Reasoning about human motion is an important prerequisite to safe and socially-aware robotic navigation. As a result, multi-agent behavior prediction has become a core component of modern human-robot interactive systems, such as self-driving cars. While there exist many methods for trajectory forecasting, most do not enforce dynamic constraints and do not account for environmental information (e.g., maps). Towards this end, we present Trajectron++, a modular, graph-structured recurrent model that forecasts the trajectories of a general number of diverse agents while incorporating agent dynamics and heterogeneous data (e.g., semantic maps). Trajectron++ is designed to be tightly integrated with robotic planning and control frameworks; for example, it can produce predictions that are optionally conditioned on ego-agent motion plans. We demonstrate its performance on several challenging real-world trajectory forecasting datasets, outperforming a wide array of state-ofthe-art deterministic and generative methods.

In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a “lazy” dynamic programming recursion on a predetermined number of probabilistically-drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As such, this algorithm combines features of both single-query algorithms (chiefly RRT) and multiple-query algorithms (chiefly PRM), and is reminiscent of the Fast Marching Method for the solution of Eikonal equations. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence rate bounds—the first in the field of optimal sampling-based motion planning. Specifically, for a certain selection of tuning parameters and configuration spaces, we obtain a convergence rate bound of order O(n−1/d+ρ), where n is the number of sampled points, d is the dimension of the configuration space, and ρ is an arbitrarily small constant. We go on to demonstrate asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius. Numerical experiments over a range of dimensions and obstacle configurations confirm our the-oretical and heuristic arguments by showing that FMT*, for a given execution time, returns substantially better solutions than either PRM* or RRT*, especially in high-dimensional configuration spaces and in scenarios where collision-checking is expensive.

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Developing safe human-robot interaction systems is a necessary step towards the widespread integration of autonomous agents in society. A key component of such systems is the ability to reason about the many potential futures (e.g. trajectories) of other agents in the scene. Towards this end, we present the Trajectron, a graph-structured model that predicts many potential future trajectories of multiple agents simultaneously in both highly dynamic and multimodal scenarios (i.e. where the number of agents in the scene is time-varying and there are many possible highlydistinct futures for each agent). It combines tools from recurrent sequence modeling and variational deep generative modeling to produce a distribution of future trajectories for each agent in a scene. We demonstrate the performance of our model on several datasets, obtaining state-of-the-art results on standard trajectory prediction metrics as well as introducing a new metric for comparing models that output distributions.

The objective of this work is to provide analytical guidelines and financial justification for the design of shared-vehicle mobility-on-demand systems. Specifically, we consider the fundamental issue of determining the appropriate number of vehicles to field in the fleet, and estimate the financial benefits of several models of car sharing. As a case study, we consider replacing all modes of personal transportation in a city such as Singapore with a fleet of shared automated vehicles, able to drive themselves, e.g., to move to a customer's location. Using actual transportation data, our analysis suggests a shared-vehicle mobility solution can meet the personal mobility needs of the entire population with a fleet whose size is approximately 1/3 of the total number of passenger vehicles currently in operation.

In this paper we develop methods for maximizing the throughput of a mobility-on-demand urban transportation system. We consider a finite group of shared vehicles, located at a set of stations. Users arrive at the stations, pick-up vehicles, and drive (or are driven) to their destination station where they drop-off the vehicle. When some origins and destinations are more popular than others, the system will inevitably become out of balance: Vehicles will build up at some stations, and become depleted at others. We propose a robotic solution to this rebalancing problem that involves empty robotic vehicles autonomously driving between stations. Specifically, we develop a rebalancing policy that lets every station reach an equilibrium in which there are excess vehicles and no waiting customers and that minimizes the number of robotic vehicles performing rebalancing trips. To do this, we utilize a fluid model for the customers and vehicles in the system. We then show that the optimal rebalancing policy can be found as the solution to a linear program. We use this solution to develop a real-time rebalancing policy which can operate in highly variable environments. We verify policy performance in a simulated mobility-on-demand environment and in hardware experiments.

Abstract-In this paper we present and analyze a queueingtheoretical model for autonomous mobility-on-demand (MOD) systems where robotic, self-driving vehicles transport customers within an urban environment and rebalance themselves to ensure acceptable quality of service throughout the entire network. We cast an autonomous MOD system within a closed Jackson network model with passenger loss. It is shown that an optimal rebalancing algorithm minimizing the number of (autonomously) rebalancing vehicles and keeping vehicles availabilities balanced throughout the network can be found by solving a linear program. The theoretical insights are used to design a robust, real-time rebalancing algorithm, which is applied to a case study of New York City. The case study shows that the current taxi demand in Manhattan can be met with about 8,000 robotic vehicles (roughly 60% of the size of the current taxi fleet). Finally, we extend our queueing-theoretical setup to include congestion effects, and we study the impact of autonomously rebalancing vehicles on overall congestion. Collectively, this paper provides a rigorous approach to the problem of system-wide coordination of autonomously driving vehicles, and provides one of the first characterizations of the sustainability benefits of robotic transportation networks.

A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or deterministically to uniformly cover the state space. Yet, the motion of many robotic systems is often restricted to "small" regions of the state space, due to, for example, differential constraints or collision-avoidance constraints. To accelerate the planning process, it is thus desirable to devise non-uniform sampling strategies that favor sampling in those regions where an optimal solution might lie. This paper proposes a methodology for non-uniform sampling, whereby a sampling distribution is learned from demonstrations, and then used to bias sampling. The sampling distribution is computed through a conditional variational autoencoder, allowing sample generation from the latent space conditioned on the specific planning problem. This methodology is general, can be used in combination with any samplingbased planner, and can effectively exploit the underlying structure of a planning problem while maintaining the theoretical guarantees of sampling-based approaches. Specifically, on several planning problems, the proposed methodology is shown to effectively learn representations for the relevant regions of the state space, resulting in an order of magnitude improvement in terms of success rate and convergence to the optimal cost. * These authors contributed equally to this work.This work was originally presented at the 2018 IEEE International Conference on Robotics and Automation (ICRA). This extended version includes new numerical experiments demonstrating generalization, iterative retraining of the generative model, and multirobot planning experiments.