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

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*la

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. For more information: Kod*La

Adaptive control of a one-legged hopping robot through dynamically embedded spring-loaded inverted pendulum template

Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 92-96.Practical realization of model-based dynamic legged behaviors is substantially more challenging than statically stable behaviors due to their heavy dependence on second-order system dynamics. This problem is further aggravated by the dif- ficulty of accurately measuring or estimating dynamic parameters such as spring and damping constants for associated models and the fact that such parameters are prone to change in time due to heavy use and associated material fatigue. In the first part of this thesis, we present an on-line, model-based adaptive control method for running with a planar spring-mass hopper based on a once-per-step parameter correction scheme. Our method can be used both as a system identifi- cation tool to determine possibly time-varying spring and damping constants of a miscalibrated system, or as an adaptive controller that can eliminate steady-state tracking errors through appropriate adjustments on dynamic system parameters. We use Spring-Loaded Inverted Pendulum (SLIP) model, which is the mostly used, effective and accurate descriptive tool for running animals of different sizes and morphologies, to evaluate our algorithm. We present systematic simulation studies to show that our method can successfully accomplish both accurate tracking and system identification tasks on this model. Additionally, we extend our simulations to Torque-Actuated Dissipative Spring-Loaded Inverted Pendulum (TD-SLIP) model towards its implementation on an actual robot platform. In the second part of the thesis, we present the design and construction of a onelegged hopping robot we built to test the practical applicability of our adaptive control algorithm. We summarize the mechanical, electronics and software design of our robot as well as the performed system identification studies to calibrate the unknown system parameters. Finally, we investigate the robot’s motion achieved by a simple torque-actuated open loop controller.Uyanık, İsmailM.S

A Bioinspired Dynamical Vertical Climbing Robot

This paper describes the inspiration, design, analysis, implementation of and experimentation with the first dynamical vertical climbing robot. Biologists have proposed a pendulous climbing model that abstracts remarkable similarities in dynamic wall scaling behavior exhibited by radically different animal species. We study numerically a version of that pendulous climbing template dynamically re-scaled for applicability to utilitarian payloads with conventional electronics and actuation. This simulation study reveals that the incorporation of passive compliance can compensate for an artifact’s poorer power density and scale disadvantages relative to biology. However the introduction of additional dynamical elements raises new concerns about stability regarding both the power stroke and limb coordination that we allay via mathematical analysis of further simplified models. Combining these numerical and analytical insights into a series of design prototypes, we document the correspondence of the various models to the variously scaled platforms and report that our approximately two kilogram platform climbs dynamically at vertical speeds up to 1.5 bodylengths per second. In particular, the final 2.6 kg final prototype climbs at an average steady state speed of 0.66 m/s against gravity on a carpeted vertical wall, in rough agreement with our various models’ predictions

Design of high-performance legged robots: A case study on a hopping and balancing robot

The availability and capabilities of present-day technology suggest that legged robots should be able to physically outperform their biological counterparts. This thesis revolves around the philosophy that the observed opposite is caused by over-complexity in legged robot design, which is believed to substantially suppress design for high-performance. In this dissertation a design philosophy is elaborated with a focus on simple but high performance design. This philosophy is governed by various key points, including holistic design, technology-inspired design, machine and behaviour co-design and design at the performance envelope. This design philosophy also focuses on improving progress in robot design, which is inevitably complicated by the aspire for high performance. It includes an approach of iterative design by trial-and-error, which is believed to accelerate robot design through experience. This thesis mainly focuses on the case study of Skippy, a fully autonomous monopedal balancing and hopping robot. Skippy is maximally simple in having only two actuators, which is the minimum number of actuators required to control a robot in 3D. Despite its simplicity, it is challenged with a versatile set of high-performance activities, ranging from balancing to reaching record jump heights, to surviving crashes from several meters and getting up unaided after a crash, while being built from off-the-shelf technology. This thesis has contributed to the detailed mechanical design of Skippy and its optimisations that abide the design philosophy, and has resulted in a robust and realistic design that is able to reach a record jump height of 3.8m. Skippy is also an example of iterative design through trial-and-error, which has lead to the successful design and creation of the balancing-only precursor Tippy. High-performance balancing has been successfully demonstrated on Tippy, using a recently developed balancing algorithm that combines the objective of tracking a desired position command with balancing, as required for preparing hopping motions. This thesis has furthermore contributed to several ideas and theories on Skippy's road of completion, which are also useful for designing other high-performance robots. These contributions include (1) the introduction of an actuator design criterion to maximize the physical balance recovery of a simple balancing machine, (2) a generalization of the centre of percussion for placement of components that are sensitive to shock and (3) algebraic modelling of a non-linear high-gravimetric energy density compression spring with a regressive stress-strain profile. The activities performed and the results achieved have been proven to be valuable, however they have also delayed the actual creation of Skippy itself. A possible explanation for this happening is that Skippy's requirements and objectives were too ambitious, for which many complications were encountered in the decision-making progress of the iterative design strategy, involving trade-offs between exercising trial-and-error, elaborate simulation studies and the development of above-mentioned new theories. Nevertheless, from (1) the resulting realistic design of Skippy, (2) the successful creation and demonstrations of Tippy and (3) the contributed theories for high-performance robot design, it can be concluded that the adopted design philosophy has been generally successful. Through the case study design project of the hopping and balancing robot Skippy, it is shown that proper design for high physical performance (1) can indeed lead to a robot design that is capable of physically outperforming humans and animals and (2) is already very challenging for a robot that is intended to be very simple

Affordances And Control Of A Spine Morphology For Robotic Quadrupedal Locomotion

How does a robot\u27s body affect what it can do? This thesis explores the question with respect to a body morphology common to biology but rare in contemporary robotics: the presence of a bendable back. In this document, we introduce the Canid and Inu quadrupedal robots designed to test hypotheses related to the presence of a robotic sagittal-plane bending back (which we refer to as a ``spine morphology\u27\u27). The thesis then describes and quantifies several advantages afforded by this morphological design choice that can be evaluated against its added weight and complexity, and proposes control strategies to both deal with the increase in degrees-of-freedom from the spine morphology and to leverage an increase in agility to reactively navigate irregular terrain. Specifically, we show using the metric of ``specific agility\u27\u27 that a spine can provides a reservoir of elastic energy storage that can be rapidly converted to kinetic energy, that a spine can augment the effective workspace of the legs without diminishing their force generation capability, and that -- in cases of direct-drive or nearly direct-drive leg actuation -- the spine motors can contribute more work in stance than the same actuator weight used in the legs, but can do so without diminishing the platform\u27s proprioceptive capabilities. To put to use the agility provided by a suitably designed robotic platform, we introduce a formalism to approximate a set of transitional navigational tasks over irregular terrain such as leaping over a gap that lend itself to doubly reactive control synthesis. We also directly address the increased complexity introduced by the spine joint with a modular compositional control framework with nice stability properties that begins to offer insight into the role of spines for steady-state running. A central theme to both the reactive navigation and the modular control frameworks is that analytical tractability is achieved by approximating the modes driving the environmental interactions with constant-acceleration dynamics

Minimalist Dynamic Climbing

Dynamics in locomotion is highly useful, as can be seen in animals and is becomingapparent in robots. For instance, chimpanzees are dynamic climbers that canreach virtually any part of a tree and even move to neighboring trees, while sloths arequasistatic climbers confined only to a few branches. Although dynamic maneuversare undoubtedly beneficial, only a few engineered systems use them, most of whichlocomote horizontally. This is because the design and control are often extremelycomplicated.This thesis explores a family of dynamic climbing robots which extend roboticdynamic legged locomotion from horizontal motions such as walking, hopping, andrunning, to vertical motions such as leaping maneuvers. The motion of these dynamicrobots resembles the motion of an athlete jumping and climbing inside achute. Whereas this environment might be an unnavigable obstacle for a slow, quasistaticclimber, it is an invaluable source of reaction forces for a dynamic climber.The mechanisms described here achieve dynamic, vertical motions while retainingsimplicity in design and control.The first mechanism called DSAC, for Dynamic Single Actuated Climber, comprisesonly two links connected by a single oscillating actuator. This simple, openlooposcillation, propels the robot stably between two vertical walls. By rotating theaxis of revolution of the single actuator by 90 degrees, we also developed a simplerrobot that can be easily miniaturized and can be used to climb inside tubes.The DTAR, for Dynamic Tube Ascending Robot, uses a single continuously rotatingmotor, unlike the oscillating DSAC motor. This continuous rotation even furthersimplifies and enables the miniaturization of the robot to enable robust climbinginside small tubes. The last mechanism explored in this thesis is the ParkourBot,which sacrifices some of the simplicity shown in the first two mechanism in favorof efficiency and more versatile climbing. This mechanism comprises two efficientspringy legs connected to a body.We use this family of dynamic climbers to explore a minimalist approach to locomotion.We first analyze the open-loop stability characteristics of all three mechanisms.We show how an open-loop, sensorless control, such as the fixed oscillationof the DSAC’s leg can converge to a stable orbit. We also show that a change inthe mechanism’s parameters not only changes the stability of the system but alsochanges the climbing pattern from a symmetric climb to a limping, non-symmetricclimb. Corresponding analyses are presented for the DTAR and ParkourBot mechanisms.We finally show how the open-loop behavior can be used to traverse morecomplex terrains by incrementally adding feedback. We are able to achieve climbinginside a chute with wall width changes without the need for precise and fast sensingand control.</p