Asynchronous approach in the plane: A deterministic polynomial algorithm

In this paper we study the task of approach of two mobile agents having the same limited range of vision and moving asynchronously in the plane. This task consists in getting them in finite time within each other's range of vision. The agents execute the same deterministic algorithm and are assumed to have a compass showing the cardinal directions as well as a unit measure. On the other hand, they do not share any global coordinates system (like GPS), cannot communicate and have distinct labels. Each agent knows its label but does not know the label of the other agent or the initial position of the other agent relative to its own. The route of an agent is a sequence of segments that are subsequently traversed in order to achieve approach. For each agent, the computation of its route depends only on its algorithm and its label. An adversary chooses the initial positions of both agents in the plane and controls the way each of them moves along every segment of the routes, in particular by arbitrarily varying the speeds of the agents. A deterministic approach algorithm is a deterministic algorithm that always allows two agents with any distinct labels to solve the task of approach regardless of the choices and the behavior of the adversary. The cost of a complete execution of an approach algorithm is the length of both parts of route travelled by the agents until approach is completed. Let $\Delta$ and $l$ be the initial distance separating the agents and the length of the shortest label, respectively. Assuming that $\Delta$ and $l$ are unknown to both agents, does there exist a deterministic approach algorithm always working at a cost that is polynomial in $\Delta$ and $l$? In this paper, we provide a positive answer to the above question by designing such an algorithm

Learning Interpretable Spatial Operations in a Rich 3D Blocks World

In this paper, we study the problem of mapping natural language instructions to complex spatial actions in a 3D blocks world. We first introduce a new dataset that pairs complex 3D spatial operations to rich natural language descriptions that require complex spatial and pragmatic interpretations such as "mirroring", "twisting", and "balancing". This dataset, built on the simulation environment of Bisk, Yuret, and Marcu (2016), attains language that is significantly richer and more complex, while also doubling the size of the original dataset in the 2D environment with 100 new world configurations and 250,000 tokens. In addition, we propose a new neural architecture that achieves competitive results while automatically discovering an inventory of interpretable spatial operations (Figure 5)Comment: AAAI 201

Navigating Your Way! Increasing the Freedom of Choice During Wayfinding

Using navigation assistance systems has become widespread and scholars have tried to mitigate potentially adverse effects on spatial cognition these systems may have due to the division of attention they require. In order to nudge the user to engage more with the environment, we propose a novel navigation paradigm called Free Choice Navigation balancing the number of free choices, route length and number of instructions given. We test the viability of this approach by means of an agent-based simulation for three different cities. Environmental spatial abilities and spatial confidence are the two most important modeled features of our agents. Our results are very promising: Agents could decide freely at more than 50% of all junctions. More than 90% of the agents reached their destination within an average distance of about 125% shortest path length