Substructuring permits parallelization of physics simulation on multi-core CPUs. We present a new substructuring approach for solving stiff multibody systems containing both bilateral and unilateral constraints. Our approach is based on non-overlapping domain decomposition with the Schur complement method, which we extend to systems involving contact formulated as a mixed bounds linear complementarity problem. At each time step, we alternate between solving the subsystem and interface constraint impulses, which leads to the identification of the active constraints. By using the active constraints to compute the effective mass of subsystems within the interface solve, we obtain an exact solution. We demonstrate that our simulations have preferable behavior compared to standard iterative solvers and substructuring techniques based on the exchange of forces at interface bodies. We observe considerable speedups for structured simulations where a user-defined partitioning can be applied, and moderate speedups for unstructured simulations, such as piles of bodies. In the latter case, we propose an automatic partitioning strategy based on the degree of bodies in the constraint graph. Because our method makes use of direct solvers, we are able to achieve interactive and real-time frame rates for a number of challenging scenarios involving large mass ratios, redundant constraints, and ill-conditioned systems.

We propose a novel integrator for implementing bilateral constraints in multibody simulation using variational integrator methods. We first construct a variational penalty method, which is used to enforce a constraint. The penalty term is simulated using an asynchronous variational integrator, allowing the penalty part of the system to be simulated using a smaller time step. We compute the Discrete Euler-Lagrange (DEL) equations for an equivalent penalty term with a larger time step and then use this rescaled system in the aforementioned variational penalty method, thereby enforcing the constraints. This enables us to incorporate some of the behavior of a very stiff system, which would only be stable on the small time scale, into the system on the large time scale. The effect is better adherence to the constraints, at a larger time step. We demonstrate the method with a simulation of a chain of rigid bodies. We then discuss the potential applications of the integrator and highlight how the work can be used to better interpret the tuned values of the coefficients used in penalty formulations.

Gait impairment is a prevalent and important difficulty for patients with multiple sclerosis (MS), a common neurological disorder. An easy to use tool to objectively evaluate gait in MS patients in a clinical setting can assist clinicians to perform an objective assessment. The overall objective of this study is to develop a framework to quantify gait abnormalities in MS patients using the Microsoft Kinect for the Windows sensor; an inexpensive, easy to use, portable camera. Specifically, we aim to evaluate its feasibility for utilization in a clinical setting, assess its reliability, evaluate the validity of gait indices obtained, and evaluate a novel set of gait indices based on the concept of dynamic time warping. In this study, ten ambulatory MS patients, and ten age and sex-matched normal controls were studied at one session in a clinical setting with gait assessment using a Kinect camera. The expanded disability status scale (EDSS) clinical ambulation score was calculated for the MS subjects, and patients completed the Multiple Sclerosis walking scale (MSWS). Based on this study, we established the potential feasibility of using a Microsoft Kinect camera in a clinical setting. Seven out of the eight gait indices obtained using the proposed method were reliable with intraclass correlation coefficients ranging from 0.61 to 0.99. All eight MS gait indices were significantly different from those of the controls (p-values less than 0.05). Finally, seven out of the eight MS gait indices were correlated with the objective and subjective gait measures (Pearson's correlation coefficients greater than 0.40). This study shows that the Kinect camera is an easy to use tool to assess gait in MS patients in a clinical setting.

Kinesthetic haptic applications employ force feedback on top of graphic and sound modalities to enable the human operator to interact with objects within a virtual world. The force feedback sensation, in particular, is created by a haptic device that displays the forces arising from this interaction. These forces must accurately emulate a real contact interaction, an objective which is commonly referred to as high-fidelity force feedback rendering. To achieve this, the current paper proposes a constrained-based rendering using a virtual tool that comes into unilateral contact with the virtual objects. Unlike common quasi-static or quasi-dynamic formulations in the haptics literature, a truly dynamic physical interaction between the virtual tool and the objects is modeled here. The paper develops analytical formulations for a canonical problem including colliding contact, sustained contact, slip and stick friction. Initial simulation and experimental evaluations show the potential of this method for handling complicated contact scenarios such as those encountered in haptic simulations of spinal or dental surgeries.

The device dynamics of haptic systems play a crucial role in the performance of the human user. Typical operation of a haptic device during simulation requires the user to perform common tasks that constitute the bases for all user actions. These common tasks include manipulation, selection, and navigation. Navigation requires the user to transition the end-effector across regions of the device workspace moving to a new location of interest within the virtual scene. In this study we investigate the role that the inertia tensor coupling has on user performance during navigational tasks. We also adapt the operation and admissible-motion space representation for haptic systems in which forces causing deviations from a desired path can be thought of as parasitic forces that degrade a users performance. Dynamic simulations were carried out to gain insight into the effects of navigating along paths of varying coupling using a 2DOF five-bar mechanism and were experimentally validated with a Quansar 2DOF Pantograph device.

The sampled-data nature and time delays induce complex dynamic behaviours in haptic systems which makes the stable, high performance force feedback challenging. Physiological factors, such as reflex delay, and the variable impedance of the human operator further complicate the modeling and analysis of these systems. Often the operator is neglected and only the dynamics of the uncoupled haptic device is investigated. When considered, the human model is typically represented by passive impedance elements attached to the device; most studies employ only simple mass-spring-damper representations. The dynamics of coupled systems with multiple degrees-of-freedom device- and human operator models have not been much investigated. In the present paper, we discuss reduced order, parametric dynamic representations for such complex models. We also consider the coupled system, and demonstrate the effect of the human operator on the combined dynamics. Structural flexibility, different grasping conditions, and active human stabilization with reflex delay are considered. The results are validated and illustrated experimentally by using a haptic device based on a five-bar mechanism.

In certain haptic applications, producing a sharp feeling of impact is important for high-fidelity force feedback rendering of virtual objects. This paper studies the direct impulse-based rendering paradigm to achieve this goal. Three main challenges are identified and some solutions are proposed. The first one is the energy deviation due to the sampled-data settings. Since the deviation tends to have a dissipative nature, it is called unsolicited dissipation and is suggested to be countered by applying a larger adaptive coefficient of restitution based on energy monitoring. The second challenge is the actuation limits which can be met by distributing the impulse into a sequence of force commands over successive intervals. The third is rendering resting contacts which is proposed to be done using a hybrid penalty-impulse-based technique. This paper develops a systematic way for collecting all the required mathematical formulations, analysis of the aforementioned issues and implementation of the solutions within a unified control-oriented framework entitled the generalized contact controller (GCC). Our initial simulation and experimental results show the promising aspects of the direct impulse-based rendering and the GCC framework for generating a sharper unfiltered feeling of impact at relatively low sampling rates compared to virtual coupling-based indirect methods.

In this work we present a method of systematically selecting regions of a haptic workspace to be used for navigation of large virtual environments. Existing navigational techniques require the partitioning of the workspace into a region of manipulation and a separate region for navigation tasks. These techniques, however, have neglected to describe an effective way to implement these concepts in a device specific manner. We propose a two step technique to define these regions based on the mechanical properties of pre-existing devices. In the first step, the kinematic properties of the device are analyzed across the entirety of the physical workspace. A well-behaved region that favours isotropic mapping from the joint actuators to the generalized forces at the end effector is selected. Having ensured high force fidelity within this region, we then perform a second step analyzing the device dynamic properties. We further subdivide the navigational space into a region with suitable inertial properties in which manipulation tasks may be performed. This procedure generates a haptic display with a highly transparent haptic manipulation region within which a user can interact with a virtual environment. This manipulation region is bounded by a well-behaved navigational region that ensures adequate force transmission. To demonstrate this technique, navigation and manipulation spaces are generated and described for the planar and spatial cases.

This paper presents the design of a locomotion interface for gait simulation and interaction with a virtual environment. The proposed mechanical interface is based on two planar two-degree-of-freedom belt-driven mechanisms which fully decouple the vertical and horizontal motion of two supporting footplates. Force sensors are mounted under the footplates in order to move the end effectors according to the user's intentions. The user's feet are rigidly attached to the footplates but a system of hinges allows an additional unactuated two-degree-of-freedom motion. A lag controller allows the user to move the end-effectors freely and a virtual floor based on a virtual spring and damper restrains the end-effectors' movements so that the user experiences an intuitive contact with the ground. Finally, preliminary experiments are reported in order to demonstrate the capability of the locomotion interface for gait simulation.

A number of applications of wheeled robots, including planetary exploration rovers and rescue missions, require that the vehicle operates in a non-structured environment. Optimizing the vehicle mobility is of key importance in such applications. Reduced mobility can limit the ability of the robot to achieve the mission goals, or even render it immobile in extreme cases. In this paper, the effect of normal contact forces on mobility is reported. A performance indicator based on the force distribution is defined and used to compare different vehicle configurations. The validity of this indicator was assessed using both simulation and experimental results obtained for a six-wheel rover prototype. Results suggest that modifying the robot configuration to alter the normal force distribution can lead to increased traction force available at the wheel-terrain interfaces, thus improving the mobility.

The dynamics behaviour of haptic interfacing can significantly depend on the mechanical properties of the haptic device. A systematic framework is outlined in this paper for the development of representative models to characterize the mechanical effects. These models reflect the influence of overall system properties in a parametric form. It is shown that simplified models can be representative in different regions of the virtual environment parameters and operating conditions. Closed-form stability conditions are obtained, which extend the linear stability conditions commonly used in the literature. Using these, quantitative performance measures can be established for the performance of haptic interfaces, which reflect the effect of mechanical design parameters.

In this paper, a velocity estimator is introduced, which results in low-delay and low-noise velocity estimation based on the sampled-quantized position measurement. The method maintains its efficiency for a broad range of velocities and excitation frequencies. The algorithm is computationally efficient and operates well at virtually any sampling frequency. Better velocity observation, increases the efficiency of virtual dampers employed in impedance control; hence, the system remains stable at higher values of virtual stiffness. This work is supported by simulations and experiments.

Enhancing the realism of the perceived contact force is a primary challenge in haptic rendering of virtual walls (VWs) and objects (VOs). For VOs, this goal directly translates into accurate rendering of not only stiffness, but also mass. The most challenging situation arises when the stiffness of the object is large, its mass is small, and sampling is slow. To address this challenge, a framework entitled high-fidelity haptic rendering (HFCR) has been developed. The HFCR framework is composed of the following three main strategies: an energy-consistent rendering of the contact force, smooth transition between contact modes, and remaining leak dissipation. The essence of all these strategies is to make the energy of the VO emulate its continuous-time counterpart. This is achieved through physically meaningful modifications in the constitutive relations to suppress artificial energy leaks. This paper reports simulation and experiments involving the one-dimensional canonical model of a VO to illustrate the HFCR framework and compare it to the existing methods. Results demonstrate the promising stability and force rendering fidelity of this framework.

A novel approach is proposed for the modeling of rigid-wheel and soft-soil interaction to efficiently compute normal and shear stress distributions in the contact area. The authors propose a velocity field in the vicinity of the contact area based on the physical nature of the problem. Thereupon, the incremental changes to the stress field are computed by resorting to elastoplasticity theory and an appropriate already existing constitutive relation for soil. The proposed approach leads to results that agree well with those obtained using well-established terramechanics models, while addressing some of their shortcomings. In addition, the proposed approach uses generalized velocities of the wheel as inputs, which makes it compatible with dynamic models of multibody systems. The dynamic slip-sinkage behavior of the wheel and the semielliptical shape of the normal stress distribution under the wheel are natural outcomes of the proposed model. Experimental investigation under various ranges of wheel slippage shows good agreement with the data available in the literature.

In this work, a multibody dynamics model of a wheeled mobile robot is developed to characterize the terrain reaction forces in terms of the physical and control parameters of the system. A common strategy for simulating the motion of mobile robots on soft soil is to compute the soil reaction forces using terramechanics models and to solve a forward dynamics problem by considering the soil reactions as a set of forces applied to the system. This intends to provide an accurate computation of the forces involved in the wheel-soil interaction; however, a series of factors such as the sensitivity of reaction forces to soil parameters limits the applicability of the existing terramechanics models in unstructured environments. We propose an alternative approach which does not rely on the soil properties, but at the same time does not intend to provide an exact computation of wheel-soil interaction forces. The main objective of this approach is to estimate the effect of changes in control and design parameters on the performance of the system, using the information provided by the dynamics model of the vehicle. To this end, the reaction forces for the wheel-terrain interaction in the ideal limit case of pure rolling and no penetration are obtained upon the specification of the motion at the contact points, via kinematic constraints. The validity of the analysis results obtained using the proposed paradigm is verified by simulation runs and experiments. The experimental results suggest that this approach is successful in predicting the variation of a set of important performance indicators in terms of the changes in the parameters of the system.

There are many applications for which a robotic device is used to recreate the sense of touch for a physical or virtual environment. Transparency and stability are two major issues in controlling haptic devices. Transparency highly depends on the quality of state observation while the stability range is mainly affected by the time-delay and sampling frequency. The control force is calculated based on the model of the environment and usually is a function of the position and the velocity at the joints. Optical encoders are commonly used for position measurement because of their high resolution, robustness to noise, and high bandwidth. The velocity, however, is usually determined by differentiating the position data over time which can be noisy at high frequencies. This noise demotes the transparency and stability. Low-pass filters are widely used to filter the noise but they make the system slow and conservatively introduce time-delay which further limits the stability range. In this paper, the method of Adaptive Frequency Differentiation (AFD) is introduced, which operates at varying frequencies and effectively removes the noise caused by the error in position data. The AFD is optimized to operate at its best performance while maintaining the reliability of the differentiation. The output of the AFD is derived by logically interpreting the available data and does not involve iterative loops, which improves the processing time. An extension to this method allows to compute low-delay and noiseless acceleration directly from the position data. The claims of this paper are supported by simulation and experimental results.

A novel approach is proposed for the modeling of rigid-wheel and soft-soil interaction using infinitesimal plasticity theory. Our motivation is the need to have a model compatible with dynamic models of multibody systems. The idea is to use a prescribed velocity field in the vicinity of the contact area based on the physics of the problem, and find the changes in the stress field by resorting to plasticity theory and an appropriate constitutive relation for soil. In this paper the Drucker-Prager constitutive relation with cap hardening is employed. The proposed approach leads to results that tally with those obtained using well-established semi-empirical models. The calibration of the semi-empirical model parameters is done by performing simulation runs using detailed FEM models with the Abaqus/Explicit software package.

In this paper, a nonlinear signal-processing scheme is developed for robotic systems that exploits a joint state-parameter formulation for simultaneous recursive estimation of the states (e.g. joint angles and rates) and uncertain parameters (e.g. inertial and friction parameters), out of noisy measurements (e.g. joint angles). Unscented Kalman filtering was employed to overcome restrictions such as linearity in the parameters and the need for availability of joint velocities and accelerations (present in linear recursive least square methods), and the linearization problems associated with extended Kalman filtering. Owing to the unscented transform concept which requires only input-output evaluations of the dynamic model, a more general and modular implementation is realizable. This allows for the utilization of computational modeling tools without the requirement of symbolically manipulating or deriving the equations of motion. Also, the recursive nature of the scheme allows for both offline processing and online implementation. The practical performance of the proposed scheme was verified through an experiment involving a five-bar linkage based haptic device configured to render a virtual box. The torque pair commands generated by the haptic controller to render the virtual box and the encoder angular measurements acquired through the experiment were processed twice in two different input-output directions: once, for state-parameter estimation of the robot; and, another time for identification of supposedly unknown environmental parameters. Results demonstrate successfulness of the scheme for recursive state-parameter estimation of the robot and the environment, as well as promising applicability in online settings.

Digitally controlled systems are getting more and more popular mainly because of their flexibility and convenience but their stability is strongly affected by the time delay introduced by different factors. For common PID type digital controllers, zero-order holds (ZOHs) are commonly employed and the stability characteristics are investigated based on that concept. Mathematical investigations show that higher-order holds may improve the stability and performance of the system and can reduce the steady state errors significantly. This is because the controller tries to learn from the history of the behavior of the system and then predict the behavior for the time period between sampling instances and generate the best possible control force. Furthermore, a new concept of Modified Holds is introduced, which clearly improves the performance of a digital controller. For most control algorithms this does not prolong the processing time significantly (e.g. less than 1%) which can be neglected in the calculations. The varying control force would need an analogue circuitry to follow the proper curve, which might make the controller's electronic circuits more complex. This can be avoided considering that in almost all digital controllers the main core operates at several orders of magnitude higher frequency than that of the control loop itself. Hence, the control force can also be generated digitally at much higher frequencies. In this paper, after investigating the stability of a 1-DoF system equipped with discrete-time PD controller with first and second order holds, the concept of modified holds is introduced and then the results are validated by simulations. Furthermore, the concept is practically implemented on a self-balancing motor bike robot and the experimental results further support the claims of the paper.