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Design Principles for a Family of Direct-Drive Legged Robots

This letter introduces Minitaur, a dynamically running and leaping quadruped, which represents a novel class of direct-drive (DD) legged robots. We present a methodology that achieves the well-known benefits of DD robot design (transparency, mechanical robustness/efficiency, high-actuation bandwidth, and increased specific power), affording highly energetic behaviors across our family of machines despite severe limitations in specific force. We quantify DD drivetrain benefits using a variety of metrics, compare our machines’ performance to previously reported legged platforms, and speculate on the potential broad-reaching value of “transparency” for legged locomotion.

For more information: Kod*lab.

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An Empirical Investigation of Legged Transitional Maneuvers Leveraging Raibert’s Scissor

We empirically investigate the implications of applying Raibert’s Scissor algorithm to the Spring Loaded Inverted Pendulum (SLIP) model in combination with other controllers to achieve transitional maneuvers. Specifically, we are interested in how the conjectured neutral stability of Raibert’s algorithm allows combined controllers to push the system’s operating point around the state space without needing to expend limited control affordance in overcoming its stability or compensating for its instability. We demonstrate 2 cases where this facilitates the construction of interesting transitional controllers on a physical robot. In the first we use the motors in stance to maximize the rate of change of the body energy; in the second we take advantage of the local environmental energy landscape to push the robot’s operating point to a higher or lower energy level without expending valuable motor affordance. We present data bearing on the energetic performance of these approaches in executing an accelerate-and-leap maneuver on a monopedal hopping robot affixed to a boom in comparison to the cost of anchoring the robot to the SLIP template.

For more information: Kod*lab

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Leg Design for Energy Management in an Electromechanical Robot

This paper examines the design of a parallel spring-loaded actuated linkage intended for dynamically dexterous legged robotics applications. Targeted at toe placement in the sagittal plane, the mechanism applies two direct-drive brushless dc motors to a symmetric five bar linkage arranged to power free tangential motion and compliant radial motion associated with running, leaping, and related agile locomotion behaviors. Whereas traditional leg design typically decouples the consideration of motor sizing, kinematics and compliance, we examine their conjoined influence on three key characteristics of the legged locomotion cycle: transducing battery energy to body energy during stance; mitigating collision losses upon toe touchdown; and storing and harvesting prior body energy in the spring during stance. This analysis leads to an unconventional design whose “knee” joint rides above the “hip” joint. Experiments demonstrate that the resulting mechanism can deliver more than half again as much kinetic energy to the body (or more than double the kinetic energy if the full workspace is used), and offers a five-fold increase in energy storage and collision efficiency relative to the conventional design.

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A drift-diffusion model for robotic obstacle avoidance

We develop a stochastic framework for modeling and analysis of robot navigation in the presence of obstacles. We show that, with appropriate assumptions, the probability of a robot avoiding a given obstacle can be reduced to a function of a single dimensionless parameter which captures all relevant quantities of the problem. This parameter is analogous to the Peclet number considered in the literature on mass transport in advection-diffusion fluid flows. Using the framework we also compute statistics of the time required to escape an obstacle in an informative case. The results of the computation show that adding noise to the navigation strategy can improve performance. Finally, we present experimental results that illustrate these performance improvements on a robotic platform.

For more information: Kod*Lab

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Coordinated Robot Navigation via Hierarchical Clustering

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.

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Semi-autonomous exploration of multi-floor buildings with a legged robot

This paper presents preliminary results of a semi-autonomous building exploration behavior using the hexapedal robot RHex. Stairwells are used in virtually all multi-floor buildings, and so in order for a mobile robot to effectively explore, map, clear, monitor, or patrol such buildings it must be able to ascend and descend stairwells. However most conventional mobile robots based on a wheeled platform are unable to traverse stairwells, motivating use of the more mobile legged machine. This semi-autonomous behavior uses a human driver to provide steering input to the robot, as would be the case in, e.g., a tele-operated building exploration mission. The gait selection and transitions between the walking and stair climbing gaits are entirely autonomous. This implementation uses an RGBD camera for stair acquisition, which offers several advantages over a previously documented detector based on a laser range finder, including significantly reduced acquisition time. The sensor package used here also allows for considerable expansion of this behavior. For example, complete automation of the building exploration task driven by a mapping algorithm and higher level planner is presently under development.

For more information: Kod*lab

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Parallel Composition of Templates for Tail-Energized Planar Hopping

We have built a 4DOF tailed monoped that hops along a boom permitting free sagittal plane motion. This underactuated platform is powered by a hip motor that adjusts leg touchdown angle in flight and balance in stance, along with a tail motor that adjusts body shape in flight and drives energy into the passive leg shank spring during stance. The motor control signals arise from the application in parallel of four simple, completely decoupled 1DOF feedback laws that provably stabilize in isolation four corresponding 1DOF abstract reference plants. Each of these abstract 1DOF closedloopdynamicsrepresentssomesimplebutcrucialspecific component of the locomotion task at hand. We present a partial proof of correctness for this parallel composition of “template” reference systems along with data from the physical platform suggesting these templates are “anchored” as evidenced by the correspondence of their characteristic motions with a suitably transformed image of traces from the physical platform.

For more information: http://kodlab.seas.upenn.edu/Avik/ICRA2015

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Robotic Measurement of Aeolian Processes

Measurements used to study wind shear stress and turbulence, surface roughness, sand flux, and dust emissions are typically obtained from stationary instrumentation, and are thus limited spatially. They are also dependent on deployment of instrumentation for specific events and thus the are limited temporally. We have been adapting a rough-terrain legged robot capable of rapidly traversing desert terrain to serve as a semi-autonomous, reactive mobile sensory platform (RHex [1]), which would not share these limitations. We report on early trials of the robotic platform at the Jornada LTER and White Sands National Monument to test the feasibility of gathering measurements of airflow and rates of particle transport on a dune, assessing the role of roughness elements such as vegetation in modifying the wind shear stresses incident on the surface, and estimating erosion susceptibility in an arid soil. The robot not only serves as a mobile platform for science instruments; it can also perform controlled “kick tests” to locally examine soil strength. We outline a strategy for mapping soil erodibility and its controlling parameters using the unique capabilities of RHex, and the implications for understanding erosion and dust emission from complex terrain.

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Averaged Anchoring of Decoupled Templates in a Tail-Energized Monoped

We refine and advance a notion of parallel composition to achieve for the first time a stability proof and empirical demonstration of a steady-state gait on a highly coupled 3DOF legged platform controlled by two simple (decoupled) feedback laws that provably stabilize in isolation two simple 1DOF mechanical subsystems. Specifically, we stabilize a limit cycle on a tailed monoped to excite sustained sagittal plane translational hopping energized by tail-pumping during stance. The constituent subsystems for which the controllers are nominally designed are: (i) a purely vertical bouncing mass (controlled by injecting energy into its springy shaft); and (ii) a purely tangential rimless wheel (controlled by adjusting the inter-spoke stepping angle).We introduce the use of averaging methods in legged locomotion to prove that this “parallel composition” of independent 1DOF controllers achieves an asymptotically stable closed-loop hybrid limit cycle for a dynamical system that approximates the 3DOF stance mechanics of our physical tailed monoped.We present experimental data demonstrating stability and close agreement between the motion of the physical hopping machine and numerical simulations of the (mathematically tractable) approximating model.

More information: http://kodlab.seas.upenn.edu/Avik/AveragingTSLIP

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Tail-Assisted Rigid and Compliant Legged Leaping

This paper explores the design space of simple legged robots capable of leaping culminating in new behaviors for the Penn Jerboa, an underactuated, dynamically dexterous robot. Using a combination of formal reasoning and physical intuition, we analyze and test successively more capable leaping behaviors through successively more complicated body mechanics. The final version of this machine studied here bounds up a ledge 1.5 times its hip height and crosses a gap 2 times its body length, exceeding in this last regard the mark set by the far more mature RHex hexapod. Theoretical contributions include a non-existence proof of a useful class of leaps for a stripped-down initial version of the new machine, setting in motion the sequence of improvements leading to the final resulting performance. Conceptual contributions include a growing understanding of the Ground Reaction Complex as an effective abstraction for classifying and generating transitional contact behaviors in robotics.