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We present a centralized online (completely reactive) hybrid navigation algorithm for bringing a swarm of n perfectly sensed and ac-tuated point particles in Euclidean d space (for arbitrary n and d) to an arbitrary goal configuration with the guarantee of no collisions along the way. Our construction entails a discrete abstraction of configurations using… (More)

— The Spring-Loaded Inverted Pendulum (SLIP) model has long been established as an effective and accurate descriptive model for running animals of widely differing sizes and morphologies, while also serving as a basis for several hopping robot designs. Further research on this model led to the discovery of several analytic approximations to its normally… (More)

— The main driving force behind research on legged robots has always been their potential for high performance lo-comotion on rough terrain and the outdoors. Nevertheless, most existing control algorithms for such robots either make rigid assumptions about their environments (e.g flat ground), or rely on kinematic planning at low speeds. Moreover, the… (More)

In this paper we introduce and study three new measures for efficient discriminative comparison of phylogenetic trees. The NNI navigation dissimilarity d nav counts the steps along a " combing " of the Nearest Neighbor Interchange (NNI) graph of binary hierarchies, providing an efficient approximation to the (NP-hard) NNI distance in terms of " edit length… (More)

— This paper introduces and solves the problem of cluster-hierarchy-invariant particle navigation in Conf R d , J. Namely, we are given a desired goal configuration, x * ∈ Conf R d , J and τ , a specified cluster hierarchy that the goal supports. We build a hybrid closed loop controller guaranteed to bring any other configuration that supports τ to the… (More)

We propose a new anytime hierarchical clustering method that iteratively transforms an arbitrary initial hierarchy on the configuration of measurements along a sequence of trees we prove for a fixed data set must terminate in a chain of nested partitions that satisfies a natural homogeneity requirement. Each recursive step re-edits the tree so as to improve… (More)

In distributed mobile sensing applications, networks of agents that are heterogeneous respecting both actuation as well as body and sensory footprint are often modelled by recourse to power diagrams — generalized Voronoi diagrams with additive weights. In this paper we adapt the body power diagram to introduce its " free subdiagram, " generating a vector… (More)

We reconsider the problem of reactive navigation in sphere worlds, i.e., the construction of a vector field over a compact, convex Euclidean subset punctured by Euclidean disks, whose flow brings a Euclidean disk robot from all but a zero measure set of initial conditions to a designated point destination, with the guarantee of no collisions along the way.… (More)

An elementary geometric construction, known as Napoleon's theorem, produces an equilateral triangle, obtained from equilateral triangles erected on the sides of any initial triangle: The centers of the three equilateral triangles erected on the sides of the arbitrarily given original triangle, all outward or all inward, are the vertices of the new… (More)