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.

Anti-Dead-Zone Integral Sliding Control and Active Vibration Suppression of a Free-floating Space Robot with Elastic Base and Flexible Links

Under the conditions of joint torque output dead-zone and external disturbance,the trajectory tracking and vibration suppression for a free-floating space robot(FFSR)system with elastic base and flexible links were discussed.First,using the Lagrange equation of the second kind,the dynamic model of the system was derived.Second,utilizing singular perturbation theory,a slow subsystem describing the rigid motion and a fast subsystem corresponding to flexible vibration were obtained.For the slow subsystem,when the width of deadzone is uncertain,a dead-zone pre-compensator was designed to eliminate the impact of joint torque output dead-zone,and an integral sliding mode neural network control was proposed.The integral sliding mode term can reduce the steady state error.For the fast subsystem,an optimal linear quadratic regulator(LQR)controller was adopted to damp out the vibration of the flexible links and elastic base simultaneously.Finally,computer simulations show the effectiveness of the compound control method.

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.

Singularity Robust Path Planning for Real Time Base Attitude Adjustment of Free-floating Space Robot

This paper presents a singularity robust path planning for space manipulator to achieve base （satellite） attitude adjustment and end-effector task. The base attitude adjustment by the movement of manipulator will save propellant compared with conventional attitude control system. A task-priority reaction null-space control method is applied to achieve the primary task of adjusting attitude and secondary task of accomplishing end-effector task. Furthermore, the algorithm singularity is eliminated in the proposed algorithm compared with conventional reaction null-space algorithm. And the singular value filtering decomposition is introduced to dispose the dynamic singularity, the unit quaternion is also introduced to overcome representation singularity. Hence, a singularity robust path planning algorithm of space robot for base attitude adjustment is derived. A real time simulation system of the space robot under Linux/RTAl （realtime application interface） is developed to verify and test the feasibility and reliability of the method. The experimental results demonstrate the feasibility of online base attitude adjustment of space robot by the proposed algorithm.

Analysis of reaction torque-based control of a redundant free-floating space robot

Owing to the dynamics coupling between a free-floating base and a manipulator, the non-stationary base of a space robot will face the issue of base disturbance due to a manipulator＇s motion. The reaction torque acted on the satellite base＇s centroid is an important index to measure the satellite base＇s disturbance. In this paper, a comprehensive analysis of the reaction torque is made, and a novel way to derive the analytical form of the reaction torque is proposed. In addition,the reaction torque null-space is derived, in which the manipulator＇s joint motion is dynamically decoupled from the motion of the satellite base, and its novel expression demonstrates the equivalence between the reaction torque null-space and the reaction null-space. Furthermore, the reaction torque acted as an optimization index can be utilized to achieve satellite base disturbance minimization in the generalized Jacobian-based end-effector Cartesian path tracking task. Besides, supposing that the redundant degrees of freedom are abundant to achieve reaction torque-based active control, the reaction torque can be used to realize satellite base attitude control, that is, base attitude adjustment or maintenance. Moreover, because reaction torque-based control is a second-order control scheme, joint torque minimization can be regarded as the optimization task in reaction torque-based active or in-active control. A real-time simulation system of a 7-DOF space robot under Linux/RTAI is developed to verify and test the feasibility and reliability of the proposed ideas. Our extensive empirical results demonstrate that the corresponding analysis about the reaction torque is correct and the proposed methods are feasible.

Hybrid task priority-based motion control of a redundant free-floating space robot

This paper presents a novel hybrid task priority-based motion planning algorithm of a space robot. The satellite attitude control task is defined as the primary task, while the leastsquares-based non-strict task priority solution of the end-effector plus the multi-constraint task is viewed as the secondary task. Furthermore, a null-space task compensation strategy in the joint space is proposed to derive the combination of non-strict and strict task-priority motion planning,and this novel combination is termed hybrid task priority control. Thus, the secondary task is implemented in the primary task＇s null-space. Besides, the transition of the state of multiple constraints between activeness and inactiveness will only influence the end-effector task without any effect on the primary task. A set of numerical experiments made in a real-time simulation system under Linux/RTAI shows the validity and feasibility of the proposed methodology.

Task space control of free-floating space robots using constrained adaptive RBF-NTSM

Trajectory tracking control of space robots in task space is of great importance to space missions,which require on-orbit manipulations.This paper focuses on position and attitude tracking control of a free-floating space robot in task space.Since neither the nonlinear terms and parametric uncertainties of the dynamic model,nor the external disturbances are known,an adaptive radial basis function network based nonsingular terminal sliding mode(RBF-NTSM)control method is presented.The proposed algorithm combines the nonlinear sliding manifold with the radial basis function to improve control performance.Moreover,in order to account for actuator physical constraints,a constrained adaptive RBF-NTSM,which employs a RBF network to compensate for the limited input is developed.The adaptive updating laws acquired by Lyapunov approach guarantee the global stability of the control system and suppress chattering problems.Two examples are provided using a six-link free-floating space robot.Simulation results clearly demonstrate that the proposed constrained adaptive RBF-NTSM control method performs high precision task based on incomplete dynamic model of the space robots.In addition,the control errors converge faster and the chattering is eliminated comparing to traditional sliding mode control.

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.

Path planning of a free-floating space robot based on the degree of controllability

An effective and more efficient path planning algorithm is developed for a kinematically non-redundant free-floating space robot(FFSR) system by proposing a concept of degree of controllability(DOC) for underactuated systems. The DOC concept is proposed for making full use of the internal couplings and then achieving a better control effect, followed by a certain definition of controllability measurement which measures the DOC, based on obtaining an explicit and finite equivalent affine system and singular value decomposition. A simple method for nilpotent approximation of the Lie algebra generated by the FFSR system is put forward by direct Taylor expansion when obtaining the equivalent system. Afterwards, a large-controlla- bility-measurement(LCM) nominal path is searched by a weighted A* algorithm, and an optimal self-correcting method is designed to track the nominal path approximately, yielding an efficient underactuated path. The proposed strategy successfully avoids the drawback of inefficiency inherent in previous path-planning schemes, which is due to the neglect of internal couplings, and illustrative numerical examples show its efficacy.

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.

Behavior of Delivery Robot in Human-Robot Collaborative Spaces During Navigation

Navigation is an essential skill for robots.It becomes a cumbersome task for the robot in a human-populated environment,and Industry 5.0 is an emerging trend that focuses on the interaction between humans and robots.Robot behavior in a social setting is the key to human acceptance while ensuring human comfort and safety.With the advancement in robotics technology,the true use cases of robots in the tourism and hospitality industry are expanding in number.There are very few experimental studies focusing on how people perceive the navigation behavior of a delivery robot.A robotic platform named“PI”has been designed,which incorporates proximity and vision sensors.The robot utilizes a real-time object recognition algorithm based on the You Only Look Once(YOLO)algorithm to detect objects and humans during navigation.This study is aimed towards evaluating human experience,for which we conducted a study among 36 participants to explore the perceived social presence,role,and perception of a delivery robot exhibiting different behavior conditions while navigating in a hotel corridor.The participants’responses were collected and compared for different behavior conditions demonstrated by the robot and results show that humans prefer an assistant role of a robot enabled with audio and visual aids exhibiting social behavior.Further,this study can be useful for developers to gain insight into the expected behavior of a delivery robot.

Reorientation and obstacle avoidance control of free-floating modular robots using sinusoidal oscillator

This paper presents that a serpentine curve-based controller can solve locomotion control problems for articulated space robots with extensive flight phases,such as obstacle avoidance during free floating or attitude adjustment before landing.The proposed algorithm achieves articulated robots to use closed paths in the joint space to accomplish the above tasks.Flying snakes,which can shuttle through gaps and adjust their landing posture by swinging their body during gliding in jungle environments,inspired the design of two maneuvers.The first maneuver generates a rotation of the system by varying the moment of inertia between the joints of the robot,with the magnitude of the net rotation depending on the controller parameters.This maneuver can be repeated to allow the robot to reach arbitrary reorientation.The second maneuver involves periodic undulations,allowing the robot to avoid collisions when the trajectory of the global Center of Mass(CM)passes through the obstacle.Both maneuvers are based on the improved serpenoid curve,which can adapt to redundant systems consisting of different numbers of modules.Finally,the simulation illustrates that combining the two maneuvers can help a free-floating chain-type robot traverse complex environments.Our proposed algorithm can be used with similar articulated robot models.

Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters

A dynamics-based adaptive control approach is proposed for a planar dual-arm space robot in the presence of closed-loop constraints and uncertain inertial parameters of the payload. The controller is capable of controlling the po- sition and attitude of both the satellite base and the payload grasped by the manipulator end effectors. The equations of motion in reduced-order form for the constrained system are derived by incorporating the constraint equations in terms of accelerations into Kane＇s equations of the unconstrained system. Model analysis shows that the resulting equations perfectly meet the requirement of adaptive controller design. Consequently, by using an indirect approach, an adaptive control scheme is proposed to accomplish position/attitude trajectory tracking control with the uncertain parameters be- ing estimated on-line. The actuator redundancy due to the closed-loop constraints is utilized to minimize a weighted norm of the joint torques. Global asymptotic stability is proven by using Lyapunov＇s method, and simulation results are also presented to demonstrate the effectiveness of the proposed approach.

Adaptive fault-tolerant control based on boundary estimation for space robot under joint actuator faults and uncertain parameters

Since the joint actuator of the space robot executes the control instructions frequently in the harsh space environment,it is prone to the partial loss of control effectiveness(PLCE)fault.An adaptive fault-tolerant control algorithm is designed for a space robot system with the uncertain parameters and the PLCE actuator faults.The mathematical model of the system is established based on the Lagrange method,and the PLCE actuator fault is described as an effectiveness factor.The lower bound of the effectiveness factors and the upper bound of the uncertain parameters are estimated by an adaptive strategy,and the estimated value is fed back to the control algorithm.Compared with the traditional fault-tolerant algorithms,the proposed algorithm does not need to predetermine the lower bound of the effectiveness factor,hence it is more in line with the actual engineering application.It is proved that the algorithm can guarantee the stability of the closed-loop system based on the Lyapunov function method.The numerical simulation results show that the proposed algorithm can not only compensate for the uncertain parameters,but also can tolerate the PLCE actuator faults effectively,which verifies the effectiveness and superiority of the control scheme.

Neural-network-based two-loop control of robotic manipulators including actuator dynamics in task space

A neural-network-based motion controller in task space is presented in this paper. The proposed controller is addressed as a two-loop cascade control scheme. The outer loop is given by kinematic control in the task space. It provides a joint velocity reference signal to the inner one. The inner loop implements a velocity servo loop at the robot joint level. A radial basis function network （RBFN） is integrated with proportional-integral （PI） control to construct a velocity tracking control scheme for the inner loop. Finally, a prototype technology based control system is designed for a robotic manipulator. The proposed control scheme is applied to the robotic manipulator. Experimental results confirm the validity of the proposed control scheme by comparing it with other control strategies.

Reduced Model Based Control of Two Link Flexible Space Robot

Model based control schemes use the inverse dynamics of the robot arm to produce the main torque component necessary for trajectory tracking. For model-based controller one is required to know the model parameters accurately. This is a very difficult task especially if the manipulator is flexible. So a reduced model based controller has been developed, which requires only the information of space robot base velocity and link parameters. The flexible link is modeled as Euler Bernoulli beam. To simplify the analysis we have considered Jacobian of rigid manipulator. Bond graph modeling is used to model the dynamics of the system and to devise the control strategy. The scheme has been verified using simulation for two links flexible space manipulator.

Impedance control of multi-arm space robot for the capture of non-cooperative targets

Robotic systems are expected to play an increasingly important role in future space activities. The robotic on-orbital service, whose key is the capturing technology, becomes a research hot spot in recent years. This paper studies the dynamics modeling and impedance control of a multi-arm free-flying space robotic system capturing a non-cooperative target. Firstly, a control-oriented dynamics model is essential in control algorithm design and code realization. Unlike a numerical algorithm, an analytical approach is suggested. Using a general and a quasi-coordinate Lagrangian formulation, the kinematics and dynamics equations are derived.Then, an impedance control algorithm is developed which allows coordinated control of the multiple manipulators to capture a target.Through enforcing a reference impedance, end-effectors behave like a mass-damper-spring system fixed in inertial space in reaction to any contact force between the capture hands and the target. Meanwhile, the position and the attitude of the base are maintained stably by using gas jet thrusters to work against the manipulators' reaction. Finally, a simulation by using a space robot with two manipulators and a free-floating non-cooperative target is illustrated to verify the effectiveness of the proposed method.

Configuration Design of an Under-Actuated Robotic Hand Based on Maximum Grasping Space

Capture is a key component for on?orbit service and space debris clean. The current research of capture on?orbit focuses on using special capture devices or full?actuated space arms to capture cooperative targets. However, the structures of current capture devices are complex, and both space debris and abandoned spacecraft are non?cooperative targets. To capture non?cooperative targets in space, a lightweight, less driven under?actuated robotic hand is proposed in this paper, which composed by tendon?pulley transmission and double?stage mechanisms, and always driven by only one motor in process of closing finger. Because of the expandability, general grasping model is constructed. The equivalent joint driving forces and general grasping force are analyzed based on the model and the principle of virtual work. Which reveal the relationship among tendon driving force, joint driving forces and grasping force. In order to configure the number of knuckles of finger, a new analysis method which takes the maximum grasping space into account, is proposed. Supposing the maximum grasped object is an envelope circle with diameter of 2.5m. In the condition, a finger grasping maximum envelope circle with different knuckles is modeled. And the finger lengths with corresponding knuckles are calculated out. The finger length which consists of three knuckles is the shortest among under?actuated fingers consists of not more than five knuckles. Finally, the principle prototype and prototype robotic hand which consists of two dingers are designed and assembled. Experiments indicate that the under?actuated robotic hand can satisfy the grasp requirements.

Unified Modeling Approach of Kinematics, Dynamics and Control of a Free-Flying Space Robot Interacting with a Target Satellite

In this paper a unified control-oriented modeling approach is proposed to deal with the kinematics, linear and angular momentum, contact constraints and dynamics of a free-flying space robot interacting with a target satellite. This developed approach combines the dynamics of both systems in one structure along with holonomic and nonholonomic constraints in a single framework. Furthermore, this modeling allows consid-ering the generalized contact forces between the space robot end-effecter and the target satellite as internal forces rather than external forces. As a result of this approach, linear and angular momentum will form holonomic and nonholonomic constraints, respectively. Meanwhile, restricting the motion of the space robot end-effector on the surface of the target satellite will impose geometric constraints. The proposed momentum of the combined system under consideration is a generalization of the momentum model of a free-flying space robot. Based on this unified model, three reduced models are developed. The first reduced dynamics can be considered as a generalization of a free-flying robot without contact with a target satellite. In this re-duced model it is found that the Jacobian and inertia matrices can be considered as an extension of those of a free-flying space robot. Since control of the base attitude rather than its translation is preferred in certain cases, a second reduced model is obtained by eliminating the base linear motion dynamics. For the purpose of the controller development, a third reduced-order dynamical model is then obtained by finding a common solution of all constraints using the concept of orthogonal projection matrices. The objective of this approach is to design a controller to track motion trajectory while regulating the force interaction between the space robot and the target satellite. Many space missions can benefit from such a modeling system, for example, autonomous docking of satellites, rescuing satellites, and satellite servicing, where it is vital to limit the con-tact force during the robotic operation. Moreover, Inverse dynamics and adaptive inverse dynamics control-lers are designed to achieve the control objectives. Both controllers are found to be effective to meet the specifications and to overcome the un-actuation of the target satellite. Finally, simulation is demonstrated by to verify the analytical results.