Spatial Operator Algebra for Free-floating Space Robot Modeling and Simulation

As the dynamic equations of space robots are highly nonlinear,strongly coupled and nonholonomic constrained,the efficiency of current dynamic modeling algorithms is difficult to meet the requirements of real-time simulation.This paper combines an efficient spatial operator algebra（SOA） algorithm for base fixed robots with the conservation of linear and angular momentum theory to establish dynamic equations for the free-floating space robot,and analyzes the influence to the base body＇s position and posture when the manipulator is capturing a target.The recursive Newton-Euler kinematic equations on screw form for the space robot are derived,and the techniques of the sequential filtering and smoothing methods in optimal estimation theory are used to derive an innovation factorization and inverse of the generalized mass matrix which immediately achieve high computational efficiency.The high efficient SOA algorithm is spatially recursive and has a simple math expression and a clear physical understanding,and its computational complexity grows only linearly with the number of degrees of freedom.Finally,a space robot with three degrees of freedom manipulator is simulated in Matematica 6.0.Compared with ADAMS,the simulation reveals that the SOA algorithm is much more efficient to solve the forward and inverse dynamic problems.As a result,the requirements of real-time simulation for dynamics of free-floating space robot are solved and a new analytic modeling system is established for free-floating space robot.

Impact dynamics analysis of free-floating space manipulator capturing satellite on orbit and robust adaptive compound control algorithm design for suppressing motion

The impact dynamics, impact effect, and post-impact unstable motion sup- pression of free-floating space manipulator capturing a satellite on orbit are analyzed. Firstly, the dynamics equation of free-floating space manipulator is derived using the sec- ond Lagrangian equation. Combining the momentum conservation principle, the impact dynamics and effect between the space manipulator end-effector and satellite of the cap- ture process are analyzed with the momentum impulse method. Focusing on the unstable motion of space manipulator due to the above impact effect, a robust adaptive compound control algorithm is designed to suppress the above unstable motion. There is no need to control the free-floating base position to save the jet fuel. Finally, the simulation is proposed to show the impact effect and verify the validity of the control algorithm.

THE ROBUST CONTROL SCHEME FOR FREE-FLOATING SPACE MANIPULATOR TO TRACK THE DESIRED TRAJECTORY IN JOINTSPACE

The control of a free-floating space manipulator system isdiscussed. With the augmentation approach, the nonlinearparameterization problem of the dynamic equations of the spacemanipulator system is overcome. Based on the results, the robustcontrol scheme for free-floating space manipulator with uncer- tainpayload parameters to track the desired trajectory in jointspace isproposed, and the global convergence of the tracking is verified byusing the Lyapunov method.

Singular perturbation composite control of a free-floating flexible dual-arm space robot

The Free-floating Flexible Dual-arm Space Robot is a highly nonlinear and coupled dynamics system. In this paper, the dynamic model is derived of a Free-floating Flexible Dual-arm Space Robot holding a rigid payload. Furthermore, according to the singular perturbation method, the system is separated into a slow subsystem representing rigid body motion of the robot and a fast subsystem representing the flexible link dynamics. For the slow subsystem, based on the second method of Lyapunov, using simple quantitative bounds on the model uncertainties, a robust tracking controller design is used during the trajectory tracking phase. The optimal control method is designed in the fast subsystem to guarantee the exponential stability. With the combination of the two above, the system can track the expected trajectory accurately, even though with uncertainty in model parameters, and its flexible vibration gets suppressed, too. Finally, some simulation tests have been conducted to verify the effectiveness of the proposed methods.

Motion planning for redundant prismatic-jointed manipulators in the free-floating mode

This paper investigates the motion planning of redundant free-floating manipulators with seven prismatic joints. On the earth, prismatic-jointed manipulators could only position their end-effectors in a desired way. However, in space, the end-effectors of free-floating manipulators can achieve both the desired orientation and desired position due to the dynamical coupling between manipulator and satellite movement, which is formally expressed by linear and angular momentum conservation laws. In this study, a tractable algorithm particle swarm optimization combined with differential evolution （PSODE） is provided to deal with the motion planning of redundant free-floating prismatic-jointed manipulators, which could avoid the pseudo inverse of the Jacobian matrix. The polynomial functions, as argument in sine functions are used to specify the joint paths. The co- efficients of the polynomials are optimized to achieve the desired end-effector orientation and position, and simulta- neously minimize the unit-mass-kinetic energy using the redundancy. Relevant simulations prove that this method pro- vides satisfactory smooth paths for redundant free-floating prismatic-jointed manipulators. This study could help to recognize the advantages of redundant prismatic-jointed space manipulators.

The effects of two free-floating plants (Eichhornia crassipes and Pistia stratiotes) on the burrow morphology and water quality characteristics of pond loach (Misgurnus anguillicaudatus) habitat

Loach exhibit conspicuous drilling behaviors in the mud of shallow waters,yet their burrow morphology and the factors affecting this behavior have received little attention.We characterized the burrow morphology and water quality of the pond loach Misgurnus anguillicaudatus in three scenarios:in tanks without plants,tanks with the free-floating plant water hyacinth Eichhornia crassipes,and tanks with water lettuce Pistia stratiotes.Water hyacinth effectively removed water TN,COD,NO3-N and NH4-N,and water lettuce removed water TP and NH4-N.Water hyacinth and water lettuce markedly reduced water turbidity and DO,increased TOC and EC.Water hyacinth purified water more effectively than water lettuce,providing a suitable habitat for loach feeding,living and burrowing.The burrow structures were V-shaped,Y-shaped,inverted L-shaped,or complicated dendritic networks composed of multiple V shapes.The hyacinth treatment was characterized by the greatest burrow volume,length,depth,and structural complexity,but the opening size was reduced by dense root mat coverage.Burrows in the water lettuce treatment were characterized by intermediate volume,length,branches and sinuosity,but they had the largest opening and pit size.The control treatment had a flat bottom with the smallest,shortest burrows.This study indicates that free-floating plants improve habitat suitability and change burrow morphology and may be used to improve loach breeding methods。

Trajectory planning and base attitude restoration of dual-arm free-floating space robot by enhanced bidirectional approach

When free-floating space robots perform space tasks,the satellite base attitude is disturbed by the dynamic coupling.The disturbance of the base orientation may affect the communication between the space robot and the control center on earth.In this paper,the enhanced bidirectional approach is proposed to plan the manipulator trajectory and eliminate the final base attitude variation.A novel acceleration level state equation for the nonholonomic problem is proposed,and a new intermediate variable-based Lyapunov function is derived and solved for smooth joint trajectory and restorable base trajectories.In the method,the state equation is first proposed for dual-arm robots with and without end constraints,and the system stability is analyzed to obtain the system input.The input modification further increases the system stability and simplifies the calculation complexity.Simulations are carried out in the end,and the proposed method is validated in minimizing final base attitude change and trajectory smoothness.Moreover,the minute internal force during the coordinated operation and the considerable computing efficiency increases the feasibility of the method during space tasks.

Free-floating bike-sharing green relocation problem considering greenhouse gas emissions

This paper introduces the problem of green bike relocation considering greenhouse gas emissions in free-floating bike-sharing systems(FFBSSs)and establishes a mathematical model of the problem.This model minimizes the total imbalance degree of bikes in the FFBSS and the greenhouse gas emissions generated by relocation in the FFBSS.Before the relocation phase,the FFBSS is divided into multiple relocation areas using a two-layer clustering method to reduce the scale of the relocation problem.In the relocation phase,the relocation route problem is converted into a pickup and delivery vehicle-routing problem.Then,an adaptive variable neighbourhood tabu search algorithm with a three-dimensional tabu list is proposed,which can simultaneously solve the relocation problem and the routing problem.A computational study based on the actual FFBSS used in Shanghai shows that this method can effectively solve the green relocation problem of FFBSSs.

Development of Sichuan Brocade with Imitating Embroidery Effect Based on Free-Floats Interlacing Weave

Owing to the diversity of consumer’s demand, the traditional Sichuan brocade products have to be innovated in order to survive in a competitive environment. Since the construction of traditional Sichuan brocade was composed of basic-weave, the surface of the fabric shows a regular interweaving planar texture and is difficult to represent a three-dimensional effect. Inspired by embroidery handcraft, this paper attempts to achieve the embroidery-like effect on the fabric through the jacquard process. Based on the multi-backed structure of traditional Sichuan brocade, we adopted the zoned-combination design mode and added extra free-floats interlacing weave in the area where we want to show the embroidered effect and arranged the interlacing points by referring to the feature of the pattern. As a result, designed Sichuan brocades by this method are capable of displaying embroidered effect with high realism and three-dimensionality. This approach improves the artistic effect of the traditional Sichuan brocade and provides a technical reference for further texture design of jacquard fabrics.

Terminal sliding mode control for coordinated motion of a space rigid manipulator with external disturbance

The control problem of coordinated motion of a free-floating space rigid manipulator with external disturbance is discussed. By combining linear momentum conversion and the Lagrangian approach, the full-control dynamic equation and the Jacobian relation of a free-floating space rigid manipulator are established and then inverted to the state equation for control design. Based on the terminal sliding mode control （SMC） technique, a mathematical expression of the terminal sliding surface is proposed. The terminal SMC scheme is then developed for coordinated motion between the base＇s attitude and the end-effector of the free-floating space manipulator with external disturbance. This proposed control scheme not only guarantees the existence of the sliding phase of the closed-loop system, but also ensures that the output tracking error converges to zero in finite time. In addition, because the initial system state is always at the terminal sliding surface, the control scheme can eliminate reaching phase of the SMC and guarantee global robustness and stability of the closed-loop system. A planar free-floating space rigid manipulator is simulated to verify the feasibility of the proposed control scheme.

Detumbling strategy based on friction control of dual-arm space robot for capturing tumbling target

The rotational motion of a tumbling target brings great challenges to space robot on successfully capturing the tumbling target.Therefore,it is necessary to reduce the target's rotation to a rate at which capture can be accomplished by the space robot.In this paper,a detumbling strategy based on friction control of dual-arm space robot for capturing tumbling target is proposed.This strategy can reduce the target's rotational velocity while maintaining base attitude stability through the establishment of the rotation attenuation controller and base attitude adjustment controller.The rotation attenuation controller adopts the multi-space hybrid impedance control method to control the friction precisely.The base attitude adjustment controller applies the dual-arm extended Jacobian matrix to stabilize the base attitude.The main contributions of this paper are as follows:(1)The compliant control method is adopted to achieve a precise friction control,which can reduce the target angular velocity steadily;(2)The dual-arm extended Jacobian matrix is applied to stabilize the base attitude without affecting the target capture task;(3)The detumbling strategy of dualarm space robot is designed considering base attitude stabilization,realizing coordinated planning of the base attitude and the arms.The strategy is verified by a dual-arm space robot with two 7-DOF(degrees of freedom)arms.Simulation results show that,target with a rotation velocity of 20(°)/s can be effectively controlled to stop within 30 s,and the final deflection of the base attitude is less than 0.15°without affecting the target capture task,verifying the correctness and effectiveness of the strategy.Except to the tumbling target capture task,the control strategy can also be applied to other typical on-orbit operation tasks such as space debris removal and spacecraft maintenance.