When multiple robots operate in the same environment, it is desirable for scalability purposes to coordinate their motion in a distributed fashion while providing guarantees about their safety. If the robots have to respect second-order dynamics, this becomes a challenging problem, even for static environments. This work presents a replanning framework where each robot computes partial plans during each cycle, while executing a previously computed trajectory. Each robot communicates with its neighbors to select a trajectory that is safe over an infinite time horizon. The proposed approach does not require synchronization and allows the robots to dynamically change their cycles over time. This paper proves that the proposed motion coordination algorithm guarantees safety under this general setting. This framework is not specific to the underlying robot dynamics, as it can be used with a variety of dynamical systems, nor to the planning or control algorithm used to generate the robot trajectories. The performance of the approach is evaluated using a distributed multi-robot simulator on a computing cluster, where the simulated robots are forced to communicate by exchanging messages. The simulation results confirm the safety of the algorithm in various environments with up to 32 robots governed by second-order dynamics.

No abstract

Abstract-Partially-Observable Markov Decision Processes (POMDPs) are used in many robotic task classes from soccer to household chores. Determining an approximately optimal action policy for POMDPs is PSPACE-complete, and the exponential growth of computation time prohibits solving large tasks. This paper describes two techniques to extend the range of robotic tasks that can be solved using a POMDP. Our first technique reduces the motion constraints of a robot, and then uses state-of-the-art robotic motion planning techniques to respect the true motion constraints at runtime. We then propose a novel task decomposition that can be applied to some indoor robotic tasks. This decomposition transforms a long time horizon task into a set of shorter tasks.We empirically demonstrate the performance gain provided by these two techniques through simulated execution in a variety of environments. Comparing a direct formulation of a POMDP to solving our proposed reductions, we conclude that the techniques proposed in this paper can provide significant enhancement to current POMDP solution techniques, extending the POMDP instances that can be solved to include large, continuous-state robotic tasks.

Abstract-Partially-Observable Markov Decision Processes (POMDPs) are a problem class with significant applicability to robotics when considering the uncertainty present in the real world, however, they quickly become intractable for large state and action spaces. A method to create a less complex but accurate action model approximation is proposed and evaluated using a state-of-the-art POMDP solver. We apply this general and powerful formulation to a robotic navigation task under state and sensing uncertainty. Results show that this method can provide a useful action model that yields a policy with similar overall expected reward compared to the true action model, often with significant computational savings. In some cases, our reduced complexity model can solve problems where the true model is too complex to find a policy that accomplishes the task. We conclude that this technique of building problem-dependent approximations can provide significant computational advantages and can help expand the complexity of problems that can be considered using current POMDP techniques.