A motion capture‐based control‐space approach for walking mannequins

Virtual mannequins need to navigate in order to interact with their environment. Their autonomy to accomplish navigation tasks is ensured by locomotion controllers. Control inputs can be user‐defined or automatically computed to achieve high‐level operations (e.g. obstacle avoidance). This paper presents a locomotion controller based on a motion capture edition technique. Controller inputs are the instantaneous linear and angular velocities of the walk. Our solution works in real time and supports at any time continuous changes of inputs. The controller combines three main components to synthesize locomotion animations in a four‐stage process. First, the Motion Library stores motion capture samples. Motion captures are analysed to compute quantitative characteristics. Second, these characteristics are represented in a linear control space. This geometric representation is appropriate for selecting and weighting three motion samples with respect to the input state. Third, locomotion cycles are synthesized by blending the selected motion samples. Blending is done in the frequency domain. Lastly, successive postures are extracted from the synthesized cycles in order to complete the animation of the moving mannequin. The method is demonstrated in this paper in a locomotion‐planning context. Copyright © 2006 John Wiley & Sons, Ltd.     

A Probabilistic Steering Parameter Model for Deterministic Motion Planning Algorithms

The simulation of two‐dimensional human locomotion in a bird's eye perspective is a key technology for various domains to realistically predict walk paths. The generated trajectories, however, are frequently deviating from reality due to the usage of simplifying assumptions. For instance, common deterministic motion planning algorithms predominantly utilize a set of static steering parameters (e.g. maximum acceleration or velocity of the agent) to simulate the walking behaviour of a person. This procedure neglects important influence factors, which have a significant impact on the spatio‐temporal characteristics of the finally resulting motion—such as the operator's physical conditions or the probabilistic nature of the human locomotor system. In overcome this drawback, this paper presents an approach to derive probabilistic motion models from a database of captured human motions. Although being initially designed for industrial purposes, this method can be applied to a wide range of use cases while considering an arbitrary number of dependencies (input) and steering parameters (output). To underline its applicability, a probabilistic steering parameter model is implemented, which models velocity, angular velocity and acceleration as a function of the travel distances, path curvature and height of a respective person. Finally, the technical performance and advantages of this model are demonstrated within an evaluation.     

A novel three‐dimensional guidance law implementation using only line‐of‐sight azimuths

A novel three‐dimensional guidance law using only line‐of‐sight azimuths based on input‐to‐state stability and robust nonlinear observer is proposed for interception of maneuvering targets. The proposed guidance law does not need any prior information of unknown bounded target maneuvers and uncertainties. Since in practice the line‐of‐sight rate is difficult for a pursuer to measure accurately, a nonlinear robust observer is introduced to estimate it. A three‐dimensional guidance law with bearing only measurement is obtained for interception of maneuvering targets. The presented algorithm is tested using computer simulations against a maneuvering target. Copyright © 2014 John Wiley & Sons, Ltd.     

Real‐time horse gait synthesis

Horse locomotion exhibits rich variations in gaits and styles. Although there have been many approaches proposed for animating quadrupeds, there is not much research on synthesizing horse locomotion. In this paper, we present a horse locomotion synthesis approach. A user can arbitrarily change a horse's moving speed and direction, and our system would automatically adjust the horse's motion to fulfill the user's commands. At preprocessing, we manually capture horse locomotion data from Eadweard Muybridge's famous photographs of animal locomotion and expand the captured motion database to various speeds for each gait. At runtime, our approach automatically changes gaits based on speed, synthesizes the horse's root trajectory, and adjusts its body orientation based on the horse's turning direction. We propose an asynchronous time warping approach to handle gait transition, which is critical for generating realistic and controllable horse locomotion. Our experiments demonstrate that our system can produce smooth, rich, and controllable horse locomotion in real time. Copyright © 2012 John Wiley & Sons, Ltd.     

Egomotion analysis based on the Frenet-Serret motion model

In this paper we propose a new model,Frenet-Serret motion, for the motion of an observer in a stationary environment. This model relates the motion parameters of the observer to the curvature and torsion of the path along which the observer moves. Screw-motion equations for Frenet-Serret motion are derived and employed for geometrical analysis of the motion. Normal flow is used to derive constraints on the rotational and translational velocity of the observer and to compute egomotion by intersecting these constraints in the manner proposed in (Duri and Aloimonos 1991) The accuracy of egomotion estimation is analyzed for different combinations of observer motion and feature distance. We explain the advantages of controlling feature distance to analyze egomotion and derive the constraints on depth which make either rotation or translation dominant in the perceived normal flow field. The results of experiments on real image sequences are presented.The support of the Air Force Office of Scientific Research under Grant F49620-93-1-0039 is gratefully acknowledged.     

A globally asymptotically stabilizing trajectory tracking controller for fully actuated rigid bodies using landmark‐based information

In this paper, we address the problem of designing a control law based on sensor measurements that provides global asymptotic stabilization to a reference trajectory defined on the . The proposed control law is a function of the angular velocity, of vector measurements characterizing the position of some given landmarks, and of their rate of change. We provide sufficient conditions for the existence of synergistic potential functions on SO(3) which are pivotal in the generation of a suitable hybrid control law. We also provide sufficient conditions on the geometry of the landmarks to solve the given problem. Finally, the proposed solution is simulated and compared with a continuous feedback control law. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐Time Stabilization of Stochastic High‐Order Nonlinear Systems

This paper considers the problem of global finite‐time stabilization in probability for stochastic high‐order nonlinear systems in which the power order is greater than or equal to one and the drift and diffusion terms satisfy weaker growth conditions. Based on stochastic Lyapunov theorem on finite‐time stability, via the combined adding one power integrator and sign function method, constructing a Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed‐loop system globally finite‐time stable in probability.     

Online real‐time locomotive motion transformation based on biomechanical observations

In the paper, we present an online real‐time method for automatically transforming a basic locomotive motion to a desired motion of the same type, based on biomechanical results. Given an online request for a motion of a certain type with desired moving speed and turning angle, our method first extracts a basic motion of the same type from a motion graph, and then transforms it to achieve the desired moving speed and turning angle by exploiting the following biomechanical observations: contact‐driven center‐of‐mass control, anticipatory reorientation of upper body segments, moving speed adjustment, and whole‐body leaning. Exploiting these observations, we propose a simple but effective method to add physical and behavioral naturalness to the resulting locomotive motions without preprocessing. Through experiments, we show that our method enables a character to respond agilely to online user commands while efficiently generating walking, jogging, and running motions with a compact motion library. Our method can also deal with certain dynamical motions such as forward roll. Copyright © 2016 John Wiley & Sons, Ltd.     

Gradient‐free method for distributed multi‐agent optimization via push‐sum algorithms

This paper studies the problem of minimizing the sum of convex functions that all share a common global variable, each function is known by one specific agent in the network. The underlying network topology is modeled as a time‐varying sequence of directed graphs, each of which is endowed with a non‐doubly stochastic matrix. We present a distributed method that employs gradient‐free oracles and push‐sum algorithms for solving this optimization problem. We establish the convergence by showing that the method converges to an approximate solution at the expected rate of , where T is the iteration counter. A numerical example is also given to illustrate the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Spatial camera orientation control by rotation‐minimizing directed frames

The use of rotation‐minimizing directed frames (RMDFs) for defining smoothly varying camera orientations along given spatial paths, in real or virtual environments, is proposed. A directed frame on a space curve is a varying orthonormal basis for ℝ³ such that coincides with the unit polar vector from the origin to each curve point, and such a frame is rotation‐minimizing if its angular velocity vector maintains a vanishing component along o . To facilitate computation of rotation‐minimizing directed frames, it is shown that the basic theory is equivalent to the established theory for rotation‐minimizing adapted frames—for which one frame vector coincides with the tangent at each curve point—if one replaces the given space curve by its anti‐hodograph (i.e., indefinite integral). A family of polynomial curves on which RMDFs can be computed exactly by a rational function integration, the Pythagorean (P) curves, is also introduced, together with algorithms for their construction. Copyright © 2009 John Wiley & Sons, Ltd.     

Singularity‐avoiding swing‐up control for underactuated three‐link gymnast robot using virtual coupling between control torques

An underactuated three‐link gymnast robot (UTGR) is a simple model of a gymnast on a high bar. The control objective of a UTGR is to swing it up from a point near the straight‐down position and to stabilize it at the straight‐up position. To achieve this, we first divide the motion space into two subspaces, swing‐up area and balancing area, and design a controller for each. The design of a swing‐up control law that ensures that the UTGR enters the balancing area is crucial because the UTGR is subject to a nonholonomic constraint and is highly nonlinear during the swing‐up motion. This study focused on how to design a swing‐up control law that contains no singularities. The key concept is the introduction of a virtual coupling between control torques, which converts the problem of avoiding singularities to one of imposing constraints on the parameters of the control law and properly selecting those parameters. A swing‐up control law thus designed ensures that the UTGR enters the balancing area in a natural stretched‐out posture. This makes it easy to stabilize the UTGR in the balancing area. Copyright © 2013 John Wiley & Sons, Ltd.     

Real‐time locomotion control by sensing gloves

Sensing gloves are often used as an input device for virtual 3D games. We propose a new method to control characters such as humans or animals in real‐time by using sensing gloves. Based on existing motion data of the body, a new method to map the hand motion of the user to the locomotion of 3D characters in real‐time is proposed. The method was applied to control locomotion of characters such as humans or dogs. Various motions such as trotting, running, hopping, and turning could be produced. As the computational cost needed for our method is low, the response of the system is short enough to satisfy the real‐time requirements that are essential to be used for games. Using our method, users can directly control their characters intuitively and precisely than previous controlling devices such as mouse, keyboards or joysticks. Copyright © 2006 John Wiley & Sons, Ltd.     

Thin‐slot formalism for the split‐field FDTD analysis of periodic structure

An expression of the thin‐slot formalism is presented to alleviate the gridding of the split‐field finite‐difference time‐domain (FDTD) solution for periodic structure. The varying auxiliary‐field ( , ) and split‐field ( , ) distributions near the slots are analytically derived from the varying field ( , ). The update equations for the split‐field FDTD are obtained by incorporating those varying field distributions into the split‐field equations in integral form. A frequency selective surface (FSS) structure is applied to verify the proposed method. The results indicate that the computational efficiency is improved.     

Improved Adaptive Controller Synthesis of Piecewise‐Affine Systems

This paper considers the adaptive control problem for piecewise affine systems (PWS), a novel synthesis framework is presented based on the piecewise quadratic Lyapunov function (PQLF) instead of the common quadratic Lyapunov function to achieve the less conservatism. First, by designing the projection‐type piecewise adaptive law, the problem of the adaptive control of PWS can be reduced to the control problem of augmented piecewise systems. Then, we construct the piecewise affine control law for augmented piecewise systems in such a way that the PQLF can be employed to establish the stability and performance. In particular, the Reciprocal Projection Lemma is employed to formulate the synthesis condition as linear matrix inequalities (LMIs), which enables the proposed PQLF approach to be numerically solvable. Finally, an engineering example is shown to illustrate the synthesis results.     

Motion Synthesis for Sports Using Unobtrusive Lightweight Body‐Worn and Environment Sensing

The ability to accurately achieve performance capture of athlete motion during competitive play in near real‐time promises to revolutionize not only broadcast sports graphics visualization and commentary, but also potentially performance analysis, sports medicine, fantasy sports and wagering. In this paper, we present a highly portable, non‐intrusive approach for synthesizing human athlete motion in competitive game‐play with lightweight instrumentation of both the athlete and field of play. Our data‐driven puppetry technique relies on a pre‐captured database of short segments of motion capture data to construct a motion graph augmented with interpolated motions and speed variations. An athlete's performed motion is synthesized by finding a related action sequence through the motion graph using a sparse set of measurements from the performance, acquired from both worn inertial and global location sensors. We demonstrate the efficacy of our approach in a challenging application scenario, with a high‐performance tennis athlete wearing one or more lightweight body‐worn accelerometers and a single overhead camera providing the athlete's global position and orientation data. However, the approach is flexible in both the number and variety of input sensor data used. The technique can also be adopted for searching a motion graph efficiently in linear time in alternative applications.     

Composite Disturbance‐Observer‐Based Control and Control for High Speed Trains with Actuator Faults

To guarantee the position and velocity tracking performance of high speed trains (HSTs) with actuator faults, a composite control algorithm consisting of the disturbance‐observer‐based control (DOBC) and control is proposed. Based on the multiple point‐mass model, the dynamics of HSTs is established by a cascade of carriages which are connected by flexible couplers, during the procedure of which, the running resistance, actuator faults and multiple disturbances are taken into account. The multiple disturbances are composed of two parts, one of which is the ramp resistance due to the track slope, the other is unknown gusts which can be modeled as a harmonic disturbance with time‐varying frequency. The unknown gusts is estimated and rejected via the DOBC methodology, meanwhile, the running resistance and the ramp resistance are attenuated by the control methodology. According to the Lyapunov stability analysis and LMI‐based algorithms, main results are derived such that the closed‐loop system is asymptotically stable and the desired performance can be guaranteed. Compared with the numeral simulation results with the single control method, it is demonstrated that the proposed control methodology is more effective and the system has a higher precision of position and velocity tracking.     

Dynamic Output‐Feedback Control for T‐S Fuzzy Systems with Input Time‐Varying Delay

This paper considers the problem of the control for T‐S fuzzy systems with input time‐varying delay via dynamic output feedback. Firstly, by applying the reciprocally convex approach, new delay‐dependent sufficient condition for performance analysis is obtained. Then, a less conservative condition for the existence of the controllers is given in terms of linear matrix inequalities (LMIs). Moreover, in the considered system, the time‐delay term is included in the measured output. This results in the difficulty in designing the controllers being increased and the obtained results being applied to a wider class of fuzzy systems than the most existing ones. The main contribution of this work lies in the application of the reciprocally convex inequality and the time‐delay term included in the measured output. Finally, the advantages and effectiveness of the present results are shown by several numerical examples.     

Input‐to‐state‐stability‐type comparison principles and input‐to‐state stability for discrete‐time dynamical networks with time delays

This paper investigates the input‐to‐state stability (ISS) issue for discrete‐time dynamical networks (DDNs) with time delays. Firstly, a general comparison principle for solutions of DDNs is proposed. Then, based on this general comparison principle, three kinds of ISS‐type comparison principles for DDNs are established, including the comparison principle for input‐to‐state ‐stability, ISS, and exponential ISS. The ISS‐type comparison principles are then used to investigate stability properties related to ISS for three kinds (linear, affine, and nonlinear) of DDNs. It shows that the ISS property of a DDN can be derived by comparing it with a linear or lower‐dimension DDN with known ISS property. By using methods such as variation of parameters, uniform M‐matrix, and the ISS‐type comparison principle, conditions of global exponential ISS for time‐varying linear DDNs with time delays are derived. Moreover, the obtained ISS results for DDNs are extended to the hybrid DDNs with time delays. As one application, the synchronization within an error bound in the sense of ISS is achieved for DDNs with coupling time delays and external disturbances. Finally, two examples are given to illustrate the results. Copyright © 2011 John Wiley & Sons, Ltd.     

Input‐output triggered control using ‐stability over finite horizons

This paper investigates stability of nonlinear control systems under intermittent information. Following recent results in the literature, we replace the traditional periodic paradigm, where the up‐to‐date information is transmitted and control laws are executed in a periodic fashion, with the event‐triggered paradigm. Building on the small gain theorem, we develop input–output triggered control algorithms yielding stable closed‐loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise in the environment, the developed algorithm yields stable, asymptotically stable, and ‐stable (with bias) closed‐loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on ‐stability are presented. The prediction of a triggering event is achieved by employing ‐gains over a finite horizon. By resorting to convex programming, a method to compute ‐gains over a finite horizon is devised. Finally, our approach is successfully applied to a trajectory tracking problem for unicycles. Copyright © 2014 John Wiley & Sons, Ltd.     

Pre‐filtering and post‐filtering in gain‐scheduled output‐feedback control

Linear matrix inequality (LMI) design conditions for gain‐scheduled output‐feedback control rely on assumptions constraining either system or controller matrices. Throughout the literature, it is common practice to avoid imposing restrictive assumptions on the controller, which may appear undesirable, in favor of state augmentations via pre‐filtering and post‐filtering to construct auxiliary augmented systems that comply with the alternative assumptions on the system matrices. This technique brings in the additional cost of increased state dimensions of the resulting gain‐scheduled output‐feedback controllers. In this paper, we explore the interplay and inherent trade‐offs between state augmentation, controller structure, and performance. We revisit LMI design conditions for quadratic output‐feedback control and demonstrate that state augmentation via pre‐filtering and post‐filtering in order to avoid constraints on the controller matrices is never advantageous even without taking into account the added complexity and propensity for numerical issues associated with state augmentation. As an additional contribution, we extend this observation to recently introduced modified LMI conditions allowing combined – however less restrictive – assumptions on system and controller matrices. Copyright © 2016 John Wiley & Sons, Ltd.