As the ability of teams of robots to move through complex environments increases we must also consider the problem of wireless network optimization. As previously discussed, there has been considerable research in optimal transport protocols over wireless links, but as the robots move
and the network topology changes, the lower layers of the OSI model, specifically the routing layer, must also adapt.
Some of the first solutions to optimal routing over networks with dynamic topology focused on minimization of the number of hops a packet must take to reach its final destination. These protocols, namely Dynamic Source Routing proposed by Johnson and Maltz [35] and Ad-Hoc On- Demand Distance Vector routing proposed by Perkins et al. in [60], rely on real-time measurements of the channels to infer the network topology and thus determine the routes that result in the minimum number of hops a packet must take. These systems result in sub-optimal solutions when applied to realistic ad-hoc networks, due mostly to the inaccuracy of determining the existence of a link. As demonstrated in [47] by Lundgren et al, there are regions where a probe signal, called the HELLO, can be successfully received over a link but data cannot. This results in a gray-zone where the link is believed to exist but data transmission is impossible.
In the work of De Couto et al, they propose a different metric for optimal routing, called expected transmission count [17]. This metric does not assume that the path with the least hops is optimal; and instead, they characterize the paths by the expected throughput, which they maximize. This approach leads to routing solutions where the optimal route may include more hops but results in significantly higher data throughput, often by a factor of two over the approaches that minimize hop-count.
Other proposed solutions for network optimization rely on a cross layer approach that controls multiple layers of the OSI model simultaneously. While this does violate the abstraction imposed by the OSI model, the interaction between the lower levels of the model in wireless networks is much greater than in traditional wired networks. To that end, one solution proposed by Eryilmaz and Srikant in [20] solves the problem by jointly scheduling the routing and congestion control, in order to provide asymptotic guarantees on the stability of the buffers and the fairness of network resource allocation. This is achieved by sharing the queue lengths across the layers of the network. In another solution which controls the transport, network, and physical layers in unison, Lin
et al. propose a “loosely coupled” cross-layer solution [45]. This solution allows for optimization of the separate layers with minimal inter-layer coordination, which aside from the physical layer can be solved optimally in a distributed manner.
In the spirit of returning the independence of the OSI model, Yi and Shakkottai present a solution that provides congestion control for a multi-hop wireless network by formulating an optimization problem, where one of the constraints is a channel access time constraint to symbolize the time-division strategy used in the lower layers, [94]. They demonstrate that in the absence of delay, this solution provides globally stable results, and in the presence of delay, areas of high load spatially are spread out over the network, resulting in bounds on the peak load of a node.
Just as the trend in communication-aware motion control moved towards probabilistic models of the channel, so to did the field of network optimization. In the work done by Ribeiro et al. in [66], they consider the inter-node links to be random quantities with know mean and variance. This approach lends itself to solutions where the decision of which node a packet is transmitted to next is determined by a probability distribution. They show that this probability distribution can be determined by a convex optimization problem which can be efficiently solved via interior point methods.
Continuing with this approach, Wu et al. proposes an extension where solutions are determined by either maximizing an average utility subject to variance constraints, or minimization of variance subject to minimum average utility [89]. They continue by showing that both of these problems can be formulated as convex optimization problems that can be solved in a distributed manner, due to the separability of the problem. They conclude with a comparison of the resulting solutions to those found by a centralized system showing no performance penalty even with a significant reduction in the overall communication.
This work is further refined by Ribeiro et al. in [67], in which they demonstrate that rate- oriented criteria such as minimum rate, weighted sum of rates, product of rates, and sources rate can be maximized by means of a stochastic routing solution. This solution is obtained by
a distributed algorithm in which dual variable are exchanged and optimality can be guaranteed under mild conditions.