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The advent of high-bandwidth data link radios, airborne broadband internet service, and Electronic Flight Bags (EFB) has enabled the development of low-cost decision support tools that improve operating efficiency. Government laboratories, private companies, and academia are developing these tools as software applications installed on EFBs and computing resources in airline dispatch centers. While these tools achieve small improvements in efficiency on a per flight basis, the cost savings is significant over the service life of an airplane and substantial for a fleet of airplanes. Considering the many unpredictable and uncontrolled variables that affect fuel burn and operating cost, the problem of quantifying the benefit over a specified service interval becomes a fundamental challenge. The basis of comparison that determines the value of a technology in today's market is very subjective. A consensus-based industry standard for measuring the monetary benefit of optimal guidance and control has not been established. GE has developed new methods for computing cost-optimal control and state trajectories for air transports and an approach to quantify the monetary benefit an operator can expect relative to a baseline control system. This method yields a fair comparison given the nature of uncontrolled variables that affect fuel burn and non-deterministic control constraints due to air traffic and weather which limit the crew's discretionary control of the airplane. This paper describes one of GE's flight path optimization applications that eliminates the simplifying assumptions applied to legacy path construction methods to improve operational efficiency. The benefits of this new approach have been assessed using a high-fidelity, physics-based computer simulation of various aircraft types. A novel approach to quantify the benefit-compares the cost of GE's state-of-the-art Flight Management System (FMS) augmented by GE's decision support tool with the cost realized by GE's FMS operating without the benefit of decision support. Weather data from NOAA's Rapid Refresh (RAP) system are used to simulate flights on different calendar days. Comparing two simulated flights removes uncertainties due to aircraft modelling, weather, and ATM routing. The results of the Monte Carlo study are characterized statistically to quantify the cost savings.

The advent of airborne connectivity technology has enabled the development of low-cost decision support tools that improve operating efficiency. Quantifying the benefit of new cost-saving technologies for a fleet of aircraft is a fundamental challenge in proving the value for a business case. Rather than costly flight trials, GE proposes a Monte Carlo simulation using physics-derived models against a standard baseline.

This paper presents a new definition of stable walking for point-footed planar bipedal robots that is not necessarily periodic. The inspiration for the definition is the commonly-held notion of stable walking: the biped does not fall. Somewhat more formally, biped walking is shown to be stable if the trajectory of each step places the robot in a state at the end of the step for which a controller is known to exist that generates a trajectory for the next step with this same property. To make the definition useful, an algorithm is given to verify if a given controller induces stable walking in the given sense. Also given is a framework to synthesize controllers that induce stable walking. The results are illustrated on a 5-link biped ERNIE in simulation and experiment.

This paper presents the development of the planar bipedal robot ERNIE as well as numerical and experimental studies of the influence of parallel knee joint compliance on the energetic efficiency of walking in ERNIE. ERNIE has 5 links--a torso, two femurs and two tibias--and is configured to walk on a treadmill so that it can walk indefinitely in a confined space. Springs can be attached across the knee joints in parallel with the knee actuators. The hybrid zero dynamics framework serves as the basis for control of ERNIE's walking. In the investigation of the effects of compliance on the energetic efficiency of walking, four cases were studied: one without springs and three with springs of different stiffnesses and preloads. It was found that for low-speed walking, the addition of soft springs may be used to increase energetic efficiency, while stiffer springs decrease the energetic efficiency. For high-speed walking, the addition of either soft or stiff springs increases the energetic efficiency of walking, while stiffer springs improve the energetic efficiency more than do softer springs.

New analysis and tools are presented that extend the hybrid zero dynamics (HZD) framework for the control of planar bipedal walkers. Results include (i) analysis of walking on a slope, (ii) analysis of dynamic (decoupling matrix) singularities, and (iii) an alternative method for choosing virtual constraints. A key application of the new tools is the design of controllers that render a passive bipedal gait robust to disturbances without the use of full actuation--while still requiring zero control effort at steady-state. The new tools can also be used to design controllers for gaits having an arbitrary steady-state torque profile. Five examples are given that illustrate these and other results.

Both new and existing naval vessels of all sizes face ever-increasing power supply requirements to support advanced mission loads including high power sensors, weapons, and launchers. Adding additional conventional generators to support these loads is infeasible given size and weight constraints and given the pulsed nature of those new loads. Instead, an optimization-based Power Management Controller (PMC) is used to dynamically control power system sources and loads in real time in order to serve system needs with a minimal amount of power supply equipment. In this paper, a Model Predictive Control (MPC) approach is used to dynamically coordinate sources and loads based on future demand. A cost function is used to prioritize various ship goals and objectives, and constraints are added to reflect hardware limitations. A Constrained Nonlinear MPC algorithm is then used to minimize the cost over a finite future horizon and generate control commands in real-time. The PMC is demonstrated to successfully control and improve system performance on a hardware test bed for ship power system research.

In this paper we present a simulator designed to handle multibody systems with changing constraints, wherein the equations of motion for each of its constraint configurations are formulated in minimal ODE form with constraints embedded before they are passed to an ODE solver. The constraint-embedded equations are formulated symbolically according to a re-combination of terms of the unconstrained equations, and this symbolic process is undertaken on-line by the simulator. Constraint-embedding undertaken on-the-fly enables the simulation of systems with an ODE solver for which constraints are not known prior to simulation start or for which the enumeration of all constraint conditions would be unwieldy because of their complexity or number. Issues of drift associated with DAE solvers that usually require stabilization are sidestepped with the constraint-embedding approach. We apply nomenclature developed for hybrid dynamical systems to describe the system with changing constraints and to distinguish the roles of the forward dynamics solver, a collision detector, and an impact resolver. We have prototyped the simulator in MATLAB and demonstrate the design using three representative examples.

Provably asymptotically stable running gaits are developed for the five-link, four-actuator bipedal robot, RABBIT. A controller is designed so that the Poincaré return map associated with periodic running gaits can be computed on the basis of a model with impulse effects that, previously, had been used only for the design of walking gaits. This feedback design leads to the notion of a hybrid zero dynamics for running, which in turn allows the existence and stability of running gaits to be determined on the basis of a scalar map. The main results are illustrated via simulations performed on models with known parameters and on models with parameter uncertainty and structural changes. Animations of the resulting running motions are available on the web.

International audience; In this paper we present the experimental validation of a framework for the systematic design, analysis, and performance enhancement of controllers that induce stable walking in N -link underactuated planar biped robots. Controllers designed via this framework act by enforcing virtual constraints—holonomic constraints imposed via feedback—on the robot’s configuration, which create an attracting two-dimensional invariant set in the full walking model’s state space. Stability properties of resulting walking motions are easily analyzed in terms of a two-dimensional subdynamic of the full walking model. A practical introduction to and interpretation of the framework is given. In addition, in this paper we develop the ability to regulate the average walking rate of the biped to a continuum of values by modification of within-stride and stride-boundary characteristics, such as step length.

The primary goal of this paper is to demonstrate a means to prove asymptotically stable walking in an underactuated, planar, five-link biped robot model. The analysis assumes a rigid contact model when the swing leg impacts the ground and an instantaneous double support phase. The specific robot model analyzed corresponds to a prototype under development by the Centre National de la Recherche Scientifique (CNRS), Paris, France. A secondary goal of the paper is to establish the viability of the theoretically motivated control law. This is explored in a number of ways. First, it is shown how known time trajectories, such as those determined on the basis of walking with minimal energy consumption, can be incorporated into the proposed controller structure. Secondly, various perturbations to the walking motion are introduced to verify disturbance rejection capability. Finally, the controller is demonstrated on a detailed simulator for the prototype which includes torque limits and a compliant model of the walking surface, and thus a noninstantaneous double support phase.

The zero dynamics of a hybrid model of bipedal walking are introduced and studied for a class of N-link, planar robots with one degree of underactuation and outputs that depend only on the configuration variables. Asymptotically stable solutions of the zero dynamics correspond to asymptotically stabilizable orbits of the full hybrid model of the walker. The Poincare map of the zero dynamics is computed and proven to be diffeomorphic to a scalar, linear, time-invariant system, thereby rendering transparent the existence and stability properties of periodic orbits.

The goal is to demonstrate a means to prove asymptotically stable walking in a planar, under actuated, five-link biped robot model. The analysis assumes a rigid contact model when the swing leg impacts the ground and an instantaneous double-support phase: under theses hypotheses, the robot is modeled by a dynamic nonlinear system and an impulse model. The controller induces finite-time stabilization of four of the robot's five degrees of freedom, resulting in a reduced Poincare stability analysis that can be carried out by computing a one dimensional map.

This paper presents an extension of a recently developed low-dimensional modeling approach for normal human gait to the modeling of asymmetric gait. The asymmetric model is applied to analyze the gait dynamics of a transtibial prosthesis user, specifically the changes in joint torque and joint power costs that occur with variations in sagittalplane alignment of the prosthesis, mass distribution of the prosthesis, and roll-over shape of the prosthetic foot being used. The model predicts an increase in cost with addition of mass and a more distal location of the mass, as well as the existence of an alignment at which the costs are minimized. The model's predictions also suggest guidelines for the selection of prosthetic feet and suitable alignments. The results agree with clinical observations and results of other gait studies reported in the literature. The model can be a useful analytical tool for more informed design and selection of prosthetic components, and provides a basis for making the alignment process systematic. Copyright � 2009 by ASME.

This paper describes the design and experimental testing of a variable effective compliance transmission for use with revolute joints in robotic systems. The transmission consists of a parallel arrangement of a torsional spring and a rotary magnetorheological (MR) fluid damper and is placed between a brush–less DC gearmotor and an end-effector. While the stiffness of the torsional spring is constant, the damping of the MR damper can be adjusted by changing the applied current, which alters the apparent rigidity of the system. Hence, the transmission exhibits a variable “effective compliance”. Experimental results show that increasing the damping can reduce position errors during acceleration and deceleration phases of motion. Impact tests indicate that for small currents applied to the damper (low damping), the presence of the torsional spring reduces impact loads during constant velocity motion. In combination, these results indicate that the variable effective compliance transmission can improve safety without sacrificing precise motion control.

This paper applies a robotics-inspired approach to derive a low-dimensional forward-dynamic hybrid model of human walking in the sagittal plane. The low-dimensional model is derived as a subdynamic of a higher-dimensional anthropomorphic hybrid model. The hybrid model is composed of models for single support (SS) and double support (DS), with the transition from SS to DS modeled by a rigid impact to account for the impact at heel-contact. The transition from DS to SS occurs in a continuous manner. Existing gait data are used to specify, via parametrization, the low-dimensional model that is developed. The primary result is a one-degree-of-freedom model that is an exact subdynamic of the higher-dimensional anthropomorphic model and describes the dynamics of walking. The stability properties of the model are evaluated using the method of Poincaré. The low-dimensional model is validated using the measured human gait data. The validation demonstrates the observed stability of the measured gait.

This paper presents a method of integrating mechanism design and hybrid system analysis for the design of single-degree-of-freedom (DOF) planar biped robots that can achieve dynamic walking gaits that are stable. Reducing the DOF in a biped can result in a reduction in the complexity of the control strategies needed to enable stable walking. Although the biped designed by this procedure is restricted to a single gait, this biped may be less complex, lighter, and less costly to construct than one whose multiple DOFs are coordinated via feedback.

Paint booths in the automotive industry require conditioned air to achieve desired product finish quality. The large amount of conditioned air required to operate a paint booth results in large amounts of energy consumption. This paper presents an analysis of the energy consumption of a paint booth and gives a means of reducing this consumption by designing and implementing a novel control strategy. This proposed strategy is expected to decrease the plant's HVAC utility costs by more than a fifth, and reduce its annual carbon dioxide emissions from natural gas combustion by roughly a quarter.

Summary. Models of bipedal robots in motion are fundamentally hybrid due to the presence of continuous phases, discrete transitions, and unilateral constraints arising from the contact forces between the robot and the ground. A major challenge in the control of bipedal robots has been to create a feedback theory that provides systematic synthesis methods, provable correctness and computational tools for designing asymptotically stable, periodic walking motions, especially walking motions that are dynamic unlike the quasi-static, flat-footed gaits that are prevalent in today’s machines. This chapter highlights the fundamental role of zero dynamics in obtaining truly dynamic walking gaits that include underactuated phases. The theoretical analysis is verified with experimental work.

This paper presents a method of integrating kinematic mechanism design and hybrid system analysis for the design of a single-degree-of-freedom (DOF) planar biped robot that can achieve dynamic walking gaits that are stable. Reducing the DOF in a biped can result in a reduction of the complexity of the control strategies needed to enable stable walking. Although the biped designed by this procedure is restricted to a single gait, this biped may be less complex, lighter, and less costly to construct than one whose multiple DOF are coordinated via feedback.

This paper presents a new definition of stable walking - that is not necessarily periodic - for a class of biped robots. The inspiration for the definition is the commonly-held notion of stable walking: the biped does not fall. To make the definition useful, an algorithm is given to verify if a given controller induces stable walking. Also given is a framework to synthesize controllers that induce stable walking. The results are illustrated on a model of a 5-link biped.

This paper investigates the energetic effects of adding springs at the passive ankles of a planar five-link, four-actuator walking biped robot. The energetic cost of walking with springs was determined by using a walking motion designed for the biped without springs added. The walking motion was then optimized for the presence of springs of various arbitrarily chosen stiffnesses and offset angles. The stability properties of the motions that resulted were checked. The energetic costs of walking and standing were then computed. It was found that standing with springs was more efficient, while walking was more costly than the same action without springs. Finally, the spring characteristics (stiffness and offset angle) and the motion were optimized simultaneously. The costs for walking and standing were computed, revealing that walking with springs was more efficient and standing was more costly than doing either without springs. A methodical approach to choosing the size of the feet based on this analysis of the spring characteristics is also presented.

This paper presents numerical and experimental studies of the influence of parallel knee joint compliance on the average power cost of walking in an underactuated planar bipedal robot, ERNIE. The use of parallel compliance does not increase the control design complexity, as would the addition of series compliance. Four scenarios were studied: one without springs, and three with springs of different stiffnesses and preloads. Optimal gaits in terms of average power cost for various speeds were designed for each scenario. It was found that for low-speed walking, soft springs are helpful to reduce power cost, while stiffer springs increase power cost. For high-speed walking, it was found that both soft and stiff springs reduce the average power cost of walking, but stiffer springs reduce the cost more than do softer springs.Copyright © 2007 by ASME

This paper presents the development of the planar bipedal robot ERNIE. ERNIE has 5 links: a torso, two femurs and two tibias without feet. ERNIE was designed and constructed to serve as a testbed for the development of novel control strategies for bipedal walking. A boom provides frontal plane stability, restricting walking motions to the sagittal plane, and ERNIE is configured to walk on a treadmill so that it can walk indefinitely in a confined space. ERNIE’s legs are modular so that morphological asymmetries and the use of feet may be explored more in future studies. Springs can be attached across the knee joints in parallel with the knee actuators to enable gaits that are more energetically efficient. ERNIE is currently controlled using the hybrid zero dynamics framework in which a function of the robot’s configuration that monotonically increases over a step is used to parameterize holonomic constraints on the robot’s motion. The constraints are designed via parameter optimization to minimize an objective function, such as the energy consumed over a step, and, at the same time, ensure gait stability. The constraints are enforced using decoupled high-gain PD control.Copyright © 2007 by ASME

This paper describes the development and validation of a control-oriented drivability model for a power-split hybrid-electric vehicle (HEV). The HEV model is capable of identifying drivability issues under critical conditions such as pedal tip-in tip-out, change of operating modes, and gear shifting. The model is useful for the design, improvement and calibration of control strategies. The model is implemented in Simulink® and is validated using data collected from a test vehicle.Copyright © 2007 by ASME

The control of power flow in a Hybrid Electric Vehicle (HEV) is challenging because of the hybrid structure of the driveline and conflicting performance objectives: fuel consumption minimization, state of charge (SOC) regulation, and drivability. The flexibility and dynamic reconfigurability of modern HEV driveline architectures enable the design of power management control strategies that are able to better address these issues. A decoupling control strategy based on such a driveline model is presented. The driveline has three power sources: an internal combustion engine, an integrated starter alternator, and an electric machine. The power management control strategy consists of a control based upon static minimization of the equivalent fuel cost combined with dynamic control of battery SOC and drivability. By exploiting the structure of the driveline’s dynamic model, decoupling is obtained in the sense that the battery SOC and drivability controls do not affect the power request constraint, nor do they affect each other.

Controllers are developed that extend the hybrid zero dynamics (HZD) control approach to the control of planar biped walking by allowing constraints to be designed by sampling a gait of interest, rather than by optimization. The technique is used to enlarge the basin of attraction of a passive biped?s gait under the assumption that ideal actuation has been introduced at each of the body coordinates. In this case, no control effort is used at steady-state. The technique also enables the systematic modification of the gaits? kinematic and dynamic properties. The main results are illustrated via two examples.

A supervisory control strategy is designed to address fuel minimization, battery state-of-charge control and drivability issues for a power-split, hybrid-electric vehicle. The energy management strategy relies solely on the current vehicle conditions and it does not require knowledge of the entire driving cycle a priori. While the state-of-charge control is largely integrated into the energy optimization strategy, the drivability control is treated separately but in such a way that the instantaneous power demand requested by the driver is still satisfied. The energy management strategy is tested on a quasi-static simulation model of the Ohio State University Challenge-X competition vehicle (a hybridized version of the GM Equinox). Simulation results show a remarkable improvement in fuel savings over the non-hybrid base vehicle.

International audience; This paper develops a class of bipedal running controllers based on the hybrid zero dynamics (HZD) framework and discusses related experiments conducted in September 2004 in Grenoble, France. In these experiments, RABBIT, a five-link, four-actuator, planar bipedal robot, executed six consecutive running steps. The observed gait was remarkably human-like, having long stride lengths (approx. 50 cm or 36% of body length), flight phases of significant duration (approx. 100 ms or 25% of step duration), an upright posture, and an average forward rate of 0.6 m/s. A video is available at [7, 17]. In the time allotted for experiments, stability of the gait could not be validated. To put the results into context, background information on hybrid robot modeling, control philosophy, and gait optimization techniques accompany final experimental observations. An additional discussion about some unmodeled dynamic and geometric effects that contributed to implementation difficulties is given.