Unknown Contact Forces Research Articles

Unified Method for Task-Space Motion/Force/Impedance Control of Manipulator With Unknown Contact Reaction Strategy

Nowadays, higher requirements are placed on the design of the controller when robots enter the factory and co-operate with human. In this letter, we propose a unified task space control method combined with the contact reaction strategy in null space of redundant manipulator, which can not only conveniently switch between different control objectives according to specific tasks, but also react to the unknown contact with compliance. Specifically, the unknown contact force applied on the manipulator’s body is online estimated based on recursive least square estimation law in joint space. Then, the closed-loop dynamics of different control objectives are unified in task space by a generalized target model, and a model-reaching law based on adaptive robust control is proposed to achieve the target model even if there exists an unknown contact. Meanwhile, the estimated contact force is not only compensated in the model-reaching control law to guarantee the correct task execution but also used for the null space impedance control design to ensure compliant behavior. The performance and stability of the proposed scheme are guaranteed and proved in theory. Experiments are conducted on a 7-DoF manipulator for the validation.

Flatness‐based disturbance observer for exoskeleton robots under time‐delayed contact forces

AbstractThe article proposes flatness‐based control and a Kalman filter‐based disturbance observer for solving the control problem of a robotic exoskeleton under time‐delayed exogenous disturbances. A two‐link lower‐limb robotic exoskeleton is used as a case study. It is proven that this robotic system is differentially flat. The robot is considered to be subject to unknown contact forces at its free‐end which in turn generate unknown disturbance torques at its joints. It is shown that the dynamic model of the robotic exoskeleton can be transformed into the input–output linearized form and equivalently into the linear canonical Brunovsky form. This linearized description of the exoskeleton's dynamics is both controllable and observable. It allows for designing a stabilizing feedback controller with the use of the pole‐placement (eigenvalues assignment) method. Moreover, it allows for solving the state estimation problem with the use of Kalman Filtering (the use of the Kalman filter on the flatness‐based linearized model of nonlinear dynamical systems is also known as derivative‐free nonlinear Kalman filtering). Furthermore, (i) by extending the state vector of the exoskeleton after considering as additional state variables the additive disturbance torques which affect its joints and (ii) by redesigning the Kalman filter as a disturbance observer, one can achieve the real‐time estimation of the perturbations that affect this robotic system. Finally, by including in the controller of the exoskeleton additional terms that compensate for the estimated disturbance torques, the perturbations' effects can be eliminated and the precise tracking of reference trajectories by the joints of this robot can be ensured.

Investigation on the performance of the expansion water seal by using isogeometric analysis with variational inequalities for the frictional contact

In this study, IGA is introduced into the performance analysis of the expansion water seal for an exact representation of its complex geometrical shape. Firstly, the incremental equilibrium equations used in the large deformation analysis are derived for the IGA discretization model based on the updated Lagrangian formulation. The unknown contact forces are directly involved in the equilibrium equations, which results in a simple expression. Then, through the investigation of the contact conditions, the normal and tangential contact forces are verified to be the solutions of two box-constrained variational inequalities representing the normal and tangential contact conditions, respectively. Furthermore, the incremental equilibrium equations for all components of the water seal system and the variational inequalities for all contacts between the components are assembled together and reformulated as a global variational inequality, which is resolved by using the Extra-gradient method. Ultimately, the new method is applied in the performance comparison of two optional expansion water seals, in which the capability and precision of the proposed method are investigated. Results verify that the proposed method is effective in the numerical simulation of the expansion water seal and has a higher precision than the traditional FEM under the same conditions.

Sensorless force estimation for industrial robots using disturbance observer and neural learning of friction approximation

Contact force estimation enables robots to physically interact with unknown environments and to work with human operators in a shared workspace. Most heavy-duty industrial robots without built-in force/torque sensors rely on the inverse dynamics for the sensorless force estimation. However, this scheme suffers from the serious model uncertainty induced by the nonnegligible noise in the estimation process. This paper proposes a sensorless scheme to estimate the unknown contact force induced by the physical interaction with robots. The model-based identification scheme is initially used to obtain dynamic parameters. Then, neural learning of friction approximation is designed to enhance estimation performance for robotic systems subject with the model uncertainty. The external force exerted on the robot is estimated by a disturbance observer which models the external disturbance. A momentum observer is modified to develop a disturbance Kalman filter-based approach for estimating the contact force. The neural network-based model uncertainty and measurement noise level are analysed to guarantee the robustness of the Kalman filter-based force observer. The proposed scheme is verified by the measurement data from a heavy-duty industrial robot with 6 degrees of freedom (KUKA AUGLIS six). The experimental results are used to demonstrate the estimation performance of the proposed approach by the comparison with the existing schemes. • A novel sensorless scheme is developed to estimate unknown contact force for robots. • NN learning of friction compensates model uncertainties with good approximation. • Disturbance Kalman filter observer is to achieve accurate contact force estimation • Observers and NN learning of friction show robust observation to small contact force.

Transforming Calculated Schemes in Geometrically Non-linear Mechanics Problems of the Sandwich Plates with Contour Reinforcing Beams

A numerical study of the geometrically nonlinear problem of deforming the cylindrical shape of a sandwich plate with a transversally soft core, supported in the end sections of absolutely rigid bodies, according to transforming calculation schemes as it is loaded, has been carried out. It is shown that such a transformation is necessary after the delamination of the adhesive layer connecting the end section of the core with the contour reinforcing beam, designed to ensure the transfer of external load on the carrier layers. The previously obtained equations were used, which are based on introducing into consideration, as unknown contact forces, the interaction of the outer layers with a core, as well as the external layers and the core with reinforcing bodies at all points of their interface surfaces. The problem under study required the sequential formulation and solving of two problems: on the stress-strain state of the structure until the beginning of the destruction of the adhesive layer between the core and the reinforcing beam and about determining the increments of the parameters of the stress-strain state after delamination. To simulate the delamination process, a method based on the parameter continuation method is proposed. This method provides for zeroing the tangential stresses formed in the adhesive layer at the first loading stage, by choosing the incremental tangent stresses specified above as the loading parameter. Numerical methods for solving the formulated problems were developed. They are based on a preliminary reduction of the initial problems to systems of integro-algebraic equations and the construction of their solutions by the finite sum method. To resolve the geometric nonlinearity, a two-layer iterative process is used.

Contact Force Estimation for Robot Manipulator Using Semiparametric Model and Disturbance Kalman Filter

Force estimation methods enable robots to interact with the environment or humans compliantly and safely without additional sensing device. In this paper, we present a novel method for estimating unknown contact forces exerted on a robot manipulator. The force estimation method is divided into two steps. The first step is to identify a robot dynamics model. A parametric model is derived first based on rigid-body dynamic (RBD) theory. To improve the model accuracy, a nonparametric compensator trained with multilayer perception (MLP) is added to compensate for errors of the RBD model. The result is a semiparametric model that provides better model accuracy than either the RBD model or the MLP model alone. The second step is to construct a force estimation observer. A novel estimation method called disturbance Kalman filter (DKF) is developed in this paper. The design of DKF based on a time-invariant composite system model is presented. DKF can take both manipulator's dynamics model and disturbance's dynamics model into account. As with Kalman filter, it can provide robust and accurate estimation against uncertainty. Simulation and experimental results, obtained using a six-degrees-of-freedom Kinova Jaco2 manipulator, demonstrate the effectiveness of the proposed method.

Robust Control of an Aerial Manipulator Interacting with the Environment

This paper deals with the problem of modelling and controlling a vertical take-off and landing aircraft equipped with a lightweight robotic arm. This system is able to perform complex operations that require the physical interaction with the environment while remaining airborne. Once the dynamical model in the 3D case is provided, a control law able to let the degrees of freedom of the system to track a desired trajectory is derived. The proposed controller takes into account the interaction between the robotic arm and the aerial platform both during free-flight and in the presence of unknown contact forces deriving from the interaction with the environment. The effectiveness and main properties of the proposed control algorithm have been analytically investigated and then demonstrated with the help of an experiment.

Contact statement of mechanical problems of reinforced on a contour sandwich plates with transversally-soft core

For the sandwich plates and shells with transversally-soft core and carrier layers having on the outer contour of the reinforcing rod, for small deformations, and middle displacements we construct refined geometrically nonlinear theory. This theory allows to describe the process of the subcritical deformation and identify all possible buckling of carrier layers and reinforcing rods. It is based on the introduction as unknown contact forces at the points of interaction mating surface of the outer layers with core and carrier layers and a core with reinforcing rods at all points of the surface of their conjugation to the shell contour. To derive the basic equations of equilibrium, static boundary conditions for the shell and reinforcing rods, as well as conditions of the kinematic coupling of the carrier layers with a core, the carrier layers and a core with reinforcing rods we use previously proposed generalized Lagrange variational principle.

CONTACT FORCE MODEL FOR A BEAM WITH DISCRETELY SPACED GAP SUPPORTS AND ITS APPROXIMATED SOLUTION

This paper proposes an approximated contact force model to identify the nonlinear behavior of a fuel rod with gap supports; also, the numerical prediction of interfacial forces in the mechanical contact of fuel rods with gap supports is studied. The Newmark integration method requires the current status of the contact force, but the contact force is not given a priori. Taylor's expansion can be used to predict the unknown contact force; therefore, it should be guaranteed that the first derivative of the contact force is continuous. This work proposes a continuous and differentiable contact force model with the ability to estimate the current state of the contact force. An approximated convex and differentiable potential function for the contact force is described, and a variational formulation is also provided. A numerical example that considers the particularly stiff supports has been studied, and a fuel rod with hardening supports was also examined for a realistic simulation. An approximated proper solution can be obtained using the results, and abrupt changes from the contacting state to non-contacting state, or vice versa, can be relieved. It can also be seen that not only the external force but also the developed contact force affects the response.

Determination of Stress Intensity Factors for a Cracked Shell under Bending with Improved Shell Theories

A formulation based on the linearized shallow shell theory has been developed by Delale and Erdogan to determine the stress intensity factors of a shell with a through-the-thickness crack. The drawback in the formulation is that the crack-face closure at the compressive edges when a cracked shell is subjected to a bending load is not taken into account, which results in the penetration of material at the crack faces. The present research is aimed to improve the formulation by including the effect of the crack-face closure on the stress intensity factors. Simulation of the closure is achieved by a line contact at the compressive edges of the crack faces. The unknown contact force is then computed by solving a mixed-boundary value problem iteratively to ensure that either the normal displacement of the crack face at the compressive edges equals zero or the contact pressure equals zero along the crack length. The results have shown that the crack-face closure significantly influences the magnitude of the stress intensity factors and tends to reduce the maximum stress intensity factor. The magnitude of the reduction varies with the curvatures of the shell and the ratio of the two curvatures as well.

Effect of crack closure in a specially orthotropic cylindrical shell containing an axial or a circumferential crack

This article presents a theoretical analysis of the crack-face closure behaviors of an axial or a circumferential crack in a specially orthotropic cylindrical shell, emphasizing the influence of material orthotropy on crack-tip stress field. The shallow shell theory developed by Delale and Erdogan is extended to incorporate the effect of crack-face closure. In the present analysis the crack-face closure is modeled by a line contact at the compressive edges of the crack faces. The unknown contact force is then computed by solving a mixed-boundary value problem iteratively to ensure that either the normal displacement of the crack face at the compressive edges equals zero or the contact pressure equals zero along the crack length. The results show that the curvature effect causes the closure behavior in cylindrical shells to differ considerably from that in flat plates. Instead of complete closure over the entire crack length in flat plates, only partial closure occurs along the crack length in shells with large curvatures. Material orthotropy is also found to strongly influence the closure behavior of an axial crack but not that of a circumferential crack. In both cases the crack closure is found to reduce the maximum stress intensity factors, which is the most pronounced for shells with large radii for a given crack length and shell thickness.

Effect of crack closure in a specially orthotropic cylindrical shell containing an axial or a circumferential crack

This article presents a theoretical analysis of the crack-face closure behaviors of an axial or a circumferential crack in a specially orthotropic cylindrical shell, emphasizing the influence of material orthotropy on crack-tip stress field. The shallow shell theory developed by Delale and Erdogan is extended to incorporate the effect of crack-face closure. In the present analysis the crack-face closure is modeled by a line contact at the compressive edges of the crack faces. The unknown contact force is then computed by solving a mixed-boundary value problem iteratively to ensure that either the normal displacement of the crack face at the compressive edges equals zero or the contact pressure equals zero along the crack length. The results show that the curvature effect causes the closure behavior in cylindrical shells to differ considerably from that in flat plates. Instead of complete closure over the entire crack length in flat plates, only partial closure occurs along the crack length in shells with large curvatures. Material orthotropy is also found to strongly influence the closure behavior of an axial crack but not that of a circumferential crack. In both cases the crack closure is found to reduce the maximum stress intensity factors, which is the most pronounced for shells with large radii for a given crack length and shell thickness.

Crack closure effect on stress intensity factors of an axially and a circumferentially cracked cylindrical shell

Crack-face closure occurs when a shell or plate containing a through-the-thickness crack is subjected to a bending load, which leads to lower stress-intensity factors than those expected from non-closure assumption. This article presents a theoretical analysis of the effect of crack-face closure on the stress intensity factors of an axially and a circumferentially cracked cylindrical shell subjected to bending moment respectively. The presented analysis extends the shallow shell theories of Delale and Erdogan by incorporating the effect of crack-face closure. In keeping consistent with the shear deformation shell theory, crack-face closure is modeled by a line contact at the compressive edges of the crack face. The unknown contact force is computed by solving a mixed-boundary value problem iteratively, i.e. along the crack length, either the normal displacement of the crack face at the compressive edges is equal to zero or the contact pressure is equal to zero. The results show that the distribution of the contact force along the crack is generally nonuniform. Furthermore, it is found that, similar to the case of spherical shells, crack closure may occur over the full length or only some segments of the crack in cylindrical shells, depending on the geometry of the shell and the nature (direction) of applied bending load. Comparisons of the stress intensity factor ratios between the closure solutions and the non-closure solutions reveal that the crack-face closure influences significantly the magnitude of the stress intensity factors and it tends to reduce the maximum stress intensity factor. The closure effect of crack face on the stress intensity factors is highest when the shell radius becomes very large for a given crack length and shell thickness.

An improved contact-impact algorithm for explicit integration FEM

Although the penalty algorithm is simple and direct in concept, it has a defect that the contact forces are badly dependent on the chosen penalty factor. An improved contact-impact algorithm for the explicit integration FEM is proposed in the present paper. Based on the fact that bodies cannot penetrate into each other on the contact faces, a set of equations with the additional unknown contact forces on the slave nodes can be formed in a new system configuration. By solving these equations, the correct contact forces could be obtained without using the penalty factor.

Bending of an Elastic Anisotropic Plate with a Circular Opening Stiffened Over Finite Areas

A contact problem is solved for an infinite anisotropic plate weakened by a circular opening, stiffened by inclusions of variable stiffness, and subjected to bending. For the unknown contact force of interaction between the plate and an inclusion, an integro-differential equation is derived and then reduced to an infinite system of linear algebraic equations. The system is analyzed for regularity.

A Note on the Use of the Instant Center as a Reference Point for Angular Momentum Theorems

The use of the instant center as a reference point in angular momentum theorems has the advantage that unknown contact forces do not appear in the equations of motion. However, care must be taken to distinguish the point as being on the body or the space centrode.