Modeling of control forces for kinematical constraints in the dynamics of multibody systems: A new approach

Conventionally kinematical constraints in multibody systems are treated similar to geometrical constraints and are modeled by constraint reaction forces which are perpendicular to constraint surfaces. However, in reality, one may want to achieve the desired kinematical conditions by control forces having different directions in relation to the constraint surfaces. The conventional equations of motion for multibody systems subject to kinematical constraints are generalized by introducing general direction control forces. Conditions for the selections of the control force directions are also discussed. A redundant robotic system subject to prescribed end-effector motion is analyzed to illustrate the methods proposed

Explicit modeling of composite plates and beams in the dynamics of multibody systems

The state of the art dynamic response analysis of flexible multibody systems is currently restricted to elastic bodies with homogeneous materials. The requirements for high speed operation has made it necessary to use lightweight multi layered composite bodies in robotic systems and space structure applications. Dynamic modeling and analysis of such systems are particularly important since the effects of body flexibility to the performance are likely to be more pronounced. The eight-noded isoperimetric quadrilateral element with independent rotational and displacement degrees of freedom is extended to laminated composite elements. The element includes an arbitrary number of bonded layers, each of which may have a different thickness. The transverse shear deformation which is a predominant factor in the analysis of laminated composite structures is taken into account in developing the stiffness and mass matrices. The corresponding 3-D mode shapes are then incorporated to the multibody system dynamical equations. Floating body reference frames allow the selection of different boundary conditions, and the dynamical equations contain all the nonlinear interactions between the rigid and elastic motion. Example simulations are presented to illustrate the methods proposed

Optimum control forces for multibody systems with intermittent motion

The objective is to address the continuity of motion when a dynamical system is suddenly subjected to constraint conditions. Motion discontinuity due to the initial constraint violation is avoided by prior control forces that adjust the motion and yield velocity and acceleration consistent at the point of application of the constraint. The optimum control forces are determined for a specified control interval. The method proposed provides an optimum adjustment of the system's motion and assures that the stresses developed at the system components are kept within acceptable limits. The procedures developed will be illustrated making use of inequality constraints applied to obstacle avoidance problems in robotics

Stability analysis of constraints in flexible multibody systems dynamics

Automated algorithms for the dynamic analysis and simulation of constrained multibody systems assume that the constraint equations are linearly independent. During the motion, when the system is at a singular configuration, the constraint Jacobian matrix possesses less than full rank and hence it results in singularities. This occurs when the direction of a constraint coincides with the direction of the lost degree of freedom. In this paper the constraint equations for deformable bodies are modified for use in the neighborhood of the singular configuration to yield the system inertia matrix which is nonsingular and also to take the actual generalized constraint forces into account. The procedures developed are applicable to both the augmented approach and the coordinate reduction methods. For the modeling of the constrained flexible multibody systems, a general recursive formulation is developed using Kane's equations, finite element method and modal analysis techniques. The system may contain revolute, prismatic, spherical or other types of joints, as well as geometrical nonlinearities; the rotary inertia is also automatically included. Simulation of a two-link flexible manipulator is presented at a singular configuration to demonstrate the utility of the method.Publisher's Versio

Stability and dynamics of constrained flexible multibody systems.

Stability and dynamics of constrained flexible multibody systems

Trajectory tracking control of flexible-joint robots

Inverse dynamics control of flexible-joint robots is addressed. It is shown that, in a flexible-joint robot, the acceleration level inverse dynamic equations are singular because the control torques do not have an instantaneou; effect on the end-effector accelerations due to the elastic media. Implicit numerical integration methods that account for the higher order derivative information are utilized for solving the singular set of differential equations. The trajectory tracking control law presented linearizes and decouples the system and yields an asymptotically stable fourth order error dynamics for each end-effector degree of freedom. A 3R spatial robot with all joints flexible is simulated to illustrate the performance of the proposed algorithm

A switching inverse dynamics controller for parallel manipulators around drive singular configurations

Despite many advantages, parallel manipulators are known to possess drive singularities where the control of one or more degrees of freedom is lost. Around these singular configurations, the required actuator forces grow unbounded. Previous efforts in the literature put forward singularity-consistent trajectory planning and singularity robust modification of the dynamic equations as a solution to this problem. However, this previous method is applicable only for the open-loop operation of the manipulator, whereas initial configuration errors, external disturbances, and modeling errors should necessarily be taken into account in a closed-loop sense in real-life applications. With this aim, a switching inverse dynamics controller is proposed in this study for the trajectory tracking control of parallel manipulators as they pass through drive singular configurations. Simulations of the application of the developed controller result in good tracking performance, even in the presence of modeling errors, while the actuator efforts remain bounded and continuous in the neighborhood of the singularity

Hybrid Force and Motion Control of a Three-Dimensional Flexible Robot Considering Measurement Noises

This work addresses the end-effector trajectory-tracking force and motion control of a three-dimensional three-link robot considering measurement noises. The last two links of the manipulator are considered as structurally flexible. An absolute coordinate approach is used while obtaining the dynamic equations to avoid complex dynamic equations. In this approach, each link is modeled as if there is no connection between the links. Then, joint connections are expressed as constraint equations. After that, these constraint equations are used in dynamic equations to decrease the number of equations. Then, the resulting dynamic equations are transformed into a form which is suitable for controller design. Furthermore, the dynamic equations are divided as pseudostatic equilibrium and deviation equations. The control torques resulting from the pseudostatic equilibrium and the elastic deflections are obtained easily as the solution of algebraic equations. On the other hand, the control torques corresponding to the deviations are obtained without any linearization. Encoders, strain gauges, position sensors and force and moment sensors are required for measurements. Low pass filters are considered for the sensors. For the crossover frequencies of the sensors, low and high values are chosen to observe the filtering effect on the robot output