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It is known that connected and autonomous vehicles are capable of maintaining shorter headways and distances when they form platoons of vehicles. Thus, such technologies can result in increases in the capacities of traffic networks. Consequently, it is envisioned that their deployment will boost the network mobility. In this paper, we verify the validity of this impact under selfish routing behavior of drivers in traffic networks with mixed autonomy, i.e. traffic networks with both regular and autonomous vehicles. We consider a nonatomic routing game on a network with inelastic (fixed) demands for the set of network O/D pairs, and study how replacing a fraction of regular vehicles by autonomous vehicles will affect the mobility of the network. Using the well known US bureau of public roads (BPR) traffic delay models, we show that the resulting Wardrop equilibrium is not necessarily unique even in its weak sense for networks with mixed autonomy. We state the conditions under which the total network delay is guaranteed not to increase as a result of autonomy increase. However, we show that when these conditions do not hold, counter intuitive behaviors may occur: the total delay can grow by increasing the network autonomy. In particular, we prove that for networks with a single O/D pair, if the road degrees of asymmetry are homogeneous, the total delay is 1) unique, and 2) a nonincreasing continuous function of network autonomy fraction. We show that for heterogeneous degrees of asymmetry, the total delay is not unique, and it can further grow with autonomy increase. We demonstrate that similar behaviors may be observed in networks with multiple O/D pairs. We further bound such performance degradations due to the introduction of autonomy in homogeneous networks.vehicle, capable of maintaining shorter headways; thus, platooning can lead to increases in the capacities of network links [LPTV17]. Such increases can be up to three-fold [LPTV17] if all the vehicles are autonomous and connected. In addition to mobility benefits, platooning can have sustainability benefits, it can also reduce energy consumption for heavy duty vehicles [AAGJ10, LMJ13, ABT + 15].The mobility benefits of platooning and autonomous capabilities of vehicles are not limited to increasing network capacities. There has been a focus on how to utilize vehicle autonomy and connectedness to remove signal lights from intersections and coordinate conflicting movements such that the network throughput is improved [ZMC16, TC15, MK14, FV18]. However, in order for such approaches to be implemented, all vehicles in the network need to have autonomous capabilities. To reach the point where all vehicles are autonomous, transportation networks need to face a transient era, when both regular and autonomous vehicles coexist in the networks. Therefore, it is crucial to study networks with mixed autonomy.In [AFKV16], the performance of traffic networks with mixed autonomy was studied via simulations. Moreover, it was shown in multiple works that in networks with mixe...

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Many robotic applications involve interactions between multiple agents where an agent's decisions affect the behavior of other agents. Such behaviors can be captured by the equilibria of differential games which provide an expressive framework for modeling the agents' mutual influence. However, finding the equilibria of differential games is in general challenging as it involves solving a set of coupled optimal control problems. In this work, we propose to leverage the special structure of multi-agent interactions to generate interactive trajectories by simply solving a single optimal control problem, namely, the optimal control problem associated with minimizing the potential function of the differential game. Our key insight is that for a certain class of multi-agent interactions, the underlying differential game is indeed a potential differential game for which equilibria can be found by solving a single optimal control problem. We introduce such an optimal control problem and build on single-agent trajectory optimization methods to develop a computationally tractable and scalable algorithm for planning multi-agent interactive trajectories. We will demonstrate the performance of our algorithm in simulation and show that our algorithm outperforms the state-of-the-art game solvers. To further show the real-time capabilities of our algorithm, we will demonstrate the application of our proposed algorithm in a set of experiments involving interactive trajectories for two quadcopters.

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In a traffic network, vehicles normally select their routes selfishly. Consequently, traffic networks normally operate at an equilibrium characterized by Wardrop conditions. However, it is well known that equilibria are inefficient in general. In addition to the intrinsic inefficiency of equilibria, the authors recently showed that, in mixed-autonomy networks in which autonomous vehicles maintain a shorter headway than human-driven cars, increasing the fraction of autonomous vehicles in the network may increase the inefficiency of equilibria. In this work, we study the possibility of obviating the inefficiency of equilibria in mixed-autonomy traffic networks via pricing mechanisms. In particular, we study assigning prices to network links such that the overall or social delay of the resulting equilibria is minimum. First, we study the possibility of inducing such optimal equilibria by imposing a set of undifferentiated prices, i.e. a set of prices that treat both humandriven and autonomous vehicles similarly at each link. We provide an example which demonstrates that undifferentiated pricing is not sufficient for achieving minimum social delay. Then, we study differentiated pricing where the price of traversing each link may depend on whether vehicles are human-driven or autonomous. Under differentiated pricing, we prove that link prices obtained from the marginal cost taxation of links will induce equilibria with minimum social delay if the degree of road capacity asymmetry (i.e. the ratio between the road capacity when all vehicles are human-driven and the road capacity when all vehicles are autonomous) is homogeneous among network links.