We study the sparsity and optimality properties of crowd navigation and find that existing techniques do not satisfy both criteria simultaneously: either they achieve optimality with a prohibitive number of samples or tractability assumptions make them fragile to catastrophe. For example, if the human and robot are modeled independently, then tractability is attained but the planner is prone to overcautious or overaggressive behavior. For sampling based motion planning of joint human-robot cost functions, for @math agents and @math step lookahead, @math samples are needed for coverage of the action space. Advanced approaches statically partition the action space into free-space and then sample in those convex regions. However, if the human is into free-space, then the partition is misleading and sampling is unsafe: free space will soon be occupied. We diagnose the cause of these deficiencies---optimization happens over space---and propose a novel solution: optimize over trajectory space by using a Gaussian process (GP) basis. We exploit the "kernel trick" of GPs, where a continuum of trajectories are captured with a mean and covariance function. By using the mean and covariance as proxies for a trajectory family we reason about collective trajectory behavior without resorting to sampling. The GP basis is sparse and optimal with respect to collision avoidance and robot and crowd intention and flexibility. GP sparsity leans heavily on the insight that joint action space decomposes into free regions; however, the decomposition contains feasible solutions only if the partition is dynamically generated. We call our approach .
@cite_45: We consider the problem of navigating a mobile robot through dense human crowds. We begin by exploring a fundamental impediment to classical motion planning algorithms called the âfreezing robot problemâ: once the environment surpasses a certain level of dynamic complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place or performs unnecessary maneuvers to avoid collisions. We argue that this problem can be avoided if the robot anticipates human cooperation, and accordingly we develop interacting Gaussian processes, a prediction density that captures cooperative collision avoidance, and a âmultiple goalâ extension that models the goal-driven nature of human decision making. We validate this model with an empirical study of robot navigation in dense human crowds 488 runs, specifically testing how cooperation models effect navigation performance. The multiple goal interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities nearing 0.8 humans m2, while a state-of-the-art non-cooperative planner exhibits unsafe behavior more than three times as often as the multiple goal extension, and twice as often as the basic interacting Gaussian process approach. Furthermore, a reactive planner based on the widely used dynamic window approach proves insufficient for crowd densities above 0.55 people m2. We also show that our non-cooperative planner or our reactive planner capture the salient characteristics of nearly any dynamic navigation algorithm. Based on these experimental results and theoretical observations, we conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.
@cite_55: Mobile robots are increasingly populating our human environments. To interact with humans in a socially compliant way, these robots need to understand and comply with mutually accepted rules. In this paper, we present a novel approach to model the cooperative navigation behavior of humans. We model their behavior in terms of a mixture distribution that captures both the discrete navigation decisions, such as going left or going right, as well as the natural variance of human trajectories. Our approach learns the model parameters of this distribution that match, in expectation, the observed behavior in terms of user-defined features. To compute the feature expectations over the resulting high-dimensional continuous distributions, we use Hamiltonian Markov chain Monte Carlo sampling. Furthermore, we rely on a Voronoi graph of the environment to efficiently explore the space of trajectories from the robot's current position to its target position. Using the proposed model, our method is able to imitate the behavior of pedestrians or, alternatively, to replicate a specific behavior that was taught by tele-operation in the target environment of the robot. We implemented our approach on a real mobile robot and demonstrated that it is able to successfully navigate in an office environment in the presence of humans. An extensive set of experiments suggests that our technique outperforms state-of-the-art methods to model the behavior of pedestrians, which also makes it applicable to fields such as behavioral science or computer graphics.
@cite_42: In this paper, we present a formal approach to reciprocal n-body collision avoidance, where multiple mobile robots need to avoid collisions with each other while moving in a common workspace. In our formulation, each robot acts fully independently, and does not communicate with other robots. Based on the definition of velocity obstacles [5], we derive sufficient conditions for collision-free motion by reducing the problem to solving a low-dimensional linear program. We test our approach on several dense and complex simulation scenarios involving thousands of robots and compute collision-free actions for all of them in only a few milliseconds. To the best of our knowledge, this method is the first that can guarantee local collision-free motion for a large number of robots in a cluttered workspace.
@cite_17: We present the hybrid reciprocal velocity obstacle for collision-free and oscillation-free navigation of multiple mobile robots or virtual agents. Each robot senses its surroundings and acts independently without central coordination or communication with other robots. Our approach uses both the current position and the velocity of other robots to compute their future trajectories in order to avoid collisions. Moreover, our approach is reciprocal and avoids oscillations by explicitly taking into account that the other robots sense their surroundings as well and change their trajectories accordingly. We apply hybrid reciprocal velocity obstacles to iRobot Create mobile robots and demonstrate direct, collision-free, and oscillation-free navigation.
@cite_55 pure sampling is observed to be ineffective for coupled models; some mechanism is required to guide sampling ( @cite_42 @cite_17 makes a similar observation, but RVO HRVO was shown brittle to noise and motion ambiguity in @cite_45 ). To guide sampling, Voronoi techniques applied to static obstacles parses the action space into convex regions. However, static Voronoi techniques (or any static convex region identifier) leads to suboptimal strategies: by ignoring motion, a human-robot decoupling assumption is made. In reactive environments, free space is dynamically generated by the probabilistic interplay of human and robot trajectory distributions (see Figure ). Sparse IGP ( @math ) achieves this high level interaction, establishing sparsity and optimality guarantees in the process.