The aim of this work is to present an efficient methodology to deal with general 3D-contact problems. This approach embraces three steps: geometrical definition of 3D-surfaces; detection of the candidate contact points; evaluation of the contact forces. The 3D-contact surfaces are generated and represented by using parametric functions due to their simplicity and easiness to handle freeform shapes. This task is carried in preprocessing, performed preliminarily to the implementation of the multibody code. The preprocessing procedure can be condensed into four steps: a regular and representative surface collection of points is extracted from the 3D-parametric surface; for each point the tangent vectors to the u and v directions of the parametric surface and the normal vector are computed; the geometrical information on each point is saved in a lookup table, including the parametric point coordinates, the corresponding Cartesian coordinates and the Cartesian components of the normal, tangent and binormal vectors; the lookup table is rearranged such that the u-v mapping is converted into a 3D-matrix form. In the last step, the surface data is saved as a direct access file. Regarding the detection of the contact points, the relative distance between the candidate contact points are computed and used to check if the bodies are in contact. The actual contact points are selected as those that correspond to the maximum relative indentation. The contact forces are determined as functions of the indentation, impact velocity and geometric and material properties of the contacting surfaces. In general, lookup tables are used to reduce the computation time in dynamic simulations. However, the application of these schemes involves an increase of memory needs. Within the proposed approach, the amount of memory used is significantly reduced, as a result of a partial upload into memory of the lookup table. A slider-crank mechanism with a cup on the top of the slider and a marble ball is used as demonstrative example. A contact pair is considered between a cup and a marble ball, being the contact forces computed using a dissipative contact model.

Recently various numerical integration schemes have been proposed for numerically simulating the dynamics of constrained multibody systems (MBS) operating. These integration schemes operate directly on the MBS configuration space considered as a Lie group. For discrete spatial mechanical systems there are two Lie group that can be used as configuration space: SE( 3 ) and SO( 3 ) × ℝ 3 . Since the performance of the numerical integration scheme clearly depends on the underlying configuration space it is important to analyze the effect of using either variant. For constrained MBS a crucial aspect is the constraint satisfaction. In this paper the constraint violation observed for the two variants are investigated. It is concluded that the SE( 3 ) formulation outperforms the SO( 3 ) × ℝ 3 formulation if the absolute motions of the rigid bodies, as part of a constrained MBS, belong to a motion subgroup. In all other cases both formulations are equivalent. In the latter cases the SO( 3 ) × ℝ 3 formulation should be used since the SE( 3 ) formulation is numerically more complex, however.

This paper presents a preliminary analysis of the robustness of a recently-proposed adaptive controller for robot manipulators based on the ℒ 1 control paradigm. Here, the use of a low-pass filter in the control input decouples the estimation loop from the control loop, thereby facilitating an arbitrary increase of estimation rates (limited only by hardware) without sacrificing robustness. Tuning of the filter also allows for shaping the nominal response and enhancing the system’s robustness. The paper further demonstrates improvements in the critical time delay associated with a static reference input achieved through the introduction of time delay in the state-predictor formulation. Guided by results from the theory of single-input-single-output ℒ 1 control systems, a linear, time-invariant system is proposed in order to derive a conservative lower bound on the system’s actuator critical time delay for static reference input in the limit of large estimation gains, as an indicator of robustness. Finally, a numerical method is proposed for quantifying the robustness against time delay of the system’s response to a given static reference input based on techniques of parameter continuation. This method computes the critical time delay at which local stability is lost in a Hopf bifurcation. The dependence of this critical time delay on control parameters, such as adaptive gains and filter bandwidth, is here obtained using advanced algorithms for computing approximate covers of implicitly defined manifolds.

Bio-filaments at sub-micron scales such as DNA perform their biological functions via well-regulated structural deformations that involve large twisting and bending. The strain energies associated with these deformations are of the order of the thermal kinetic energies of surrounding solvent molecules. Therefore, the bio-filaments at such small length scales also exhibit large fluctuations in their shape due to the random collisions of the solvent molecules with them. These thermal fluctuations may, on one hand, help the bio-filaments explore functionally desirable configuration space, while, on the other hand, hinder the regulation of their deformations by motor proteins. Nevertheless, it seems indispensable to model the thermal fluctuations to accurately study the dynamics of deformation of bio-filaments. This paper presents the first elastic rod formulation that incorporates the thermal fluctuations by modeling the impacts of solvent molecules as distributed stochastic force. For quasi-static fluctuations, this formulation leverages the simplicity of a rod formulation noted by Anker et al. [1] that allows solving it as an initial value problem (IVP) in single iteration, and yet capturing arbitrarily large (nonlinear) deformations with rigorous description of constitutive laws.

In this paper, mixed kinetic-kinematic equations for a multibody system have been studied in order to resolve the difficulties of non-integrability of angular velocity vectors. As for the kinetic equations, the Newton-Euler equations of motion are considered. They are derived in terms of angular velocity and angular acceleration vectors expressed in the body fixed reference frames. As for the kinematic compatibility equations, two different equations are considered. One is from the relationship between the angular velocity vector and the time derivatives of Euler parameters. The other is from the relationship between the rotational orientation matrix, its time derivative, and the angular velocity vector. In order to investigate the accuracy of the solution methods using two different kinematic compatibility equations, simulations of a spherical pendulum model and a 1/6 robot vehicle model have been carried out. With different integration step-sizes, the constraint violation errors have been also investigated.

This paper develops a simple continuation method for the approximate solution of optimal control problems with pure state variable inequality constraints. The method is based on transforming the inequality constraints into equality constraints using nonnegative slack variables. The resultant equality constraints are satisfied approximately using a quadratic loss penalty function. The solution of the original problem is obtained by solving the transformed problem with a sequence of penalty weights that tends to zero. The penalty weight is treated as the continuation parameter. The necessary conditions for a minimum are written as a boundary value problem involving index-1 differential-algebraic equations (BVP-DAE). The BVP-DAE include the complementarity conditions associated with the inequality constraints. The paper shows that the necessary conditions for optimality of the original problem and the transformed problems are remarkably similar. In particular, the BVP-DAE for each problem differ by a linear term related to the Lagrange multipliers associated with the state variable inequality constraints. Numerical examples are presented to illustrate the efficacy of the proposed technique. Specifically, the paper presents results for; (1) the optimal control of a simplified model of a gantry crane system, (2) the optimal control of a rigid body moving in the vertical plane, and (3) the trajectory optimization of a planar two-link robot. All problems include pure state variable inequality constraints.

A necessary condition for high-fidelity dynamic simulation of belt-drives is to accurately predict the normal and tangential contact forces between the belt and the pulleys. In previous papers those contact forces were predicted using one dimensional thin beam elements and approximate Coulomb friction models. However, typically flat belts have a small thickness and the reinforcements are typically near the top surface of the belt. In this paper the effect of the belt thickness on the normal and tangential contact forces and on the average slip between the belt and the pulleys is studied using a two-pulley belt-drive. The belt rubber matrix is modeled using three-dimensional brick elements. The belt reinforcements are modeled using one dimensional truss elements at the top surface of the belt. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure.

A linearized parametric continuum model of a long-span suspension bridge is coupled with a nonlinear quasi-steady aerodynamic model giving the aeroelastic partial differential equations of motion reduced to the state-space ordinary differential form by adopting the Galerkin method. Numerical time-domain simulations are performed to investigate the limit cycle oscillations occurring in the range of post-flutter wind speeds. Continuation tools are thus employed to path follow the limit cycles past the flutter speed where the Hopf bifurcation occurs. The stable post-flutter behavior, which can significantly affect the bridge by fatigue, terminate at a fold bifurcation. This result represents an important assessment of the conducted aeroelastic investigations. The stability range of the limit cycle oscillations is evaluated by carrying out sensitivity analyses with respect to the main design parameters, such as the structural damping and the initial wind angle of attack.

In this paper, we characterize the orthogonal complement-based divide-and-conquer (ODCA) [1] algorithm in terms of the constraint violation error growth rate and singularity handling capabilities. In addition, we present a new constraint stabilization method for the ODCA architecture. The proposed stabilization method is applicable to general multibody systems with arbitrary number of closed kinematic loops. We compare the performance of the ODCA with augmented [2] and reduction [3] methods. The results indicate that the performance of the ODCA falls between these two traditional techniques. Furthermore, using a numerical example, we demonstrate the effectiveness of the new stabilization scheme.

The modeling of High Speed Machining (HSM) spindles is a complex task due to the numerous physical phenomena involved in the dynamic behavior. Modeling is still rarely used in the industry, although sophisticated research work has been achieved. The boundary conditions of rotor models, which correspond to the ball bearings, are crucial and difficult to define. Indeed, they affect the dynamic behavior of the rotor in a non-linear and sometimes in an unpredictable way. The aim of the paper is to determine a relevant spindle model, i.e. the adequate level of complexity. To do so, a dynamic bearing model is introduced and the axial model of a spindle is established in relation to the preloaded bearing arrangement. Then, the operating stiffness of the spindle has been obtained experimentally with a new specific device that applies axial load and measures the resulting displacement, whatever the spindle speed. The model updating with the experimental data combined to sensibility analysis have led to the model refinement with additional physical phenomena, in order to account for non-linearities observed experimentally. The parameters of the model are also identified experimentally. As a result, a relevant spindle model is obtained and validated by the good agreement between simulations and experiments.

Transparency is a key performance evaluation criterion for haptic devices, which describes how realistically the haptic force/torque feedback is mimicked from a virtual environment or in case of master-slave haptic device. Transparency in haptic devices is affected by disturbance forces like friction between moving parts. An accurate estimate of friction forces for observer based compensation requires estimation techniques, which are computationally efficient and gives reduced error between measured and estimated friction. In this work different estimation techniques based on Kalman filter, such as Extended Kalman filter (EKF), Iterated Extended Kalman filter (IEKF), Hybrid extended Kalman filter (HEKF) and Unscented Kalman filter (UKF) are investigated with the purpose to find which estimation technique that gives the most efficient and realistic compensation using online estimation. The friction observer is based on a newly developed friction smooth generalized Maxwell slip model (S-GMS). Each studied estimation technique is demonstrated by numerical and experimental simulation of sinusoidal position tracking experiments. The performances of the system are quantified with the normalized root mean-square error (NRMSE) and the computation time. The results from comparative analyses suggest that friction estimation and compensation based on Iterated Extended Kalman filter both gives a reduced tracking error and computational advantages compared to EKF, HEKF, UKF, as well as with no friction compensation.

This paper is focused on the optimization of friction element parameters in blade shrouds for various types of excitation. In order to create and validate a proper modelling methodology an experimental stand and a numerical simulation of blades interaction by means of a friction element placed in the shrouds were prepared. Mathematical models are based on the finite element method combined with rigid bodies. The interaction of the friction element and blades is described by normal contact and tangential friction forces derived for particular geometrical parameters of the studied mechanical system. The models can be analyzed both in frequency domain (by the harmonic balance method) or in time domain (by the numerical integration). The results of the optimization of friction element parameters with respect to the bending vibration suppression are documented in the paper. Another contact modelling approach intended for more complex contact surfaces is based on the decomposition of a contact surface into a set of elementary areas and on the expression of contact and friction forces between these areas. All methodologies are implemented in the MATLAB system and the results for the chosen test cases are compared with the results obtained by a measurement or by the ANSYS software.

The dynamic equations of motion for constrained multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. It is known that the standard resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general review of the main methods commonly used to control or eliminate the violation of the constraint equations in the context of multibody dynamics formulation is presented and discussed. Furthermore, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is also presented. The basic idea of this approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations.

Pitching dynamics are an important component of the dynamics of legged locomotion. We develop an energy-open pitching stabilization model to achieve full asymptotic stability of locomotion. This model is called the pitched-actuated Spring-Loaded Inverted Pendulum (pitched-actuated SLIP) model. It extends the conservative SLIP model to include a trunk as well as net nonzero hip torque and leg damping. The hip torque is governed by a proportional and derivative controller which uses only the angle between body and leg as feedback during stance. During the swing phase of the leg, inertial frame feedback is used to reset the leg to a fixed angle in space. The use of body-frame feedback in stance is thought to be relevant to biology and robotic control, as time delays and uncertainty in inertial frame feedback could be challenging in stance. Further, this method of control during stance could be implemented in a neural feedforward manner using antagonistic pairs of muscle or muscle-like actuators around the hip joint. This model of pitching dynamics exhibits full asymptotic stability over a range of model parameters. Further, derivative control significantly impacts disturbance mitigation. Periodic locomotion solutions of the model with large energy cost tend to be unstable. Whereas, the most energy efficient locomotion solutions found tend to be within the stable region of the parameter space. The correlation between energy efficiency and stability found in this model may have significant implications for locomotion with pitching.

The main objective of this work is to present a study on the use of different hydrodynamic force models on the dynamic response of mechanical systems with lubricated revolute joints. For this purpose, the fundamental issues related to the classical theory of lubrication for dynamically loaded journal-bearings are revised, which is used to evaluate the Reynolds’ equation for dynamic regime. The hydrodynamic forces that develop at the lubricated revolute joints are determined and included into the dynamic equations of motion. In this study, three different approaches are considered to evaluate the hydrodynamic forces, namely the Pinkus and Sternlicht approach for long journal-bearings and the Frêne et al. models for both long and short journal-bearings. Results for a mechanical system with a lubricated revolute joint are presented and used to discuss the main assumptions and procedures adopted in this work. From the computational simulations performed, it can be observed that the hydrodynamic force model play a crucial role in predicting the dynamic behavior of mechanical systems and originate some uncertainties in their dynamic responses.

The control system of a highly dynamic robot requires the ability to respond quickly to changes in the robot’s state. This type of system is needed in varying fields such as dynamic locomotion, multicopter control, and human-robot interaction. Robots in these fields require software and hardware capable of hard real-time, high frequency control. In addition, the application outlined in this paper requires modular components, remote guidance, and mobile control. The described system integrates a computer on the robot for running a control algorithm, a bus for communicating with microcontrollers connected to sensors and actuators, and a remote user interface for interacting with the robot. Current commercial solutions can be expensive, and open source solutions are often time consuming. The key innovation described in this paper is the building of a control system from existing — mostly open source — components that can provide realtime, high frequency control of the robot. This paper covers the development of such a control system based on ROS, OROCOS, and EtherCAT, its implementation on a dynamic bipedal robot, and system performance test results.

This work presents the integration of a detailed biomechanical model of the arms of a helicopter pilot and an equivalently detailed aeroservoelastic model of a helicopter, resulting in what has been called a ‘bioaeroservoelastic’ analysis. The purpose is to investigate potential adverse interactions, called rotorcraft-pilot couplings, between the aeroservoelastic system and the controls involuntarily introduced by the pilot into the control system in response to rotorcraft vibrations transmitted to the pilot through the cockpit, the so-called biodynamic feedthrough. The force exerted by the pilot on the controls results from the activation of the muscles of the arms according to specific patterns. The reference muscular activation value as a function of the prescribed action on the controls is computed using an inverse kinetostatics/inverse dynamics approach. A first-order quasi-steady correction is adopted to mimic the reflexive contribution to muscle activation. Muscular activation is further augmented by activation patterns that produce elementary actions on the control inceptors. These muscular activation patterns, inferred using perturbation analysis, are applied to control the aircraft through the pilot’s limbs. The resulting biomechanical pilot model is applied to the aeroservoelastic analysis of a helicopter model expressly developed within the same multibody modeling environment to investigate adverse rotorcraft pilot couplings. The model consists of the detailed aeroelastic model of the main rotor, using nonlinear beams and blade element/momentum theory aerodynamics, a component mode synthesis model of the airframe structural dynamics, and servoactuator dynamics. Results in terms of stability analysis of the coupled system are presented in comparison with analogous results obtained using biodynamic feedthrough transfer functions identified from experimental data.

This paper proposes a measurement method of cubic non-linear elasticity. The measurement system consists of a vibrator and a control circuit. We apply a nonlinear feedback to actuate the vibrator for inducing van der Pol type self-excited oscillation, so that the response amplitude of the oscillation can be arbitrarily set by changing the nonlinear feedback gain. We focus on the fact that the nonlinear elasticity causes a natural frequency shift related to the vibration amplitude of the object. We can set the response amplitude various values by changing the nonlinear feedback gain and measure the shift of the response frequency depending on the magnitude of the response amplitude. As a result, the bend of the backbone curve reflecting the nonlinear elasticity of the object is obtained.

Legged locomotion has been a subject of study for many years. However, the role of the knee in whole-body dynamics of locomotion is not well understood, especially for non-conservative dynamics. Based upon a hip actuated Spring-Loaded Inverted Pendulum (Hip-actuated SLIP) model, we develop a more human-like, two-segment leg model with a pin-jointed springy knee, to see what effects a knee has in the context of an applied hip torque. Overall, we find that the governing equations for the two-segment (knee) version have a distinct structure when compared to the telescoping version of SLIP. The two-segment model with a knee spring influences forces acting on the mass center in a more complex way than a telescoping spring. While a wide variation of behavior is possible for the two-segment model, here we focus on comparing the dynamics for a special case when the knee spring resting angle is 90° . For this particular choice of resting knee angle we find that the knee version of actuated SLIP can have similar locomotion dynamics to the telescoping version of actuated SLIP. This result provides one explanation for how animals and robots with multi-segmented legs could produce overall center-of-mass dynamics that are similar to models with telescoping legs. Nonetheless, despite overall similarities for this special case, small differences in the stability of locomotion are still observed. In particular, we find that the knee version tends to be slightly more stable than the telescoping SLIP in terms of the allowable size of perturbations, while requiring higher input power.

Mooring cable system, fastening the floating platform is an indispensable segment in the development and utilization of ocean energy. However, the nonlinear cable geometry and nonlinear hydrodynamic forces perplex the construction of numerical modelling of mooring cable. Traditionally, the cable modelling is constructed just considering the geometry of cable, the normal, and the tangential directions. Not only the geometry of cable, but also the relative velocity of fluid is involved in constructing of the numerical modelling of cable in this paper. The expression of external loads by this numerical modelling is effective and accurate taking advantage of explicit separation of external loads in transverse and lengthwise directions. This modelling also simplified the formulation of hydrodynamic drag forces which is dominant among external loads. The stiffness and damping of cable, apparent weight, hydrodynamic drag forces, effect of added mass, and Froude-Krylov force are considered during building of this numerical modelling. The mooring cable fastening a floating sphere stands on buoyancy forces due to the submerged sphere. The simulation results of this numerical modelling were compared and verified with the results from ProteusDS which is an offshore simulation code.