# Resource Assignment Algorithms for Autonomous Mobile Robots with Task Offloading
## 2 Literature Review  
The problem of jointly managing the radio and computational resources, and finding an optimal assignment for multiple users, has already been coped with in recent works. Thus, for the sake of brevity, only a selection of recent papers is reviewed in the following. In [16], the authors propose an iterative algorithm to solve the nonconvex problem of optimizing the radio and computation resource assignment among a group of users, while considering bounds on latency and energy consumption. Their algorithm adopts successive convex approximations to achieve the suboptimal solution. They also show that, by leveraging the multiple-input multiple-output (MIMO) capabilities of the BSs, the energy efficiency of the terminals is maximized and the handovers are carefully handled. The same authors also propose another similar method in [17], which is suitable for a distributed implementation in the radio cell controllers. [PERSON] et al. [18] decide to assign communication and computation resources to web cameras that provide a multi-view scene to a fog computing system. The quadratic mixed-integer optimization problem is intractable and they propose an approximation using the Dyer-Zemel algorithm, which is further simplified into an iterative algorithm. A branch-and-bound solution of the mixed-integer nonlinear programming (MINLP) resource allocation problem is presented in [19], which also introduces a solution based on the Gini coefficient, with a predictable polynomial complexity, and may employ a local execution of the task. The authors of [20] consider resource allocation as a game between users and cloud providers, constrained on service delay, transmission quality, and power control. The MINLP problem is solved using a student-project allocation matching game, which may also evolve into user-oriented cooperation to find the optimal solution. [PERSON] and [PERSON] [21] optimize uplink transmission power, receive beamforming, computation task assignment, and computation resource allocation by reformulating the MINLP into a dual problem solved with the coordinate descent method. The authors of [13] employ a queuing model to describe a complex scenario of thousands of users offloading video-based tasks through Wi-Fi to edge servers. They model also the capacity bottlenecks and present a resource optimization solution using Pareto-optimal edges. In [22], the authors propose EdgeFlow, a mobile edge/cloud computing system, which minimizes the latency by considering two different states and simple convex optimization. [PERSON] et al. [23] transform the mixed-binary nonlinear programming (MBNLP) problem into a geometric programming problem and try to solve this using general bender decomposition. To reduce complexity, this solution is simplified with a recursive algorithm that exploits also some randomness. The authors of [24] show how to simultaneously meet the request of sensing, communication, and computation by employing a carefully crafted wireless scheduling architecture. They rely on multi-attribute decision-making theory to express the problem, reformulated as a two-sided matching problem, and the solution is found in an iterative manner through a modified matching technique. [PERSON] et al. [14] investigate an ultra-low-latency communication scheme that involves packet request rates, computation latency and rates, communication power, data length, and transmission information amounts. The nondeterministic polynomial (NP)-hard problem is simplified and solved thanks to successive convex approximations, and the efficiency is verified through monotonic optimization. More recently, in [25], the authors propose to execute locally or to offload to neighboring robots some tasks generated by a network of sensors, for jointly minimizing end-to-end delay and energy consumption. They use a deep reinforcement learning approach to plan the best offloading pattern and trajectory of each robot in a restricted scenario, after formulating the problem as a Markov decision process.