Abstract-We present a novel approach for determining robot movements that efficiently accomplish the robot's tasks while not hindering the movements of people within the environment. Our approach models the goal-directed trajectories of pedestrians using maximum entropy inverse optimal control. The advantage of this modeling approach is the generality of its learned cost function to changes in the environment and to entirely different environments. We employ the predictions of this model of pedestrian trajectories in a novel incremental planner and quantitatively show the improvement in hindrancesensitive robot trajectory planning provided by our approach. I. INTRODUCTIONDetermining appropriate robotic actions in environments with moving people is a well-studied [15], [2], [5], but often difficult task due to the uncertainty of each person's future behavior. Robots should certainly never collide with people [11], but avoiding collisions alone is often unsatisfactory because the disruption of almost colliding can be burdensome to people and sub-optimal for robots. Instead, robots should predict the future locations of people and plan routes that will avoid such hindrances (i.e., situations where the person's natural behavior is disrupted due to a robot's proximity) while still efficiently achieving the robot's objectives. For example, given the origins and target destinations of the robot and person in Figure 1, the robot's hindrance-minimizing trajectory would take the longer way around the center obstacle (a table), leaving a clear path for the pedestrian.One common approach for predicting trajectories is to project the prediction step of a tracking filter [9], [13], [10] forward over time. For example, a Kalman filter's [7] future positions are predicted according to a Gaussian distribution with growing uncertainty and, unfortunately, often high probability for physically impossible locations (e.g., behind walls, within obstacles). Particle filters [16] can incorporate more sophisticated constraints and non-Gaussian distributions, but degrade into random walks of feasible motion over large time horizons rather than purposeful, goal-based motion. Closer to our research are approaches that directly model the policy [6]. These approaches assume that previously observed trajectories capture all purposeful behavior, and the only uncertainty involves determining to which previously observed class of trajectories the current behavior belongs. Models based on mixtures of trajectories and conditioned action distribution modeling (using hidden Markov models) have been employed [17]. This approach often suffers from over-fitting to the particular training trajectories and context of those trajectories. When changes to the environment occur (e.g., rearrangement of the furniture), the model will confidently predict incorrect trajectories through obstacles.

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Abstract-The principle of maximum entropy provides a powerful framework for estimating joint, conditional, and marginal probability distributions. However, there are many important distributions with elements of interaction and feedback where its applicability has not been established. This work presents the principle of maximum causal entropy-an approach based on directed information theory for estimating an unknown process based on its interactions with a known process. We demonstrate the breadth of the approach using two applications: a predictive solution for inverse optimal control in decision processes and computing equilibrium strategies in sequential games.

In many animal societies, groups of individuals form stable social units that are shaped by well-delineated dominance hierarchies and a range of affiliative relationships. How do socially complex groups maintain cohesion and achieve collective movement? Using high-resolution GPS tracking of members of a wild baboon troop, we test whether collective movement in stable social groups is governed by interactions among local neighbours (commonly found in groups with largely anonymous memberships), social affiliates, and/or by individuals paying attention to global group structure. We construct candidate movement prediction models and evaluate their ability to predict the future trajectory of focal individuals. We find that baboon movements are best predicted by 4 to 6 neighbours. While these are generally individuals’ nearest neighbours, we find that baboons have distinct preferences for particular neighbours, and that these social affiliates best predict individual location at longer time scales (>10 minutes). Our results support existing theoretical and empirical studies highlighting the importance of local rules in driving collective outcomes, such as collective departures, in primates. We extend previous studies by elucidating the rules that maintain cohesion in baboons ‘on the move’, as well as the different temporal scales of social interactions that are at play.

We present PROCAB, an efficient method for Probabilistically Reasoning from Observed Context-Aware Behavior. It models the context-dependent utilities and underlying reasons that people take different actions. The model generalizes to unseen situations and scales to incorporate rich contextual information. We train our model using the route preferences of 25 taxi drivers demonstrated in over 100,000 miles of collected data, and demonstrate the performance of our model by inferring: (1) decision at next intersection, (2) route to known destination, and (3) destination given partially traveled route.