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Abstract

This research develops a gravity compensation method that determines the mass of a task object easily and compensates for the external force caused by the task object when it is conveyed by a hydraulic teleoperation construction robot. Moreover, this study establishes a master–slave system for this robot; two joysticks act as the master, and an excavator with four links (fork glove, swing, boom, and arm) represents the slave. To compensate for the influence of gravity, a previous gravity compensation method is proposed and applied to the boom and arm. However, it is ineffective during the conveyance process especially when the task object is heavy because the driving force is influenced by gravity of the task object. Therefore, this research presents a gravity compensation method that can effectively determine the mass of a grasped object and compensate for the external force induced by its gravity, as verified through pressing, grasping, and conveying experiments.

Keywords

Gravity compensation construction robot teleoperation master–slave system force feedback

Introduction

In a master–slave system, a human operator manipulates joysticks to govern the remote robot’s positions, velocities, and contact forces with the environment. Thus, this master–slave system enables the operator to perform given tasks remotely and successfully. In recent years, master–slave systems have been sufficiently studied, and these studies have been motivated by various applications,¹ such as space explorations,² underwater explorations^3,4 and mining,⁵ and surgeries^6–8 as well as applications in dangerous environments, such as nuclear power plants.⁹ In these applications, the human operators need enough information about the slave systems and remote environments to feel physically present at the remote sites.¹⁰ This condition of teleoperation is typically referred to as telepresence. If the slave side transmits correct and sufficient signals back to the operator in a natural way, the effect of telepresence can be immersive.¹¹ It can be achieved through a variety of feedback signals which flow from the remote environments to human operators,¹² such as haptic feedback,^12,13 force feedback,^14,15 and visual feedback.¹⁶

Robotic systems need to resist gravitational torques generated by the masses of links, thus actuators can be smaller after gravity compensation method is proposed.¹⁷ Mechanical solutions of gravity compensation method including compensation by counterweights, springs, and auxiliary actuators can resist most joint torques. However, mechanical solutions are not sufficient when joint angles are changed, especially when robots are grasping objects. In this condition, operators need to overcome more reaction torques to manipulate the joysticks. Many methods in the literature were performed with gravity compensation to achieve precise control performance.^18–20 A hybrid method to achieve gravity balancing of a human leg over its range of motion is proposed in Banala et al.²¹ Incomplete gravity compensators for a 4-degree-of-freedom (DOF) humanlike manipulator are treated in Kim and Cho.²² The stability and regulation performance of the closed-loop system when the compensation for the gravitational torque is provided by a non-collocated controller is studied in Liu and Chopra.²³ Some researchers²⁴ consider the estimation and compensation of the gravity force and static friction for robot motion control. In Yamada and colleagues,^25,26 velocity-driving force characteristics of links $(v_{s} - f_{s})$ and threshold driving force $(f_{pre})$ are introduced to compensate for gravity through the symmetric-position method in a hydraulic teleoperation construction robot. However, operators considered the movements of joysticks under symmetric-position control to be strange because the most commonly used control for excavators in the market is position-velocity control. The position-velocity control (velocity control) method, in which velocity of piston is used as feedback instead of position of it, was introduced as a master–slave control method in our system. Besides, the $v_{s} - f_{s}$ and $f_{pre}$ are both used in the velocity control method.

In teleoperation systems, the slave-side robot should interact with the environment, such as grasping or conveying an object and touching or pressing the ground. In our research, when the slave robot lifts and conveys an object in a hydraulic teleoperation construction robot, especially a heavy one, the reaction torque (force) is generated by the gravity of the grasped object; since the operator has to overcome the reaction torque to manipulate the joysticks, he/she will feel tired and inconvenient after a long-time operation.

To compensate for the external force caused by the gravities of links (boom and arm) and the gravity of the grasped object in the hydraulic construction robot, a gravity compensation method is proposed in this research. This method can determine the mass of an object, distinguish the moment the construction robot lifted and released an object in the hydraulic teleoperation construction robot, and provide the operator with a noticeable sense of reaction force during pressing objects by the arm or boom.

The remainder of this article is organized as follows: section “Master–slave system” describes the master–slave system of our research. Section “Gravity compensation of the boom and arm” and section “Compensation for the gravity of an object” propose a method to compensate the external force induced by the gravity of the grasped object and the gravities of links (boom and arm), respectively. Section “Experiment and analysis” describes experiments on grasping and conveyance of heavy objects. Concluding remarks follow in section “Conclusions.”

Master–slave system

Figure 1 shows the schematic of the master–slave system used for the hydraulic teleoperation construction robot in this research. A typical teleoperation system is composed of master and slave sides. As shown in Figure 1, the master–slave system consists of two joysticks (SideWinder Feedback 2 manufactured by Microsoft Co., Ltd.), which act as the master. The construction robot (a commercially available excavator modified based on Hitachi LandyKID-EX5) is the slave. The joysticks enable movements forward/reverse and right/left. Its displacements are detected by position sensors. Each joystick is composed of two direct current motors that enable an operator to sense the grasping of an object by the fork glove and to feel the work reaction force induced by the construction robot. The construction robot is represented by a robot armed with 4 DOFs which consist of four hydraulic cylinders (fork glove, arm, boom, and swing). Cylinder displacement is measured by magnetic stroke sensors embedded in the pistons. Pressure sensors are installed on the cap end and rod end of the cylinder for measuring the pressure. The magnitude and direction of the piston velocity change with the magnitude and direction of the joysticks by the velocity control method. The piston velocity of the hydraulic cylinders is zero when the joystick is in the intermediate position. The control relationship of the construction robot with two joysticks is shown in Figure 2. The operator manipulates the joysticks to control the construction robot as guided by the reaction force to the joystick and the visual prompting on the screen.

Figure 1.

Schematic of the master–slave system for a hydraulic teleoperation construction robot.

Figure 2.

Illustration of the construction robot and joysticks.

Gravity compensation of the boom and arm

A gravity compensation method, which can eliminate the external force generated by the gravities of the boom and arm, is described in Liu and Quach.²⁴ Free motion experiments are then conducted on the boom to verify the effectiveness of the parameters by velocity control method with gravity compensation. Object pressing experiments are conducted to confirm that velocity control can provide an operator with a realistic sensation of force feedback when it is applied to the boom and arm.

Gravity compensation method

Kinematics equation of the robot

The gravities of the boom and arm can strongly influence the driving force when the postures of the four links (fork glove, arm, boom, and swing) change on the slave side. The influence of gravities of the swing and fork glove on the driving force is omitted when the postures of the swing and the fork glove vary. The robot arm then obtains 2-DOF by disregarding the swing and fork gloves. In this research, the construction robot is placed horizontally on the ground. Table 1 shows the link parameters. With respect to the relation between the links and cylinders displayed in Figure 3, the joint angles $θ_{b}$ and $θ_{a}$ can therefore be calculated as follows

{\begin{matrix} θ_{b} = x_{b} - a_{b 1} - a_{b 2} \\ x_{b} = co s^{- 1} {\frac{[b_{b}^{2} + c_{b}^{2} - {(y_{sb} + s_{b})}^{2}]}{2 b_{b} c_{b}}} \end{matrix}

(1)

{\begin{matrix} θ_{a} = x_{a} - π + a_{a 1} + a_{a 2} \\ x_{a} = co s^{- 1} {\frac{[b_{a}^{2} + c_{a}^{2} - {(y_{sa} + s_{a})}^{2}]}{2 b_{a} c_{a}}} \end{matrix}

(2)

Table 1.

Link parameters.

Arm						Boom
Length (m)				Angle (°)		Length (m)				Angle (°)
$l_{a}$	$b_{a}$	$c_{a}$	$s_{a}$	$a_{a 1}$	$a_{a 2}$	$l_{b}$	$b_{b}$	$c_{b}$	$s_{b}$	$a_{b 1}$	$a_{b 2}$
$1.085$	$0.624$	$0.167$	$0.475$	$151$	$42$	$1.15$	$0.652$	$0.165$	$0.5$	$22$	$54$

Figure 3.

Relation between the links and the cylinders.

Dynamic equation of the robot

As shown in Figure 3, the angles between the link and its center of mass are expressed as $φ_{a}$ and $φ_{b}$ , whereas the lengths from the joint to the center of mass of the link are described as $l_{ga}$ and $l_{gb}$ , respectively. The construction robot is small and works slowly; thus, the influence of the inertia item and Coriolis, as well as of the centripetal item, should be omitted relative to that of gravity in the calculation of the dynamic equation of the boom and arm in this research. When the construction robot does not touch the surroundings or grasp an object, the joint torque of the robot arm is determined as follows

\begin{matrix} [\begin{matrix} τ_{b} \\ τ_{a} \end{matrix}] = [\begin{matrix} m_{b} l_{gb} C_{b} + m_{a} l_{b} & m_{a} l_{ga} C_{a} \\ 0 & m_{a} l_{ga} C_{a} \end{matrix}] [\begin{matrix} C θ_{a} \\ C θ_{ba} \end{matrix}] g \\ - [\begin{matrix} m_{b} l_{gb} S_{b} & m_{a} l_{ga} S_{a} \\ 0 & m_{a} l_{ga} S_{a} \end{matrix}] [\begin{matrix} S θ_{a} \\ S θ_{ba} \end{matrix}] g \end{matrix}

where $C_{b} = \cos φ_{b}$ , $C_{a} = \cos φ_{a}$ , $S_{b} = \sin φ_{b}$ , $S_{a} = \sin φ_{a}$ , $C θ_{b} = \cos θ_{b}$ , $C θ_{ba} = \cos (θ_{b} + θ_{a})$ , $S θ_{b} = \sin θ_{b}$ , and $S θ_{ba} = \sin (θ_{b} + θ_{a})$ .

Identification of the dynamic parameters

When equation (3) is used to calculate joint torque, the following dynamic parameters must be derived: the mass values of the links $(m_{a}, m_{b})$ , lengths $(l_{ga}, l_{gb})$ , and angles $(φ_{a}, φ_{b})$ . The dynamic parameters of the boom and arm are obtained using the least-square method, the cylinder displacements, and driving force as the postures of the arm and boom vary. The parameters are calculated and shown as in Table 2.

Table 2.

New dynamic parameters.

Torque (N m)
$(m_{b} l_{gb} \cos φ_{b} + m_{a} l_{b}) g = 917$	$(m_{b} l_{gb} \sin φ_{b}) g = 134$
$(m_{a} l_{ga} \cos φ_{a}) g = 478$	$(m_{a} l_{ga} \sin φ_{a}) g = 42$

Calculation of $f'_{sb}$ and $f'_{sa}$

In terms of sine theorem, angle $x'_{b}$ is employed to calculate the perpendicular distance from the action line of $f_{sgb}$ to point $O_{b}$ . $τ_{b}$ is strongly influenced by the gravity of the boom described in the dynamic equation of the robot. External force $f'_{sb}$ induced by the gravity of the boom $f_{sgb}$ and driving force $f_{sb}$ can be obtained using equation (4). $f_{sga}$ can also be obtained by substituting $a$ for the subscript $b$ in the correlation equations

{\begin{matrix} x'_{b} = si n^{- 1} [c_{b} \sin x_{b} / (y_{sb} + s_{b})] \\ f_{sgb} = τ_{b} / (b_{b} \sin x'_{b}) \\ f'_{sb} = f_{sb} - f_{sgb} \end{matrix}

(4)

Experiments and analysis

Free motion experiment on the boom

As indicated in Figure 4, the experimental results confirm that piston displacement varies with $f'_{sb}$ and that the dynamic parameters are appropriate. $f'_{sb}$ varies around zero position when the boom moves vertically in free space. It is similar to the motion state of the fork glove. As a result, $v_{s} - f_{s}$ and $f_{pre}$ can then be applied to the boom and arm.

Figure 4.

Result of the free motion experiment on the boom.

Reaction torque to the joystick

The reaction torque to the joystick $τ_{ri}$ is expressed in equation (5) in terms of velocity control method. $τ_{s}$ is noticeable reaction torque to the joystick (= 0.097 N m), $k_{pmi}$ and $k_{tmi}$ are master proportional gain and master torque gain, respectively. $Y_{mi}$ and $V_{si}$ are non-dimensional quantities of master displacement $y_{mi}$ $(Y_{mi} = y_{mi} / 0.06)$ and velocity of piston $v_{si}$ $(V_{si} = v_{si} / 0.1)$ , respectively. The overall gain of the master $(T_{i})$ is described in equation (6). $f_{prea}$ and $f_{preb}$ are obtained using equations (7) and (8), according to the measured $v_{s} - f_{s}$ . The identification parameters in equations (7) and (8) are obtained as follows: first, $f'_{si}$ was obtained when the construction robot (arm and fork glove) made various gestures at various velocities $v_{si}$ without grasping anything. Next, quadratic fitting was chosen to obtain the relation between $f'_{si}$ and $v_{si}$ by linear least-square method. Since the influence of oil temperature and the wear on cylinder, a certain margin needs to be supplied for the $v_{s} - f_{s}$ . Finally, the offset value was gradually increased until the value of $T$ always equaled to zero. The constant coefficients of the offset curve are the identification parameters. The $v_{s} - f_{s}$ are used for all links of construction robot (swing, boom, arm, and fork glove); they are useful for a hydraulic system. Due to the $v_{s} - f_{s}$ are influenced by link’s gravity, the identification parameters of each freedom are different. $f_{e_\max}$ (11.7 kN) and $f_{c_\max}$ (−6.8 kN) express the maximum driving forces of the piston in the expansion and contraction directions, respectively. The boom hydraulic cylinder is the same as the arm hydraulic cylinder in our research. The values of $f_{e_\max}$ and $f_{c_\max}$ are obtained in the case of no load acted on a piston rod of the hydraulic cylinder placed horizontally when output pressure of the pressure pump is 10 MPa. Subscript $i$ represents either $a$ (arm) or $b$ (boom)

{\begin{matrix} τ_{hi} = T_{i} [k_{pmi} (Y_{mi} - V_{si}) + k_{tmi} f'_{si}] \\ τ_{ri} = τ_{hi} + sgn (τ_{hi}) τ_{s} \end{matrix}

(5)

T_{i} = {\begin{matrix} 0 & | f'_{si} | \leq | f_{prei} | \\ 0 < \frac{f'_{si} - f_{prei}}{f_{e_\max} - f_{prei}} \leq 1 & f'_{si} > 0 \cap f'_{si} > f_{prei} \\ 0 < \frac{f'_{si} - f_{prei}}{f_{c_\max} - f_{prei}} \leq 1 & f'_{si} < 0 \cap f'_{si} < f_{prei} \end{matrix}

(6)

f_{prea} = {\begin{matrix} (88 {\overset{\cdot}{v}}_{sa}^{2} + 9 v_{sa} + 1.3) \times 10^{3} & v_{sa} \geq 0 \\ (338 {\overset{\cdot}{v}}_{sa}^{2} + 41 v_{sa} - 1.1) \times 10^{3} & v_{sa} < 0 \end{matrix}

(7)

f_{preb} = {\begin{matrix} (- 5123 {\overset{\cdot}{v}}_{sb}^{2} + 176 v_{sb} + 0.8) \times 10^{3} & v_{sb} \geq 0 \\ (7238 {\overset{\cdot}{v}}_{sb}^{2} + 258 v_{sb} - 0.7) \times 10^{3} & v_{sb} < 0 \end{matrix}

(8)

Pressing experiment

Figure 5 depicts the results of the pressing experiment, which involved the pressing of a soft object (a piece of urethane foam) by the tip of the fork glove. The arm alone was controlled. (A) shows that the construction robot pressed the urethane foam slowly, and (B) indicates that the construction robot stopped pressing when the operator experienced the reaction torque to the joystick during the process. Furthermore, $τ_{r}$ changed gradually as it pressed the urethane foam in (A). The shadowed area in Figure 5 corresponds to an imperceptible moment when the urethane foam is pressed by the arm. This area of the crushed urethane foam measures approximately 5 cm. The estimated dynamic parameters vary from the actual values as a result of the influence of the posture of the fork glove. In practice, however, the arm can handle most objects through velocity control with gravity compensation. The findings confirm that the dynamic parameters in Table 2 are suitable for the application of velocity control to the arm.

Figure 5.

A piece of urethane foam is pressed by the arm.

Figure 6 depicts the pressing of a concrete block and of a piece of urethane foam, respectively, by the boom. As shown in Figure 6, $τ_{r}$ shifts rapidly. Moreover, $f'_{sb}$ decreases sharply; hence, no imperceptible moment is observed when the construction robot presses a concrete block (a hard object). However, $τ_{r}$ changes more slowly in the process of pressing the urethane foam than that in the process of pressing the concrete block. By considering the reaction torque, the operator can distinguish between soft and hard objects. Furthermore, the shadowed area in (B) exhibits an imperceptible moment as the urethane foam is pressed. This area of crushed urethane foam measures roughly 3 cm.

Figure 6.

A concrete block and a piece of urethane foam are pressed by the boom.

In general, the experiment results prove that the velocity control method with gravity compensation can be applied to the boom and arm and can generate a realistic reaction force for the operator. These findings also confirm that the dynamic parameters are effective and appropriate when the velocities of the arm and the boom are controlled.

Compensation for the gravity of an object

Control of the boom to grasp a heavy object

Figure 7 shows how a fork glove grasps a concrete block (9.7 kg) when the boom is controlled. The fork glove grasped the block in approximately 10 s and released it in roughly 155 s. $f'_{sb}$ initially increases immediately as the block is grasped, and its value continues to increase throughout the entire process. The weight of the concrete block (9.7 kg) influenced the result; thus, object gravity should be considered in the calculation of compensated driving force. This observation also proves that the dynamic parameters identified in Table 2 are appropriate. In addition, reaction torque is observed when the boom moves vertically because $f'_{sb}$ is larger than $f_{preb}$ (when the external force induced by the gravity of the object as it is grasped and conveyed is ignored). This reaction torque is detrimental to the operation because the operator must overcome it to handle the joysticks. Furthermore, the operator may also fail to perceive the feedback force from the joystick of the fork glove (grasping operation) when the reaction torque to the boom joystick is provided with the operator in the process of conveying an object. Therefore, the external force generated by the gravity of the grasped object must be compensated when the object is conveyed. Following this compensation, the operator can only sense the feedback force from the fork glove joystick in the process of grasping and conveying the object through velocity control. The mass of an object is shown to the operator on screen during object conveyance.

Figure 7.

Grasping a concrete block through boom control.

Dynamic equation of the robot arm as it grasps an object

When the robot arm grasps an object, it is considered as a system with 2-DOF. Its coordinates are presented in Figure 8. The center of mass of the grasped object is located at the end of the robot arm (the tip of the fork glove), and the length between the center of mass and the joint is $l_{a}$ . As mentioned above, since the construction robot works slowly, the influence of inertia item and Coriolis as well as centripetal item is omitted in the calculation of the dynamic equation. Thus, the dynamic equation of the robot as it grasps an object is thus expressed as follows

\begin{matrix} [\begin{matrix} τ_{b} \\ τ_{a} \end{matrix}] = [\begin{matrix} m_{b} l_{gb} C_{b} + m_{a} l_{b} + m_{o} l_{b} & m_{a} l_{ga} C_{a} + m_{o} l_{a} \\ 0 & m_{a} l_{ga} C_{a} + m_{o} l_{a} \end{matrix}] \\ [\begin{matrix} C θ_{a} \\ C θ_{ba} \end{matrix}] g - [\begin{matrix} m_{b} l_{gb} S_{b} & m_{a} l_{ga} S_{a} \\ 0 & m_{a} l_{ga} S_{a} \end{matrix}] [\begin{matrix} S θ_{a} \\ S θ_{ba} \end{matrix}] g \end{matrix}

(9)

Figure 8.

Coordinate system of the robot arm with an object.

Identification of the mass of an object and the calculation of $f'_{si}$

Joint torque consists of two variables, as given in equation (9) The first is generated by the gravities of the boom and arm, whereas the other is caused by the object. Therefore, equation (4) should be modified as in equation (10). $f_{mb}$ expresses the external force on boom induced by the gravity of the grasped object. If the mass of an object is known, compensated driving force can then be computed. The mass of an object is a variable parameter because the robot grasps and lifts various objects with different mass. Thus, the least-square method used to determine the dynamic parameters of the boom and arm cannot calculate the mass of objects

{\begin{matrix} x'_{b} & = si n^{- 1} [c_{b} \sin x_{b} / (y_{sb} + s_{b})] \\ f_{sgb} + f_{mb} & = τ_{b} / (b_{b} \sin x'_{b}) \\ f'_{sb} & = f_{sb} - (f_{sgb} + f_{mb}) \end{matrix}

(10)

Hence, this research introduces a parameter $f_{sv}$ to detect when the robot conveys an object and to calculate the mass of the grasped object. This parameter is the driving force to compute this mass. Given that the relationship between $f'_{s}$ and piston velocity $v_{s}$ appears linear, the linear fit method is used to obtain the function of $f_{sv}$ in terms of $f'_{s}$ and $v_{s}$ when the robot moves in free space without grasping anything. In addition, the arm is positioned almost vertically when it conveys an object. Therefore, $f_{mb}$ is predominantly influenced by the gravity of the object rather than by $f_{ma}$ (which expresses the external force on arm induced by the gravity of the grasped object). This research therefore considers boom data. Moreover, the piston stops when the absolute value $| v_{s} |$ is smaller than 0.001 m/s. Equation (11) depicts the fitting result using the experiment data in Figure 4. Figure 9 suggests that in the results of $f'_{sb}$ and $f_{sv}$ , two lines are nearly superposed. These findings confirm that equation (11) is viable and accurate. $f'_{sb}$ increases when the construction robot lifts a heavy object. Thus, the mass of an object can be determined based on the discrepancy between $f'_{sb}$ and $f_{sv}$ . Prior to the estimation of the mass of an object, however, the moments during which the construction robot lifted and released an object must be distinguished. The moment of grasping and lifting is the period when the difference between $f'_{sb}$ and $f_{sv}$ is greater than a positive threshold (this threshold is defined to distinguish the moments of grasping and lifting). The moment of releasing is the period when the difference $(f'_{sb} - f_{sv})$ is smaller than the negative threshold. The appropriate threshold value must therefore be determined

f_{sv} = {\begin{matrix} 27, 500 v_{sb} + 550 & v_{sb} > 0.001 \\ 27, 500 v_{sb} - 450 & v_{sb} < 0.001 \end{matrix}

(11)

Figure 9.

Compensated driving and putative forces.

Although $f'_{sb}$ and $f_{sv}$ are almost identical when the boom shifts in free space, their values vary slightly. According to the boom data in Figure 9, the mean and standard deviation of the difference between $f'_{sb}$ and $f_{sv}$ are (95 ± 94) N. The positive threshold should be larger than 189 (95 ± 94) N; hence, its value is set to 300 N for an acceptable tolerance level. When $f'_{sb} - f_{sv} > 300 N$ , the construction robot is in the process of grasping and lifting an object. Given that the difference between $f'_{sb}$ and $f_{sv}$ is attributed to the gravity of the grasped object, equation (12) is used to determine the mass of the grasped object. In each sampling period, the mass of an object is computed in real time and shown on screen. Its mean value is the estimated mass of the object in real-time processing. The external forces on the boom and arm as generated by the object are determined using equations (13) and (14). When $f'_{sb} - f_{sv} < - 300 N$ , the grasped object has been released and $m_{o}$ is zero. Figure 10 illustrates the process of computing the mass of an object and compensated driving force

m_{o} = \frac{(f'_{sb} - f_{sv}) b_{b} \sin x'_{b}}{g [l_{b} \cos θ_{b} + l_{a} \cos (θ_{a} + θ_{b})]}

(12)

f_{mb} = \frac{m_{o} g [l_{b} \cos θ_{b} + l_{a} \cos (θ_{a} + θ_{b})]}{b_{b} \sin x'_{b}}

(13)

f_{ma} = \frac{m_{o} g l_{a} \cos (θ_{a} + θ_{b})}{b_{a} \sin x'_{a}}

(14)

Figure 10.

Identification of the mass of an object and the calculation of $f'_{si}$ .

Experiment and analysis

Experiment on the grasping of heavy objects

Three task objects whose mass were 9.7, 4.2, and 20.5 kg were placed in area Ⓐ, Ⓑ and Ⓓ, as illustrated in Figure 1. The operator manipulated the construction robot to grasp and lift the task objects one by one using joysticks. The experimental data are shown in Figure 11, in which (A), (B), and (C) represent the process of grasping and lifting three task objects, respectively. The estimated curve in relation to mass of objects, $m_{o}$ , is shown in Figure 11. Furthermore, the mean values of the mass of the objects are 9.8 ± 0.3, 4.2 ± 0.3, and 20.7 ± 2.7 kg, respectively. These values are almost consistent with the actual values. Given the estimates of the mass of the objects, the solid line $f_{sgb}$ increases in the (A), (B), and (C) processes. $f'_{sb}$ and $f_{sv}$ are nearly identical except at the beginning and end of (C). At the beginning of (C), the estimated object mass is small, and a slightly significant discrepancy is observed between $f'_{sb}$ and $f_{sv}$ . This discrepancy decreases gradually when the estimated value is similar to the actual one for a brief moment. When the mass of a task object is great in (C), a sharp valley is detected when the object is released suddenly at approximately 92 s. The gravity compensation method can thus determine the mass of a grasped object and calculate the total external force generated by the boom, arm, and grasped object. The stiffness of a grasped object can be obtained using the pressure of a piston obtained by the pressure sensors and the closed and opened states of the fork glove.

Figure 11.

Grasping of heavy objects when the boom is controlled.

Experiment on the conveyance of heavy objects

The practical process of transferring an object through the construction robot was simulated in a conveyance experiment. The operator manipulated the construction robot to grasp and convey the block using joysticks.

Concrete blocks whose mass were 3.2, 5.4, 9.1, 15.1, and 20.5 kg, respectively, were utilized as task objects, along with an empty tin can (0.4 kg) and one with water (4.0 kg). The total number of task objects is 7. Task objects were placed in area Ⓐ, as illustrated in Figure 1, in descending order by mass, respectively. The conveyance experiment was conducted 7 times by an operator. Six males with a mean age of 26.1 years were enrolled in this research. So, a single task object was conveyed 24 times, as shown in Table 3.

Table 3.

The actual and measured mass of task objects except empty tin can.

	Mass of task objects (kg)
Measured	Actual
	20.5	15.1	9.1	5.4	4	3.2
Operator 1	21.25	15.06	9.57	5.31	4.21	3.32
	19.71	15.78	10.03	5.02	3.95	3.26
	20.77	16.21	9.21	5.26	3.87	3.06
	18.66	14.56	8.98	5.47	4.39	3.16
Operator 2	20.56	16.4	10.05	5.9	4.16	3.33
	20.21	13.23	9.65	4.98	4.38	3.26
	22.27	14.43	8.78	5.23	4.19	3.21
	20.38	15.34	8.54	5.25	3.86	3.51
Operator 3	21.05	16.02	9.17	4.99	3.79	3.28
	20.41	13.98	9.62	5.16	4.08	3.29
	19.48	15.33	8.72	5.75	4.27	3.44
	19.61	14.51	8.83	5.37	4.53	2.97
Operator 4	20.44	14.33	8.55	5.49	3.72	3.15
	21.46	13.55	8.02	5.26	3.98	3.08
	20.78	14.52	9.5	5.64	3.86	3.32
	18.46	15.24	8.76	4.95	4.18	3.49
Operator 5	20.24	14.66	9.55	5.37	4.22	3.44
	22.01	15.23	8.47	5.67	4.38	3.26
	21.38	16.01	8.96	5.18	4.21	3.04
	20.56	14.23	9.16	5.13	3.94	3.38
Operator 6	20.98	15.22	9.35	4.96	4.06	3.46
	22.34	14.82	8.81	5.27	4.47	3.18
	19.38	15.02	9.65	5.21	4.18	3.14
	20.57	16.08	9.43	4.9	4.48	2.97
Mean (kg)	20.54	14.99	9.14	5.28	4.14	3.25
SD (kg)	1.00	0.84	0.52	0.27	0.23	0.16

SD: standard deviation.

The conveyance sequence was as follows:

First, the task object was conveyed and dropped to area Ⓑ from area Ⓐ.

Second, grasped and conveyed the object to area Ⓓ.

Then conveyed to area Ⓒ;

Finally, returned back to area Ⓐ.

During conveyance, the mass of the empty tin can was zero. This finding can be attributed to the following reasons: Given that cylinders are nonlinear systems in real life, the $f'_{sb}$ is difficult to calculate using a mathematical method. Furthermore, $f'_{sb}$ and $f_{sv}$ vary slightly. This variation is induced by light objects with a mass of 1.07 ± 1.07 kg based on 95 ± 94 N. Therefore, the mass of an object may be read as zero when an object with a small mass (less than or approximately 2.14 kg) is grasped and lifted by the construction robot. However, the reaction force sensed by an operator is noticeable in the initial grasping stage. The variance of this reaction force changes with the deformation of a very soft object when it is grasped by a fork glove under velocity control. Thus, the operators can infer that the mass of a grasped object is smaller than or approximately 2.14 kg when they experience a reaction torque from the fork glove joystick even though the mass shown on screen is zero. Figure 12 shows the experiment results, with the exception of those for the empty tin can. The estimated mass of all objects is almost equal to their actual mass. Given that $f'_{sb}$ is greater than $f_{sv}$ , the gravity compensation method is effective only when the robot conveys a heavy object. The conveyance experiment confirms the effectiveness of the gravity compensation method in computing the mass of an object.

Figure 12.

Results of the conveyance of heavy objects.

In this research, the experimental results are validated by the NASA–Task Load Index (NASA-TLX), which measures mental strain. NASA-TLX is easy to implement and is sensitive to low mental workloads.²⁷ It consists of six subscales: mental demand, physical demand, temporal demand, personal performance, effort, and frustration level.

The procedure of NASA-TLX for an operator is expressed as follows:

A pairwise comparison test is conducted to obtain the weight of the six subscales ( $w_{i}$ , $i = 1, 2, \dots, 6$ ). The sum of $w_{i}$ is 15.

An evaluation experiment that is the conveyance experiment mentioned above is executed.

Each subscale is evaluated. After the conveyance experiment, scores, $s_{i}$ , have been assigned to each subscale by the operator according to percentile rank.

The mean weighted workload (WWL) score is calculated in terms of equation (15) and recommended based on the evaluation of workload by NASA-TLX.²⁸ The lower the WWL score, the lower the operator’s mental strain

WWL = \frac{1}{15} \sum_{i = 1}^{6} w_{i} s_{i}

(15)

Figure 13 shows the result of NASA-TLX. In terms of paired sample t-test and p value $(p = 0.045)$ , the difference between operation with and without the gravity compensation appears to be statistically significant in the result for NASA-TLX. Because operators do not need to overcome the feedback force generated by the gravity of the grasped object when the robot lifts and conveys an object, especially a heavy object, the lower WWL scores are obtained. We therefore conclude that the mental strain on the operator can be alleviated using the gravity compensation method.

Figure 13.

NASA-TLX subjective measure.

Conclusion

In teleoperation, an operator must perceive a reasonable sense of force from the construction robot. In this research, the master–slave control (velocity control) method with gravity compensation is applied to the boom and arm. Pressing experiments were conducted, and its results proved that the velocity control method can generate the realistic reaction force for an operator. This research used blocks and tin cans of different mass as task objects, and the gravity compensation method was effectively used to compute the mass of these grasped objects. The effectiveness of this gravity compensation method has been verified through conveying experiments. The experimental results indicate the feasibility of our proposed method.

Footnotes

Academic Editor: Yangmin Li

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to thank the financial support from the National Natural Science Foundation of China (Nos 51575219 and 51305153).

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