Robust nonlinear control of spacecraft formation flying using constraint forces

A robust nonlinear control method is presented for spacecraft precise formation flying.With the constraint forces and consid-ering nonlinearity and perturbations,the problem of the formation keeping is changed to the Lagrange systems with the holonomic constraints and the differential algebraic equations (DAE).The nonlinear control laws are developed by solving the DAE.Because the traditional numerical solving methods of DAE are very sensitive to the various errors and the resulting con-trol laws are not robust in engineering application,the robust control law designed method is further developed by designing the correct coefficients to correct the errors of the formation array constraints.A numeral study simulated the robustness of this method for the various errors in the formation flying mission,including the initial errors of spacecraft formation,the reference satellite orbit determination errors,the relative perturbation forces model errors,and so on.

Constraint Force Analysis of Metamorphic Joints Based on the Augmented Assur Groups

In order to obtain a simple way for the force analysis of metamorphic mechanisms, the systematic method to unify the force analysis approach of metamorphic mechanisms as that of conventional planar mechanisms is proposed. A force analysis method of metamorphic mechanisms is developed by transforming the augmented Assur groups into Assur groups, so that the force analysis problem of metamorphic mechanisms is converted into the force analysis problems of conventional planar mechanisms. The constraint force change rules and values of metamorphic joints are obtained by the proposed method, and the constraint force analysis equations of revolute metamorphic joints in augmented Assur group RRRR and prismatic metamorphic joints in augmented Assur group RRPR are deduced. The constraint force analysis is illustrated by the constrained spring force design of paper folding metamorphic mechanism, and its metamorphic working process is controlled by the spring force and geometric constraints of metamorphic joints. The results of spring force show that developped design method and approach are feasible and practical. By transforming augmented Assur groups into Assur groups, a new method for the constraint force analysis of metamorphic joints is proposed firstly to provide the basis for dynamic analysis of metamorphic mechanism.

On Mechanical Property of Constraint

In this paper. the mechanical properties of holonomic systems and mon-holonomicsystems are strdied. This is an important and urgent problem.

New method for multibody dynamics based on unknown constraint force

This paper presents a new method for the dynamics of multibody systems based on unknown constraint force. The method can uniformly solve multibody systems with typical configurations, including the system with rigid-flexible coupling, the system in tree topology, and the system with loop constraints. Unlike common methods, the proposed method can model the loop system without “cutting off” loop constraints, leading to the exact same modelling process as the tree-like system performs. Based on graph theory, a topological record matrix M_(rec) is proposed to capture the arbitrary system configuration. Moreover, constraint forces are selected as the key variables in semi-recursive framework. With the recursive kinematics relationship between adjacent bodies, the constraint force equation is further assembled to achieve the full-state system solution. The numerical simulations demonstrate the accuracy of the proposed method.

THE GENERAL METHOD FOR SOLVING DYNAMIC PROBLEMS

In this paper the author has used the normalized Routh equations[1]to .solve the dynamic problems and establish the general method for. finding out the constraint forces and the variations of the state of motion for the complicated system.

Type Synthesis of Two-Degrees-of-Freedom Rotational Parallel Mechanism with Two Continuous Rotational Axes

The two-rotational-degrees-of-freedom（2R） parallel mechanism（PM） with two continuous rotational axes（CRAs） has a simple kinematic model.It is therefore easy to implement trajectory planning,parameter calibration,and motion control,which allows for a variety of application prospects.However,no systematic analysis on structural constraints of the 2R-PM with two CRAs has been performed,and there are only a few types of 2R-PM with two CRAs.Thus,a theory regarding the type synthesis of the 2R-PM with two CRAs is systematically established.First,combining the theories of reciprocal screw and space geometry,the spatial arrangement relationships of the constraint forces applied to the moving platform by the branches are explored,which give the 2R-PM two CRAs.The different distributions of the constraint forces in each branch are also studied.On the basis of the obtained structural constraints of branches,and considering the geometric relationships of constraint forces in each branch,the appropriate kinematic chains are constructed.Through the reasonable configuration of branch kinematic chains corresponding to every structural constraint,a series of new 2R-PMs with two CRAs are finally obtained.

Tracking Control Design for Nonholonomic Mechanical Systems with Affine Constraints

The trajectory tracking control is considered for nonholonomic mechanical systems with affine constraints and dynamic friction. A new state transformation is proposed to deal with affine constraints, and then an integral feedback compensation strategy is used to identify the dynamic friction. The proposed controller ensures that the output tracking errors converge to zero as t →∞.As an application, a detailed example is presented to illustrate the effectiveness of the control scheme.

Behavior Analysis of Biomimetic Soft Bending Actuators in Free Motion and Contact

Bioinspired Soft Bending Actuators (SBA) are increasingly being used in rehabilitation, assistant robots, and grippers. Despite many investigations on free motion modeling, understanding how these actuators interact with the environment requires more detailed research. It is caused by high compliance and nonlinearity of bioinspired soft material, which leads to serious challenges in contact conditions. In this paper, a continuous deformation analysis is presented to describe the free motion nonlinear behavior of the actuator. Based on the achieved result, this study proposes static modeling of SBA affected by a concentrated external force. For this purpose, the finite rigid element method is utilized, which is based on discretizing the actuator into smaller parts and assuming these parts as rigid serial links connected by nonlinear torsional springs. To verify the proposed model, two kinds of forces are considered to be acting on the actuator, i.e. following force and constant direction force. In addition, the effect of gravity on the actuator configuration is also investigated. The validity of the model has been demonstrated through experiments in free motion, contact conditions and the presence of gravity. It generally shows that the prediction error of robot configuration is lower than 7.5%.