated to solve the problem. To decouple these two constraints, the Lagrangian dual method is applied. Then, Lagrangian dual function corresponding to (6) is given by
(10)L=∑k=1KαkEk+∑k=1KηkEk−EkRe,where η=η1,⋯,ηnT is Lagrangian multipliers.According to (10), the dual problem is defined as
(11)maxη≥0mintKss,DKol,tKolL,which is convex on η.After decoupling, we can split the problem (P3) into three subproblems. First, the subproblem (SP1) is to minimize the weighted energy consumption of SRs during the first stage, which is given by(12)mintKss,dK∑k=1Kαk+ηkEksss.t.6a,6d,6fNext, (SP2) is to minimize the weighted energy consumption of SRs during the local computation and task offloading at the second stage, which is given by(13)mindKol,tKol∑k=1Kαk+ηkEkco+Ektrs.t.6b,6e,6gAlgorithm 1
An optimal resource allocation scheme.Initialize: System parameters, MR and BS; set ηk=0; set R=0 as the number of executed tasks.While: MRC system can complete task, i.e., problem (P1) has a feasible solution: The Interior Point Method applied to the (SP1) to obtain the globally optimal solution dR,k∗,tR,kss∗. And BCD method is used to solve the (SP2) to obtain the globally optimal solution dR,kol∗,tR,kol∗; Gradient Descent (GD) method is applied to update parameters ηk; jump to step 4 until convergence; compute total energy consumption of SRs, and update ER,kRe=ER,kRe−ER,k, which represents the remaining energy of each SR after processing the current task; similarly, get the optimal solution dR,Mol∗,tR,Mol∗ by solving the (P2) using BCD method; compute energy consumption ER,M at the MR, and ER,MRe=ER,MRe−ER,M; update R=R+1.With Lagrange multipliers,η, (SP1), and (SP2) are all convex optimization problems. In particular, (SP1) is linear programming problems, which can be solved by the Interior Point Method. The Block Coordinate Descent (BCD) [25] optimization technique can be used to obtain the optimal solution of (SP2). After achieving the optimal solution of the subprime problem E∗,Ekss∗,Ekco∗,Ektr∗, the Lagrange dual problem is a linear programming problem, which is formulated as
(14)maxηLtKss,dKol,tKol,ηs.t.ηk≥0,k∈S.The updating rule in the following Algorithm1 can be applied to derive the optimal η.Based on the Interior Point Method, the solution of (P2) can be achieved and the optimal task offloading and resource management scheme can be derived for the MR since it is a convex optimization problem. According to the above analysis, the optimal joint computation and communication resource scheme is concluded in Algorithm1.


## 5. Numerical Results

In this section, the performance of proposed task and resource allocation scheme is investigated using computer simulation on MATLAB. We will refer to our scheme, i.e., Algorithm1 as “ROOP.” In order to reflect the performance of the algorithm, the robust scheme, which named as “MRC-RP,” we proposed in [23], is considered. The key parameters used in the simulations are listed in Table 1.Table 1
Simulation Parameters.
Number of SR3Number of MR1The initial battery energy of each SR3,4,1 JThe initial battery energy of MR10 JLow power mode threshold0.2 JTs800 msTsco40 msBk,BM10 MHzTMco10 mseks∈18,22 nJ/bitD5×106bitsCk∈100,1000 cycles/bitpkss∈0.05,0.13WFk100,⋯,800 MHzFM2.4 GHzpMco1000×10−11 J/cycleWM2.4×109 cycles/sNk∈−86,−96 dBmCM100 cycles/bitWk∈100,⋯,800×106 cycles/spkco∈100,500×10−11 cycles/bitPass loss model15.3+α×10log10Distance,α=3.75, α=5,distance∈1,100m


### 5.1. ROOP Scheme Performance

Figure3 shows the sensing data size allocation and offloading data size versus the number of accomplished tasks in ROOP. On the one hand, since we define a fairness factor αk, the SR3 with the least battery will hardly participate in the task to save the battery energy. On the other hand, due to good channel conditions of SR2 in this simulation scenario, their transmission energy consumption per bit is lower than local computing. Therefore, SR2 are more inclined to offload more data to the MR. Furthermore, the time limit has a great constraint on the offloading of the SR1, since the SR1 has a bad channel state. Then, the results show that SR1 is not willing to offload.Figure 3
. The sensing data size allocation and data offloading.Figure4 demonstrates the remaining energy at each SR versus the number of implementing tasks. It can be observed that, in ROOP, since SR3 is assigned more tasks, it consumes more energy than MRC-RP. However, SR3 consumes less energy to performing tasks than SR1 and SR2, which means the ROOP scheme is more friendly to the energy-less robots. We can observe in Figure 3 that the overall energy consumption in ROOP is smaller than MRC-RP. And as the number of accomplished tasks increases, more energy would be consumed and the remaining energy at the SRs decreases as well.Figure 4
. The remaining battery energy corresponding to the three SRs.


### 5.2. Performance Comparison

Figure5 depicts the total energy consumption of SRs that complete different numbers of tasks. We consider the baseline greedy offloading policy (GOP) for comprehensive performance comparisons. The specific strategy of the GOP is that the SR will offload as many task bits as time permits. We observe that the total energy consumption of SR for GOP and MRC-RP schemes is always much larger than ROOP when the number of tasks is accumulated, which verifies the effectiveness of our task and resource allocation scheme.Figure 5
The comparison of energy consumption by ROOP, MRC-RP, and GOP.


## 5.1. ROOP Scheme Performance

Figure3 shows the sensing data size allocation and offloading data size versus the number of accomplished tasks in ROOP. On the one hand, since we define a fairness factor αk, the SR3 with the least battery will hardly participate in the task to save the battery energy. On the other hand, due to good channel conditions of SR2 in this simulation scenario, their transmission energy consumption per bit is lower than local computing. Therefore, SR2 are more inclined to offload more data to the MR. Furthermore, the time limit has a great constraint on the offloading of the SR1, since the SR1 has a bad channel state. Then, the results show that SR1 is not willing to offload.Figure 3
. The sensing data size allocation and data offloading.Figure4 demonstrates the remaining energy at each SR versus the number of implementing tasks. It can be observed that, in ROOP, since SR3 is assigned more tasks, it consumes more energy than MRC-RP. However, SR3 consumes less energy to performing tasks than SR1 and SR2, which means the ROOP scheme is more friendly to the energy-less robots. We can observe in Figure 3 that the overall energy consumption in ROOP is smaller than MRC-RP. And as the number of accomplished tasks increases, more energy would be consumed and the remaining energy at the SRs decreases as well.Figure 4
. The remaining battery energy corresponding to the three SRs.


## 5.2. Performance Comparison

Figure5 depicts the total energy consumption of SRs that complete different numbers of tasks. We consider the baseline greedy offloading policy (GOP) for comprehensive performance comparisons. The specific strategy of the GOP is that the SR will offload as many task bits as time permits. We observe that the total energy consumption of SR for GOP and MRC-RP schemes is always much larger than ROOP when the number of tasks is accumulated, which verifies the effectiveness of our task and resource allocation scheme.Figure 5
The comparison of energy consumption by ROOP, MRC-RP, and GOP.


## 6. Conclusion

This work studies task and resource allocation for MRC system. First, a task implementation framework is proposed for MRC system based on MEC. Next, aiming to save the energy of SRs and MR and prolong the MRC system function time, we proposed a time-critical and computation-intensive resource allocation scheme for MEC-based MRC system, in which an MR acts as an edge server to provide computation and communication services to SRs. Simulation results revealed that proposed scheme greatly outperforms the baseline.



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