Haptic based teleoperation with master-slave motion mapping and haptic rendering for space exploration

Gunyng LIU,Xud GENG,Lingzhi LIU,*,Yn WANG

aState Key Lab of Virtual Reality Technology and Systems,Beihang University,Beijing 100083,China

bSchool of Mechanical Engineering and Automation,Beihang University,Beijing 100083,China

cKey Laboratory of Space Utilization,Technology and Engineering Center for Space Utilization,Chinese Academy of Sciences.Beijing 100094,China

KEYWORDS Teleoperation;Haptic device;Remote control;Haptic rendering;Space exploration

Abstract This paper presents a new solution to haptic based teleoperation to control a large-sized slave robot for space exploration,which includes two specially designed haptic joysticks,a hybrid master-slave motion mapping method,and a haptic feedback model rendering the operating resistance and the interactive feedback on the slave side.Two devices using the 3R and DELTA mechanisms respectively are developed to be manipulated to control the position and orientation of a large-sized slave robot by using both of a user's two hands respectively.The hybrid motion mapping method combines rate control and variable scaled position mapping to realize accurate and efficient master-slave control.Haptic feedback for these two mapping modes is designed with emphasis on ergonomics to improve the immersion of haptic based teleoperation.A stiffness estimation method is used to calculate the contact stiffness on the slave side and play the contact force rendered by using a traditional spring-damping model to a user on the master side stably.Experiments by using virtual environments to simulate the slave side are conducted to validate the effectiveness and efficiency of the proposed solution.

1.Introduction

Teleoperation is an innovative robotics technology that helps humans perform tasks in remote,dangerous or subtle environments.1-5For a haptic based teleoperation,the haptic-visual feedback builds a transparent connection between the master side and remote robots as people stay in the remote environment in person.2Besides slave robots designed for different operating tasks,the key technology to establish such a haptic based teleoperation system also includes a haptic device,master-slave motion mapping,and feedback force rendering for accurate,safe,and convenient manipulation.

For example,for a haptic based teleoperation system used for space exploration,its master haptic device should have six degrees of freedom(DOFs)to control the position and orientation of a large-sized slave robot's end-effector.Moreover,one point should be emphasized that a master device for space exploration should not only be able to be manipulated to translate or rotate along one axis of fixed world coordinates,but also be able to be manipulated to translate or rotate along any direction or axis in its whole workspace.In this paper,this function is de fined as the capacity of coupled and decoupled motions.

Master-slave motion mapping is used to calculate the movement of a slave robot based on an operator's hand action,and two problems in this method need to be solved.The workspace and position resolutions of a master device and a largesized slave robot are mismatched,and how to control a slave robot efficiently should be considered.The location accuracy of a slave robot is often higher than the resolution of a human's hand motion,so how to accurately control the position and orientation of a slave robot based on a measured human's hand motion should also be solved.

Haptic feedback should not only provide the operating resistance to bene fi t users in manipulating devices friendly,but also re fl ect the slave interactive condition.The record and play method is often used in previous research to play forces measured from the slave side on the master side.However,this approach sometimes leads to an instability of a master haptic device because of time delay and singular data.6Based on previous research,impedance-typed haptic devices are more suitable to use a spring-damping model to render the feedback force.Therefore,this paper aims to apply a spring-damping model to render the force feedback reflecting the slave interaction.

Commercial haptic devices such as PHANToM Premium,PHANToM OMNI,and VIRTUOSE 6D7-9have ever been used as master devices of some haptic based teleoperation systems.These devices usually provide a large workspace,but lack strength and compactness.It is difficult for a user to move the handle of such a device along one axis of fixed world coordinates,since the motion of the handle is coupled.

Typically,haptic devices are divided into serial and parallel structures.Parallel haptic devices have closed kinematic structures so that they provide a smaller workspace but show high strength and precision,for example,Omega 3-DOF and Omega 7 are this type of haptic devices.

Researchers also focus on special devices designed for haptic based teleoperation.Several 5-DOF haptic devices10,11and a 6-DOF device12are developed by using different kinematics structures.Vishard1013is designed to have ten DOFs and provide a maximum feedback force of 170 N.LHIfAM is developed to provide a large workspace for the virtual assembly of aircraft engines.Some devices14,15are presented to provide feedback forces by using other types of drivers which are different from DC motors.For all these mentioned devices,users use only one hand to manipulate devices to control the orientation and position of a slave robot at the same time.

If a user can use both of his/her hands to manipulate two haptic devices to control the orientation and the position respectively,the user should be able to complete operating tasks more efficiently and accurately.

Another key problem to build a haptic based teleoperation system is master-slave motion mapping,which is the control law to compute the required motion of a slave robot based on the hand motion of a user on the master side.Because a master device and a slave robot have different configurations and workspaces in nearly all of the haptic based teleoperation systems,haptic based teleoperation is also called scaled teleoperation in which the position and the force need to be scaled on both sides of a system.16

Space exploration typically uses compact haptic devices to teleoperate large robotic arms.17-19Three important issues should be considered in ampli fi ed teleoperation:workspace mapping,precise positioning,and efficient control of a slave robot.

Scholars have proposed a recalibration direct position mapping based on the concept of clutching.20Though a direct position mapping method works well for fine positioning tasks,its repositioning process is inefficient.In order to reduce the use of clutches,Conti and Khatib proposed21a workspace drift control that repositions the working space of the end-effector without disturbing the operators.This approach is more suitable for a teleoperation system with an identified environment.18Then,a resynchronization control method,using the slave-side visual information,is proposed to achieve automatic relocation.22However,if a large-sized slave robot is required in the remote environment,operators still need to spend much time in relocation.

One widely used mapping method is position scaling23in which the motion of a master device is ampli fi ed and transferred to the slave side by using a scaling factor.In order to avoid amplifying the noise on the master side,rate control24is proposed in which the slave robot's speed is proportional to the master device's position.However,this method is not suitable for scenes that require precise positioning,because the slave robot is vulnerable to excessive impact if the slave movement is too fast.

In haptic based teleoperation,haptic feedback not only provides the operating resistance to users to bene fi t them in manipulating devices friendly and comfortably,but also reflects the interaction between the slave robot and the remote environment to build a transparent connection between the master and the slave side.25A realistic and accurate haptic feeling is critical for users to complete remote control tasks in unidentified remote environments.26,27

There is no doubt that visual feedback is essential for operators to acquire the position and shape information of a remote environment so as to plan a series of orientations and positions of a slave robot.However,when a slave robot is being controlled to contact an object,haptic feedback becomes the dominant information for an operator to perceive the interaction between the robot and the object.28,29Controlling a slave robot to accurately touch and even grasp a wide variety of previously unidentified objects is always a challenging problem,since these unidentified objects have various and different properties,from soft to hard,light to heavy,and fragile to solid.

Accurate force sensors and encoders are mounted on a slave robot to measure its contact force and motion in a remote environment accurately.Accordingly,master haptic devices should also provide an accurate feedback force and stiffness to users.Moreover,haptic rendering algorithms have to play the force signal recorded on the slave side stably.However,only outputting a series of force signals without considering the current movement of the master haptic device being manipulated may lead to oscillation and instability easily.

That is also why the spring-damping model is mostly used for haptic rendering.It is really a problem to reproduce the Hi-Fi force signal measured from the slave side and output it to a user through a master haptic device.That is also why,for most robot teleoperation systems,force feedback is just auxiliary information to partly enhance the transparency of a teleoperation system to improve the operating performance of a user.29-32

This paper aims to propose a general solution to haptic based teleoperation systems used for space exploration.Two haptic devices are designed as the master devices providing three DOF translations and three DOF rotations.The principle of manipulation is that a user uses both of his/her hands to manipulate the two devices to control the orientation and position of a slave robot respectively.That one three-translational DOF device and one three-rotational DOF device are combined to control one large-sized slave robot is evaluated to be the best solution to meet the human physiological law in completing robot teleoperation tasks.The 3R parallel mechanism and the DELTA mechanism are chosen to design the two devices,and all the aforementioned requirements of a master haptic device can be satis fi ed very well.

In this paper,an improved rate-location hybrid mapping algorithm is proposed to map the motion of a master device to a remote space robot for accurate and efficient teleoperation.The scale factor of the rate and position control can be adjusted as needed via a button on the haptic device.In order to avoid undesired movements when stopping the robot or switching the mode,a dead zone is set near the starting point of the master device where the speed is zero in the rate control mode.Based on ergonomics,friendly feedback is set to assist operators in speed control and accurate positioning.Haptic feedback reflecting the slave interaction is rendered by using a conventional spring-damping model,and its variables are measured and identified by the data obtained on the slave side.This stiffness estimation method is validated to be effective and stable in haptic rendering to enable operators to feel the slave environment.

2.Master haptic device design

2.1.Requirements

For haptic based teleoperation,the general requirements of a master haptic device can be listed as follows:

1.The master device should have totally six DOFs including three DOF translations and three DOF rotations.Accordingly,it can output six dimensional forces and torques.

2.A function of coupled and decoupled manipulations should be provided.A user can move the master device along one axis or rotate it around one axis.At the same time,the user should also be able to move the device along any direction or rotate it around any axis in the whole workspace.

3.The handle of the master haptic device should be able to stand still at its initial position or orientation of the whole workspace automatically without being touched by users.If a user leaves the handle,the handle can move back to its initial position automatically and stably.

Considering meeting all the aforementioned requirements and bene fi ting users in manipulating master devices conveniently and friendly,two three-DOF haptic devices are designed for a user to manipulate them with both hands.One device is designed by using the 3R mechanism providing three DOF rotations,and the other one uses the DELTA mechanism to provide three DOF translations.

2.2.3R mechanism based haptic device

A three-DOF haptic device is presented in Fig.1(a).33The manipulator utilizes the 3R spherical parallel architecture.This mechanism was proposed by Asada and Granito34in 1985,and has a variety of applications since then.Gosselin and Hamel built a famous camera-orienting device called‘‘the Agile Eye”using this parallel mechanism in 1994.35Malosio took advantage of the ergonomic feature of the 3R parallel mechanism,and developed a robot that met the ankle-foot rehabilitation requirement.36

The manipulator has three pure rotational DOFs.In Fig.2,coordinate systems are established on the rotational center.Frame X0Y0Z0is fixed to the static platform,and frame X′0Y′0Z′0is fixed to the mobile platform.Parameters α1,α2,β1,and β2are the mechanism parameters,while θ1,θ2,and θ3are the three joint angles.From Fig.2,all joint axes intersect at a common point,37which is the center of rotation of the end-effector.This configuration is similar to the wrist structure of a human body,so it is quite user-friendly.The parallel design leads to good dynamic properties,since the mass and inertia of the mobile platform is considerably reduced,which is essential to the transparency of a haptic device.A joystick is fixed to the mobile platform for operators to grasp.In order to exert force feedback to an operator,three DC motors are used as actuators.Absolute encoders are mounted on the joints to achieve a high position resolution and save the trouble of searching reference points as well.

Solving the kinematic problem is the prerequisite and foundation of force control,since the feedback force is calculated by a mass-spring model which is dependent on the orientation of the joystick.Kinematic analysis of the 3R spherical parallel mechanism has been studied in literature.37,38

Fig.1 CAD models of designed haptic manipulators.33

Fig.2 Geometry of the 3R mechanism.

In designing a 3R based haptic manipulator,we propose a novel numerical approach based on neural network to solve the problem of forward kinematics.33We aim to improve the real-time performance and computational accuracy of the haptic rendering algorithm in order to meet the high sampling frequency demanded by a haptic loop.An overlapping division technique is developed to avoid estimation errors,and then a simple structured multilayer perceptron neural network is established for each of the subspaces so as to improve the performance while reducing the computation cost.For a continuous motion trajectory,it is proven that the rough estimation process of the neural network can be omitted,which further increases the computing speed.33The computational accuracy and execution time of the proposed approach is testi fi ed to be ultrafast and effective in the forward kinematic solution of haptic applications.

2.3.DELTA mechanism based haptic device

The other three-DOF haptic device used as a master manipulator in the teleoperation system is presented in Fig.1(b).35The manipulator utilizes the DELTA parallel structure.The DELTA mechanism is a fully parallel mechanism,and its mobile platform can only translate along the three Cartesian axes,with respect to the base in Fig.3.In Fig.3,coordinate systems,xyz and x′y′z′,are established on the centers of the stationary and moving platforms,respectively.O and O′are the centers of the stationary and moving platforms,respectively.The DELTA robot has been one of the most common translational parallel manipulators,since it exhibits high stiffness in nearly all configurations with a good dynamic performance.

Fig.3 Geometry of the DELTA mechanism.

High stiffness is also the reason why numerous haptic devices are developed by the DELTA mechanism,39,40including commercial devices,such as Omega and Falcon.The most challenging problem in designing a DELTA robot is the dimensional synthesis for a given workspace,since the major drawback of a parallel mechanism is always the limited workspace.Especially when the DELTA mechanism is used as a haptic joystick,it is required to provide a desired largest cube workspace and a best performance in haptic display.

We solve the dimensional synthesis problem by using GA and SQP optimizations to interchange objectives and constraints in the process of optimization step by step.The initial constraint is the con fined space of the DELTA mechanism,and the condition of the Jacobian matrix in the force domain is considered as the standard to evaluate the performance of a mechanism in haptic display,which is also the only objective at the final step of the optimization to obtain the optimal dimensions of the DELTA mechanism as a haptic device.Experimental results clearly show that the combination of SQP and GA(SQP using the results of GA as the starting points of all design variables)gives the optimal solution.

2.4.Operating rule

The 3R mechanism based haptic device is used to control the orientation of a slave robot,and the DELTA based haptic device is manipulated to control its position.Here,controlling the movement of a slave robot means controlling its endeffector's position and orientation;therefore,the reverse kinematics has to be conducted to calculate each joint motion of the slave robot.If both of the two master devices are manipulated at the same time,the computational burden and difficulty of the reverse kinematics algorithm will be increased greatly.

Therefore,we de fine that a user should manipulate the two master devices alternately to regulate the position or orientation of the end-effector of a slave robot.In each sampling period,the slave robotcontroller only receives a signal representing the position or orientation from only one device;therefore,the joint motion of a slave robot can be computed immediately by using the reverse kinematics solution.

If a user manipulates the two master devices at the same time,only the motion information of the three-translational DOF device is transferred from the master side to the slave side to control the translation of the slave robot.

3.Hybrid master-slave motion mapping method and operating resistance rendering

3.1.Operating rule

Fig.4 Flow chart of haptic feedback generated for operating resistance on the slave side.

A variable scale factor hybrid teleoperation method for rapidly approaching a remote target and accurately positioning is proposed for space exploration41in Fig.4.In Fig.4 and hereinafter,Fais the force applied to the device by the operator.xmand θmare the displacement and angular rotation of the master device,respectively.kvis a changeable speed factor,and kfis the stiffness of the spring-damping force model.vsand ωsare the moving and rotation speeds of the slave robot,respectively.kscaleis the scaled factor in position mapping ranging from 0-1.f is a constant default force parameter.xsand θsare the displacement and angular rotation of the slave robot,respectively.Fmand Tmare the feedback force and torque representing the operating resistance,respectively.Letter s represents the integration element to calculate the displacement and angular rotation of the slave arm with νsand ωs.

Rate control is used as the coarse motion control mode;the motion of the end-effector of a slave robot is proportional to the deviation of the handle of a master device.The dead zone of the master device is designed in the rate control,where the slave robot is controlled to keep still in Fig.5.In Fig.5,rdzis the dead zone radius,and rmaxis the maximum radius of the effective zone.

Mode switch between rate control and position mapping is implemented by touching a button on the keyboard.The position scaling factor can be regulated through a button on each haptic device,which is close to an operator's fi nger while he/she is holding the device handle.Haptic feedback is rendered in the combined mapping approach to assist users to manipulate the devices friendly and comfortably,since the variation of the force and torque feedback benefits users in accurately controlling the position and velocity of a slave robot.

Fig.5 Theory of the rate control approach and utilization of the workspace of a master device.

3.2.Rate control

The rate control algorithm is illustrated in Fig.5.For each one of the two designed haptic devices,the dead zone is set around the center of the whole workspace to avoid wrong operations.Based on the rate control mode,the position and orientation of the end-effector of a slave robot are calculated by

where Psand Qsare the end effector's position and orientation,respectively,Psoand Qsoare the original position and orientation of the end effector,respectively,and Pmand Qmare the two master devices'positions and orientations related to their initial points,respectively.An operator can adjust Pmor Qmto regulate the speed or direction of a slave robot for obstacle avoidance or target fast approaching.

From Fig.4,the feedback force and torque,Fmand Tm,are expressed as

where b is the damping coefficient to keep the device to work stably.The higher velocity a slave robot has,the higher resistance an operator feels.If a slave robot is controlled to move or rotate too fast,it will be very difficult for a user to continue accelerating the slave robot,since he/she has already felt very high operating resistance from the master devices,which can guarantee safe manipulation.

As mentioned above,the handle of a haptic device should be able to move back to its home position automatically when a user leaves it.The proposed spring-damping model can implement the function very well,which is validated in experiments.

3.3.Variable scaled position mapping

In order to accurately match a master system with a slave system,the scaled master position information is used for scaled teleoperation to implement accurate positioning of a slave robot,especially for applications that the location accuracy is much higher than the resolution of a human's hand motion.Rate control as the coarse control mode is used to enable a slave robot to approach a target as fast as possible.To reach and touch the target with very high precision,a scaled position mapping method is necessarily required.

The variable scaled position mapping approach is presented as where kscalecan be increased/decreased through two buttons on the two haptic devices.The scale step size is set at 0.05.Under certain circumstances,when a master device moves or rotates to the boundary of its working space,an operator can stop the movement of a slave robot through the keyboard,and then the operator can relocate the master device to its original position or orientation.

The feedback force in this mode is inversely proportional to the scaling factor as follows:

When an operator decreases the scale factor to do more sophisticated fine operations,the haptic device adds extra feedback force to prevent the operator from moving or spinning too fast and helps him/her in accurate positioning.The higher accuracy of the location a slave robot has,the higher resistance an operator feels.The feedback force is in the opposite direction of a slave robot's motion.By using this method,an operator could accurately control a slave robot to reach a target position,and the location accuracy depends on the motion accuracy of the slave robot thoroughly.

4.Feedback force rendering

Haptic feedback is greatly bene fi cial to effective operations.42,43However,in haptic based teleoperation,besides the operating resistance,a user should also feel contact and collision force to supervise the interactive condition on the slave side.44The interactive condition means the contact or collision between a slave robot and its staying environment,which is critical for users to feel and perceive the properties of an unidentified environment,such as rigidity,stiffness,and mass.

Force/torque sensors and encoders mounted on a slave robot can record and depict the contact and collision between a slave robot and a remote environment.The problem is how to render the interactive force measured on slave side on the master side.A direct solution is to play the data recorded on the slave side by using the record and play method.Referring to record and play,this paper aims to solve the problem by using the conventional spring-damping model.The spring model is usually used as the force model to compute the feedback force in a haptic based VR system.If the stiffness of a slave interaction can be estimated or calculated,the spring model can also be used to render the operating and interactive forces,Fdand Td,on the master side,and then the only required information from the slave side to the master side for haptic rendering is the estimated stiffness kpin Fig.6.Hereinafter,Fsor Tsis the suddenly increasing force or torque an operator feels when a slave robot is moved or rotated to contact an object in the rate control mode.

Fig.6 Flow chart of haptic feedback generated for interactive forces on the slave side.

Based on the measured contact force and motion information of a slave robot,the stiffness of a slave environment being touched can be calculated and estimated.In previous research,the relationship between the deformation and penetration of a body being contacted and the contact force is represented by using a spring and a viscous damper.We use the Hunt-Crossley model45to estimate the contact impedance,which has been proven to be suitable for describing the contact dynamics of both stiff and soft objects.The model is formulated as

where x is the penetration depth of the end-effector of a slave robot into an object being contacted,which is calculated by using the current displacement or angle the slave robot moves or rotates after it initially collides with the object.Parameters k and λ are the elastic and viscous coefficients,respectively,which are decided by the stiffness and hardness of the object being touched.These two parameters can make a difference among all objects with different properties.n is a constant which relates to the contact geometry.The online estimation algorithm in Ref.46is used to calculate parameters k and λ in Eq.(7)as follows:

Based on the aforementioned algorithm,the spring model coefficient kpis proportional to the parameter k of an object being touched as follows:

where keis a scaling factor which converts the elastic parameter obtained on the slave side to the spring model based on the haptic device on the master side.

It has to be emphasized that any collision between a slave robot and a remote environment should be avoided in the rate control mode,since this mode is set to enable a slave robot to be controlled to approach a target fast and efficiently.Therefore,the proposed feedback force model is used in the scaled position mapping model.If a slave robot is moved or rotated to contact an object in the rate control mode,a user will feel a suddenly increasing force or torque,Fsor Ts(Fig.6),which is proportional to the slave contact force or torque.Now,based on the operating regulation,the user has to move or rotate the device handle back to its original position or orientation to stop the slave robot immediately.What to do in the next step should be decided after observing the slave environment carefully and thoroughly.

5.Experiment

To validate the proposed solution to haptic based teleoperation for space exploration,experiments are conducted based on the designed master devices,the master-slave motion mapping method,and haptic rendering algorithms.

In the experiments(Fig.7),we use virtual environments to simulate two large-sized slave robots and the outer space.The virtual environments are generated by using VC++and OpenGL library based on PCs.

The experiments are conducted step by step.Firstly,the feature and function of the two designed haptic devices are testi fi ed.Secondly,the hybrid motion mapping approach is utilized to implement the accurate location of a virtual slave robot.Finally,a general demo is developed to validate the proposed solution for a special task of space exploration.

5.1.verification of the two designed haptic devices

5.1.1.Three-DOF rotational haptic device

Firstly,the home function is testi fi ed in Fig.8,where T is the angle of rotation from the origin.Set the stiffness of the spring model as kf=8 N·mm/(°),and change the damping coefficient of the spring-damping model from 0.5 N·mm/(r·min-1)to 1.6 N·mm/(r·min-1).Rotate the device handle from its original orientation to any orientation in its workspace,and then leave the handle to test the home function.

Fig.7 Experimental system built based on two haptic devices and virtual environments.

Fig.9 shows that increasing the damping coefficient from 0.5 N·mm/(r·min-1)to 1.6 N·mm/(r·min-1)can decrease and avoid oscillation of the handle around its original axis.Fig.10 shows the relationship between the home function and the spring stiffness of the spring-damping force model.It is obvious that a higher stiffness can improve the accuracy of the home function;however,a high stiffness may lead to ossi fi cation and instability of the haptic device,since the maximum simulated stiffness of a haptic device is limited based on motors,encoders,and mechanical structure.

Therefore,in order to stably and accurately implement the home function,variables of the spring-damping model should be selected suitably.The force model to render the operating resistance,F in Fig.11,is the same as that of the home function;therefore,a virtual wall experiment is conducted to testify it again(Fig.11).

The virtual wall experiment clearly illustrates that the device can provide the operating resistance required for the proposed hybrid motion mapping method (Fig.12).Position-velocity motion mapping is tested by using the device to control a virtual ball.In Fig.13,Pjis the deviation of the handle,and vsis the velocity of the virtual ball.It depicts the relationship between the deviation of the handle and the velocity signal of the virtual ball.In Fig.14,the blue line represents the velocity of the virtual ball which is proportional to the deviation of the handle from its original axis represented by the red line.Below the blue dotted line is the dead zone required for safe operation.The device can meet the requirement of the hybrid motion mapping method.

5.1.2.Three-DOF translational haptic device

Considering the configuration of the DELTA mechanism,users not only feel the operating resistance and rendered slave contact force,but also feel the gravity of the handle and mechanical chains.Feeling gravity definitely affects the operating effect,which should be avoided and compensated for.Different from the 3R mechanism based haptic device,the three-DOF translational device has to have a function of gravity compensation so that the handle can stay at any position of its whole workspace without being grasped before the operating resistance and the contact force are rendered.

Fig.15 shows the handle staying at its original position without being touched by using a gravity compensation method.The output torques of the three motors mounted on the device are 16.18,16.28,and 16.34 mN·m,respectively.

Fig.8 Testing the home function of the 3RRR mechanism.

Fig.9 Relationship between the effectiveness of the home function and the damping coefficient of the spring-damping model in feedback force computation.

Fig.16 shows the handle staying at a random position of its workspace by using gravity compensation,and the current position of the handle is[1.5243,17.6991,33.3409].The current output torques of the three motors are 15.62,13.45,and 18.76 mN·m,respectively.

As introduced in the three-DOF rotational device experiments,the home function is also testi fi ed that a larger damping coefficient can avoid oscillation and decrease the error of the home function in Fig.17,where x is the deviation of the master device and b is the damping coefficient of the spring-damping model.

A virtual wall experiment(Fig.18)is also conducted to testify that the device can meet the requirement of the proposed hybrid motion mapping method to output an operating resis-tance.The simulated contact force is computed based on the same spring-damping model used to render the operating resistance.The measured stable maximum stiffness reaches 5 N/mm.

Fig.10 Relationship between the effectiveness of the home function and the stiffness of the spring-damping model in feedback force computation.

Fig.11 Testing the 3RRR mechanism based haptic device by using the conventional spring-damping model.

Fig.12 Experimental results of rendering operating resistance by using the spring-damping model.

Fig.13 Testing the 3RRR mechanism based haptic device by using the motion mapping approach proposed in this paper.

Fig.14 Experimental results of the slave robot motion velocity and the master device deviation.

Fig.15 Testing the handle of the DELTA mechanism based haptic device staying at its original center position without being touched.

Fig.16 Testing the handle of the DELTA mechanism based haptic device staying at any position in its workspace without being touched.

5.2.verification of the proposed master-slave motion mapping approach

In general,remote robot control is divided into three steps:firstly,move the end-effector of a slave robot very close to a target quickly;secondly,rotate the end-effector of the slave robot to a right orientation; finally,move the end-effector to grasp or touch the target accurately.Although the orientation of the end-effector requires regulation at the final step slightly,the final contact manipulation is implemented by controlling the translation of the end-effector of a slave robot.

Thus,an experiment is conducted by using the hybrid master-slave motion mapping method based on the three-DOF translational haptic device.

Table 1 lists the specifications of both the master device and the virtual slave robot arm(Fig.19),and the dead and effective zones of the whole workspace are set.The speed factor kvand the scaled position mapping factor kscaleare initialized to be 60 and 0.8,respectively.Operators can adjust these two factors for different tasks in the whole process of the experiment.

There are two processes in operation tasks:path tracking and target positioning.Fig.19 shows the tracking path and target in a virtual environment.Four linear sections and three quarter turns compose the path.A small ball is displayed at each turning point.The task is to move the virtual model of the robot arm,along the given path,from the starting point to the target point.A ball will turn red when the robot passes through a turning point.All the balls must be passed before the robot moving to the target.The actual trajectory of the slave robot is also displayed in red in the virtual environment.The task is accomplished when operators manipulate the robot as quickly and accurately as possible along the given path to reach the target point with different mapping methods.

Twenty volunteers aged from 21 to 30 are invited to participate in the experiment.They are all right-handed and familiar with the two designed haptic devices.

There are three mapping modes representing three mapping methods for all participants to complete the task.Subjects can use the keyboard and buttons on a device to switch modes and regulate scaling factors conveniently.Mode 1 is the proposed hybrid mapping that all participants can switch between rate control and scaled position mapping.To locate turning points and the target point,the scaled position mapping method is used.On the contrary,to move along the straight line,rate control is used to move quickly.Mode 2 is rate control that the scaled position mapping method cannot be used.Mode 3 is scaled position mapping that the rate control method cannot be used.

Subjects are required to execute two trails for each method mode.In order to minimize the learning effects,the order of the sub-paths is displayed at random.Before the experiment,each participant is given an introduction about the experiment and a pre-trail to bene fi t them in grasping these mapping methods and the operating task.

Fig.17 Relationship between the effectiveness of the home function and the damping coefficient of the spring-damping model used in feedback force computation.

Fig.18 Testing the DELTA mechanism based haptic device by using the conventional spring-damping model.

Table 2 illustrates the total times and errors of all subjects for all these three operating modes.It is obvious that the proposed method is more effective and efficient in bene fi ting usersto complete the operating task.All subjects give comments on these three operating modes.

Table 1 Teleoperation experiment specification.

Fig.19 Virtual environment simulating a controlled three-DOF slave robot by using the DELTA mechanism based haptic device.

Table 2 Experimental data.

For rate control,the slave robot can be moved very fast;however,the slave robot is prone to overshoot at the target point and turning points.It is nearly impossible for them to accurately locate at a specific position,unless they control the slave robot to move very slowly and spend a lot of time to complete the task.In scaled position control,much time is spent in moving the slave robot along the straight line,although the positioning accuracy is high.Many times of relocating the device really confuse operators.The proposed hybrid method solves the conflict between efficiency and effectiveness,and the switch between rate control and scaled motion mapping is very convenient.All subjects prefer to the hybrid master-slave motion mapping approach.

5.3.General demo

Fig.20 D-H method of the simulated six-DOF slave robotic arm.

Fig.21 Simulation of a controlled slave robot to finish tasks in a virtual space environment.

In Fig.20,a six-DOF robotic arm is simulated in a virtual environment,where X1Y1Z1,X2Y2Z2,X3Y3Z3,X4Y4Z4,X5Y5Z5,and X6Y6Z6are the local coordinates.By using the D-H theory,each joint motion of the slave robot can be calculated based on the orientation and position of its end-effector controlled by the two master devices.

The operating task requires a user to control the motion of the slave robot to grasp a spacecraft and drag it to be connected to the base.The user needs to manipulate the two master haptic devices to control the slave robot to grasp the spacecraft at the right position with the right orientation,and drag the craft to the right position of the base with the right orientation.

The user needs to switch between the two devices to control the position or orientation at one time,since reverse kinematics computation of the slave robot has to be considered.When the robot is far from the spacecraft or base,the rate control method is used to improve efficiency of the operation.After the robot is controlled to move very close to the craft or base,the operation mode is switched to scaled positioning,and the scaling factor can be regulated by the user.

One point should be emphasized that the stiffness of the spring-damping model to render the operating resistance is changed after the robot is controlled to grasp the spacecraft firmly,since the user should feel different resistance whether the robot has a load or not.

If the robot is controlled to grasp the spacecraft at the right position and move the craft to be connected with the base at the right position,the user will feel a suddenly increasing feedback force,and then the feedback force disappears.This feeling means that the user completes the operating task very well.

If a wrong operation happens that the user controls the robot to contact or even impact the spacecraft or base,he/she will feel increasing force and torque feedback rendered by using the aforementioned stiffness estimation springdamping model.In this condition,the user feels an increasing force similar to a spring force,so he/she has to stop his/her operation and leave the handles of the two devices.The home function can move or rotate the handles back to their initial positions or orientations,and then no signal will be transferred to the slave side,so the slave robot will keep still.The user should check the current condition and interaction,and then decide the operation in next step.

Fig.21 shows the whole process of completing such a proposed operating task.

6.Conclusions

This paper presents a solution to haptic based teleoperation for space exploration,which includes two specially designed haptic joysticks,a hybrid master-slave motion mapping method,and a haptic feedback model rendering operating resistance and interactive feedback on the slave side.Two devices using 3R and DELTA mechanisms respectively are developed for a user to be manipulated to control the position and orientation of a large-sized slave robot by using both of his/her hands respectively.The motion mapping method combines the advantages of rate control and position mapping of variable scale factors to achieve accurate and efficient teleoperation.The ergonomically designed haptic feedback under these two mapping modes is used to improve the immersion of teleoperation.A stiffness estimation method is used to calculate the contact stiffness on the slave side and play the contact force by using a traditional spring-damping model to output feedback to users stably.Experiments by using a virtual environment to simulate the slave side are conducted to validate the effectiveness of the proposed approach.

The next work is applying the method to a physical space teleoperation system,and further evaluation experiments will be conducted on that system.

Acknowledgement

The project was supported by the Open Research Fund of Key Laboratory of Space Utilization,Chinese Academy of Sciences(No.LSU-YKZX-2017-02).