Arslan, Omur
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Publication Anytime Hierarchical Clustering(2014-04-13) Arslan, Omur; Koditschek, Daniel EWe 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 a local measure of cluster homogeneity that is compatible with a number of commonly used (e.g., single, average, complete) linkage functions. As an alternative to the standard batch algorithms, we present numerical evidence to suggest that appropriate adaptations of this method can yield decentralized, scalable algorithms suitable for distributed/parallel computation of clustering hierarchies and online tracking of clustering trees applicable to large, dynamically changing databases and anomaly detection.Publication Smooth Extensions of Feedback Motion Planners via Reference Governors(2017-05-29) Arslan, Omur; Koditschek, Daniel E.In robotics, it is often practically and theoretically convenient to design motion planners for approximate low-order (e.g., position- or velocity-controlled) robot models first, and then adapt such reference planners to more accurate high-order (e.g., force/torque-controlled) robot models. In this paper, we introduce a novel provably correct approach to extend the applicability of low-order feedback motion planners to high-order robot models, while retaining stability and collision avoidance properties, as well as enforcing additional constraints that are specific to the high-order models. Our smooth extension framework leverages the idea of reference governors to separate the issues of stability and constraint satisfaction, affording a bidirectionally coupled robot-governor system where the robot ensures stability with respect to the governor and the governor enforces state (e.g., collision avoidance) and control (e.g., actuator limits) constraints. We demonstrate example applications of our framework for augmenting path planners and vector field planners to the second-order robot dynamics.Publication Integration of Local Geometry and Metric Information in Sampling-Based Motion Planning(2018-02-25) Pacelli, Vincent; Arslan, Omur; Koditschek, Daniel E.The efficiency of sampling-based motion planning algorithms is dependent on how well a steering procedure is capable of capturing both system dynamics and configuration space geometry to connect sample configurations. This paper considers how metrics describing local system dynamics may be combined with convex subsets of the free space to describe the local behavior of a steering function for sampling-based planners. Subsequently, a framework for using these subsets to extend the steering procedure to incorporate this information is introduced. To demonstrate our framework, three specific metrics are considered: the LQR cost-to-go function, a Gram matrix derived from system linearization, and the Mahalanobis distance of a linear-Gaussian system. Finally, numerical tests are conducted for a second-order linear system, a kinematic unicycle, and a linear-Gaussian system to demonstrate that our framework increases the connectivity of sampling-based planners and allows them to better explore the free space. For more information: Kod*lab.Publication Clustering-Based Robot Navigation and Control(2016-05-16) Arslan, Omur; Guralnik, Dan P; Koditschek, Daniel E.In robotics, it is essential to model and understand the topologies of configuration spaces in order to design provably correct motion planners. The common practice in motion planning for modelling configuration spaces requires either a global, explicit representation of a configuration space in terms of standard geometric and topological models, or an asymptotically dense collection of sample configurations connected by simple paths. In this short note, we present an overview of our recent results that utilize clustering for closing the gap between these two complementary approaches. Traditionally an unsupervised learning method, clustering offers automated tools to discover hidden intrinsic structures in generally complex-shaped and high-dimensional configuration spaces of robotic systems. We demonstrate some potential applications of such clustering tools to the problem of feedback motion planning and control. In particular, we briefly present our use of hierarchical clustering for provably correct, computationally efficient coordinated multirobot motion design, and we briefly describe how robot-centric Voronoi diagrams can be used for provably correct safe robot navigation in forest-like cluttered environments, and for provably correct collision-free coverage and congestion control of heterogeneous disk-shaped robots. For more information: Kod*labPublication Coordinated Robot Navigation via Hierarchical Clustering(2015-07-06) Arslan, Omur; Guralnik, Dan P.; Koditschek, Daniel E.We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the continuous space of configurations to the combinatorial space of trees. We formalize and exploit this relation, developing computationally effective reactive algorithms for navigating through the combinatorial space in concert with geometric realizations for a particular choice of hierarchical clustering method. These constructions yield computationally effective vector field planners for both hierarchically invariant as well as transitional navigation in the configuration space. We apply these methods to the centralized coordination and control of n perfectly sensed and actuated Euclidean spheres in a d-dimensional ambient space (for arbitrary n and d). Given a desired configuration supporting a desired hierarchy, we construct a hybrid controller which is quadratic in n and algebraic in d and prove that its execution brings all but a measure zero set of initial configurations to the desired goal with the guarantee of no collisions along the way.Publication Sensor-Based Legged Robot Homing Using Range-Only Target Localization(2017-12-01) Vasilopoulos, Vasileios; Arslan, Omur; De, Avik; Koditschek, Daniel EThis paper demonstrates a fully sensor-based reactive homing behavior on a physical quadrupedal robot, using onboard sensors, in simple (convex obstacle-cluttered) unknown, GPS-denied environments. Its implementation is enabled by our empirical success in controlling the legged machine to approximate the (abstract) unicycle mechanics assumed by the navigation algorithm, and our proposed method of range-only target localization using particle filters. For more information: Kod*labPublication Clustering-Based Robot Navigation and Control(2016-08-01) Arslan, OmurIn robotics, it is essential to model and understand the topologies of configuration spaces in order to design provably correct motion planners. The common practice in motion planning for modelling configuration spaces requires either a global, explicit representation of a configuration space in terms of standard geometric and topological models, or an asymptotically dense collection of sample configurations connected by simple paths, capturing the connectivity of the underlying space. This dissertation introduces the use of clustering for closing the gap between these two complementary approaches. Traditionally an unsupervised learning method, clustering offers automated tools to discover hidden intrinsic structures in generally complex-shaped and high-dimensional configuration spaces of robotic systems. We demonstrate some potential applications of such clustering tools to the problem of feedback motion planning and control. The first part of the dissertation presents the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. We reinterpret this classical method for unsupervised learning as an abstract formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions, by relating the continuous space of configurations to the combinatorial space of trees. Based on this new abstraction and a careful topological characterization of the associated hierarchical structure, a provably correct, computationally efficient hierarchical navigation framework is proposed for collision-free coordinated motion design towards a designated multirobot configuration via a sequence of hierarchy-preserving local controllers. The second part of the dissertation introduces a new, robot-centric application of Voronoi diagrams to identify a collision-free neighborhood of a robot configuration that captures the local geometric structure of a configuration space around the robot’s instantaneous position. Based on robot-centric Voronoi diagrams, a provably correct, collision-free coverage and congestion control algorithm is proposed for distributed mobile sensing applications of heterogeneous disk-shaped robots; and a sensor-based reactive navigation algorithm is proposed for exact navigation of a disk-shaped robot in forest-like cluttered environments. These results strongly suggest that clustering is, indeed, an effective approach for automatically extracting intrinsic structures in configuration spaces and that it might play a key role in the design of computationally efficient, provably correct motion planners in complex, high-dimensional configuration spaces.Publication Navigation of Distinct Euclidean Particles via Hierarchical Clustering(2014-08-01) Arslan, Omur; Koditschek, Daniel E; Guralnik, Dan P.We present a centralized online (completely reactive) hybrid navigation algorithm for bringing a swarm of n perfectly sensed and actuated 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 cluster hierarchies, and relies upon two prior recent constructions: (i) a family of hierarchy-preserving control policies and (ii) an abstract discrete dynamical system for navigating through the space of cluster hierarchies. Here, we relate the (combinatorial) topology of hierarchical clusters to the (continuous) topology of configurations by constructing “portals” — open sets of configurations supporting two adjacent hierarchies. The resulting online sequential composition of hierarchy-invariant swarming followed by discrete selection of a hierarchy “closer” to that of the destination along with its continuous instantiation via an appropriate portal configuration yields a computationally effective construction for the desired navigation policy.Publication Coordinated Robot Navigation via Hierarchical Clustering(2016-03-21) Arslan, Omur; Guralnik, Dan P.; Koditschek, Daniel E.We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the continuous space of configurations to the combinatorial space of trees. We formalize and exploit this relation, developing computationally effective reactive algorithms for navigating through the combinatorial space in concert with geometric realizations for a particular choice of hierarchical clustering method. These constructions yield computationally effective vector field planners for both hierarchically invariant as well as transitional navigation in the configuration space. We apply these methods to the centralized coordination and control of n perfectly sensed and actuated Euclidean spheres in a d-dimensional ambient space (for arbitrary n and d). Given a desired configuration supporting a desired hierarchy, we construct a hybrid controller which is quadratic in n and algebraic in d and prove that its execution brings all but a measure zero set of initial configurations to the desired goal with the guarantee of no collisions along the way. For more information: Kod*labPublication Sensor-Based Reactive Navigation in Unknown Convex Sphere Worlds(2018-05-28) Arslan, Omur; Koditschek, Daniel E.We construct a sensor-based feedback law that provably solves the real-time collision-free robot navigation problem in a compact convex Euclidean subset cluttered with unknown but sufficiently separated and strongly convex obstacles. Our algorithm introduces a novel use of separating hyperplanes for identifying the robot’s local obstacle-free convex neighborhood, affording a reactive (online-computed) continuous and piecewise smooth closed-loop vector field whose smooth flow brings almost all configurations in the robot’s free space to a designated goal location, with the guarantee of no collisions along the way. Specialized attention to planar navigable environments yields a necessary and sufficient condition on convex obstacles for almost global navigation towards any goal location in the environment. We further extend these provable properties of the planar setting to practically motivated limited range, isotropic and anisotropic sensing models, and the nonholonomically constrained kinematics of the standard differential drive vehicle. We conclude with numerical and experimental evidence demonstrating the effectiveness of the proposed sensory feedback motion planner.