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Convergence of Bayesian Histogram Filters for Location Estimation

We prove convergence of an approximate Bayesian estimator for the (scalar) location estimation problem by recourse to a histogram approximant. We exploit its tractability to present a simple strategy for managing the tradeoff between accuracy and complexity through the cardinality of the underlying partition. Our theoretical results provide explicit (conservative) sufficient conditions under which convergence is guaranteed. Numerical simulations reveal certain extreme cases in which the conditions may be tight, and suggest that this procedure has performance and computational efficiency favorably comparable to particle filters, while affording the aforementioned analytical benefits. We posit that more sophisticated algorithms can make such piecewise-constant representations similarly feasible for very high-dimensional problems.

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Robot Parkour: The Ground Reaction Complex & Dynamic Transitions

Many locomotion tasks on real, complex terrain are poorly modeled as deviations from limit cycles of steady state running. As obstacles become larger and larger relative to leg length, every step is novel and challenging: the leap onto a ledge in Fig. 1 is quite unlike any running step. We seek to organize and systematically reduce this space to a finite set of dynamic transition “words” in order to enable dramatic outdoor transitional behaviors.

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Toward a Vocabulary of Legged Leaping

As dynamic robot behaviors become more capable and well understood, the need arises for a wide variety of equally capable and systematically applicable transitions between them. We use a hybrid systems framework to characterize the dynamic transitions of a planar “legged” rigid body from rest on level ground to a fully aerial state. The various contact conditions fit together to form a topologically regular structure, the “ground reaction complex”. The body’s actuated dynamics excite multifarious transitions between the cells of this complex, whose regular adjacency relations index naturally the resulting “leaps” (path sequences through the cells from rest to free flight). We exhibit on a RHex robot some of the most interesting “words” formed by these achievable path sequences, documenting unprecedented levels of performance and new application possibilities that illustrate the value of understanding and expressing this vocabulary systematically.

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Toward Dynamical Sensor Management for Reactive Wall-following

We propose a new paradigm for reactive wallfollowing by a planar robot taking the form of an actively steered sensor model that augments the robot’s motion dynamics. We postulate a foveated sensor capable of delivering third-order infinitesimal (range, tangent, and curvature) data at a point along a wall (modeled as an unknown smooth plane curve) specified by the angle of the ray from the robot’s body that first intersects it. We develop feedback policies for the coupled (point or unicycle) sensorimotor system that drive the sensor’s foveal angle as a function of the instantaneous infinitesimal data, in accord with the trade-off between a desired standoff and progress-rate as the wall’s curvature varies unpredictably in the manner of an unmodeled noise signal. We prove that in any neighborhood within which the thirdorder infinitesimal data accurately predicts the local “shape” of the wall, neither robot will ever hit it. We empirically demonstrate with comparative physical studies that the new active sensor management strategy yields superior average tracking performance and avoids catastrophic collisions or wall losses relative to the passive sensor variant.

This work was supported by AFOSR MURI FA9550–10–1−0567.

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Free-Standing Leaping Experiments with a Power-Autonomous, Elastic-Spined Quadruped

We document initial experiments with Canid, a freestanding, power-autonomous quadrupedal robot equipped with a parallel actuated elastic spine. Research into robotic bounding and galloping platforms holds scientific and engineering interest because it can both probe biological hypotheses regarding bounding and galloping mammals and also provide the engineering community with a new class of agile, efficient and rapidly-locomoting legged robots. We detail the design features of Canid that promote our goals of agile operation in a relatively cheap, conventionally prototyped, commercial off-the-shelf actuated platform. We introduce new measurement methodology aimed at capturing our robot’s “body energy” during real time operation as a means of quantifying its potential for agile behavior. Finally, we present joint motor, inertial and motion capture data taken from Canid’s initial leaps into highly energetic regimes exhibiting large accelerations that illustrate the use of this measure and suggest its future potential as a platform for developing efficient, stable, hence useful bounding gaits.

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Legged Self-Manipulation

This paper introduces self-manipulation as a new formal design methodology for legged robots with varying ground interactions…

This work was supported by the ARL/GDRS RCTA project under Cooperative Agreement Number W911NF-10–2−0016.

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Variable Stiffness Legs for Robust, Efficient, and Stable Dynamic Running

Humans and animals adapt their leg impedance during running for both internal (e.g., loading) and external (e.g., surface) changes. To date, the mechanical complexity of designing usefully robust tunable passive compliance into legs has precluded their implementation on practical running robots. This work describes the design of novel, structure-controlled stiffness legs for a hexapedal running robot to enable runtime modification of leg stiffness in a small, lightweight, and rugged package. As part of this investigation, we also study the effect of varying leg stiffness on the performance of a dynamical running robot.

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Standing Self-Manipulation for a Legged Robot

On challenging, uneven terrain a legged robot’s open loop posture will almost inevitably be inefficient, due to uncoordinated support of gravitational loads with coupled internal torques. By reasoning about certain structural properties governing the infinitesimal kinematics of the closed chains arising from a typical stance, we have developed a computationally trivial self-manipulation behavior that can minimize both internal and external torques absent any terrain information. The key to this behavior is a change of basis in torque space that approximates the partially decoupled nature of the two types of disturbances. The new coordinates reveal how to use actuator current measurements as proprioceptive sensors for the approximate gradients of both the internal and external task potential fields, without recourse to further modeling. The behavior is derived using a manipulation framework informed by the dual relationship between a legged robot and a multifingered hand. We implement the reactive posture controller resulting from simple online descent along these proprioceptively sensed gradients on the X-RHex robot to document the significant savings in standing power.

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Toward a Memory Model for Autonomous Topological Mapping and Navigation:

We propose a self-organizing database for per- ceptual experience capable of supporting autonomous goal- directed planning. The main contributions are: (i) a formal demonstration that the database is complex enough in principle to represent the homotopy type of the sensed environment; (ii) some initial steps toward a formal demonstration that the database offers a computationally effective, contractible approximation suitable for motion planning that can be ac- cumulated purely from autonomous sensory experience. The provable properties of an effectively trained data-base exploit certain notions of convexity that have been recently generalized for application to a symbolic (discrete) representation of subset nesting relations. We conclude by introducing a learning scheme that we conjecture (but cannot yet prove) will be capable of achieving the required training, assuming a rich enough exposure to the environment.

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