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... taken into account. This problem is generally referred to as “asteroid avoidance”, and approaches typically extrapolate the observed velocities in order to estimate the future positions of obstacles =-=[8, 9, 12, 19, 21, 27]-=-. The problem of collision avoidance becomes harder when the obstacles are not simply moving without considering their environment, but are also intelligent decision-making entities that try to avoid ...

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... and a local planner reacts to the dynamic component of the environment [17, 18, 35]. One attempt to extend the local planner to uncertain environments is the Probabilistic Velocity Obstacle approach =-=[26]-=-, where uncertainty associated with the obstacle geometry and velocity vector is used to artificially grow the velocity obstacle in an open-loop fashion. Planning algorithms for stochastic systems hav...

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...a notion of uncertainty in the future behavior of other vehicles through probabilistic trajectory models, but these too are heavily biased towards the vehicles continuing their exact current behavior =-=[10]-=-. Sometimes, such models are the best we can do as we have no additional information to draw upon, but in structured environments such as roads and intersections we can exploit this structure to gener...

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...lly by attempting to incorporate the reactive behavior of the other entities in the environment. Variations such as reciprocal velocity obstacles [6], [12], recursive probabilistic velocity obstacles =-=[13]-=-, [14], and common velocity obstacles [15] use various means to handle reciprocity, but each have their own shortcomings. Specifically, the approach of [14] may fail to converge, while other concepts ...

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...he set of colliding relative velocities between robot and moving object. Under the assumption of constant velocities, any relative velocity within the VO is causing a collision. The VO is extended in =-=[13]-=- by a probabilistic version (PVO), where the perception system is modeled probabilistically while the obstacle model itself remains deterministic. Modeling of dynamic obstacles is also extensively cov...

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...s what may be a safe escape maneuver with respect to one obstacle may be a collision course with respect to another obstacle. In [13], velocity obstacles are defined for the special case of a car-like robot that controls its speed and turning radius, and incorporates second-order constraints on the speed. Other related concepts include non-linear velocity obstacles [16] and generalized velocity obstacles [20]. The former accounts for higher-order motion of obstacles, while the latter defines “control input obstacles” for kinematically constrained robots. The probabilistic velocity obstacle of [6] addresses uncertainty in the future trajectory of obstacles. Existing approaches that address reciprocal collision avoidance include [1], [17], [10], [18]. The approach of [19] guarantees collision avoidance for multiple robots. However, none of these approaches deal with acceleration constraints. We will combine the approach of [19] with accelerationvelocity obstacles to guarantee collision-free navigation of multiple robots subject to acceleration constraints. A. Notation We will use the following notational convention in this paper: Scalars x are set in lower case italics, vectors x in low...

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...leoperator exceeded that of the autonomous navigation algorithm. C. Description of Untested Navigation Algorithms We survey existing navigation approaches and explain why our test algorithms are sufficiently representative. Inevitable collision states (ICS) are limited to deterministic settings, and so are inapplicable. Probabilistic ICS ([35]) is designed to handle predictive uncertainty. However, Probabilistic ICS is a special case of [14], and so V-B.1 (our noncooperative planner) is representative. Velocity obstacles (VOs) are limited to deterministic scenarios, and thus inappropriate. In [36], VOs are generalized for noise. However, Probabilistic VOs use linear extrapolation, and so V-B.1 is representative. We tested reciprocal velocity obstacles (RVOs, [37]). However, noisy pedestrian tracks caused RVO to behave erratically (unresponsive to a single person walking directly at the robot), and RVO assumes all agents choose velocities in a pre-specified manner, which is untrue for humans. Furthermore, we adjusted the value of the collision cone to be less aggressive; nevertheless, RVO still struggled with natural human environments. Although other modifications may indeed make this ...