WO2018113966A1

WO2018113966A1 - System and method for automatically adjusting a gravity vector of a robot

Info

Publication number: WO2018113966A1
Application number: PCT/EP2016/082287
Authority: WO
Inventors: Henrik Nilsson; Stig Moberg
Original assignee: Abb Schweiz Ag
Priority date: 2016-12-22
Filing date: 2016-12-22
Publication date: 2018-06-28

Abstract

A method and a system for automatically adjusting a gravity vector of a robot (1). The robot (1) includes at least one axis (4), an actuator (5) arranged for driving the at least one axis (4), and a kinematic model of the robot (1). The method further includes obtaining at least one robot parameter indicating an actuator torque, or measuring at least one robot parameter indicating an inclination of the robot (1); and adjusting a gravity vector of a dynamic model of the robot (1) based on the at least one robot parameter.

Description

System and method for automatically adjusting a gravity vector of a robot Technical field

The present disclosure relates to technology for robots, and in particular to a system and a method for automatically adjusting a gravity vector of a robot.

Background

In order for a robot to be able to accurately perform work in a working

environment, a calibrated kinematic model is required. In the calibration process, the true relative positions of joints and links of the robot are determined. The kinematic model then corresponds better with the kinematics of the real robot which is crucial when the robot performs position work. Calibration of the robot is typically performed at the manufacturing facility before the robot is delivered, and at later times when wear causes the real kinematics to differ from the modelled one. The kinematic model is normally included in a controller of the robot.

A dynamic model describes the motion of the robot if a certain torque or force is applied to the robot. As understood, the dynamic model parameters depends on the mass properties of the robot, thus on the masses, centres of gravity and own inertias of the links, joints, actuators, drivetrains etc. The dynamic model parameters also include the gravitational direction of the robot. In a calibration process of the robot, the dynamic properties of the dynamic model are commonly determined. It is common that a robot is mounted on a plane which is not perpendicular to the Earth's gravity field. In some cases, in order to increase the accuracy of the robot, the robot can be placed on a tilted surface to reduce the effect of e.g. backlash in the gearbox of axis 1 . In other cases the robot can be mounted on a wall or upside-down in the ceiling to better suit the application at hand. There are also some applications where the robot is moved and/or reoriented by an external

mechanism. In these cases where the direction of the gravitational force exerted on the robot is constantly changing it can be hard to know which orientation to use in the dynamic model at any given moment.

For optimal performance of the robot, its orientation with respect to gravity has to be known to the control system. As described, the orientation can be difficult to estimate and/or calculate, and the actual/true orientation might not be provided to the control system.

Summary

It is an object of the disclosure to provide a method to find a true orientation of a robot with respect to gravity. It is a further object of the disclosure to provide an automatic method for adjusting a gravity vector of a dynamic model of the robot. These objects and others are at least partly achieved by the method and the system according to the independent claims, and by the embodiments according to the dependent claims.

According to a first aspect, the disclosure proposes a method for automatically adjusting a gravity vector of a robot. The robot includes at least one axis, an actuator arranged for driving the at least one axis, and a kinematic model of the robot. The method includes obtaining at least one robot parameter indicating a torque of the actuator, or measuring at least one robot parameter indicating an inclination of the robot, and adjusting a gravity vector of a dynamic model of the robot based on the at least one robot parameter. With the method, the gravity vector of the dynamic model of the robot is automatically adjusted. This simplifies the set-up of the robot for the operator. The automatic estimation could make the orientation of the robot with respect to gravity known to the control system on-the-fly without the need for interaction from the operator. Moreover the probability that the orientation is correct will likely increase. According to some embodiments, the measuring includes measuring at least one robot parameter indicating an inclination of the robot with a known position and orientation with respect to an internal reference system of the robot. According to some embodiments, the kinematic model is a calibrated kinematic model.

According to some embodiments, the method includes estimating the at least one robot parameter indicating a torque r_actuator of the actuator on the basis of an output torque of a controller of the control system.

According to some embodiments, the method includes measuring the at least at one robot parameter indicating a torque r_actuator of the actuator. According to some embodiments, wherein adjusting the gravity vector includes performing an optimization of the dynamic model with an estimated robot orientation with respect to gravity of the robot as optimization parameter in order to minimize an error between a calculated torque T_model of the dynamic model and a torque r_actuator of the actuator determined based on the at least one robot parameter indicating the torque of the actuator.

According to some embodiments, the robot includes a plurality of axes and a respective actuator arranged for driving each axis, wherein the method includes obtaining for a plurality of actuators robot parameters indicating torques of the actuators, and adjusting the gravity vector of the dynamic model of the robot based on the obtained robot parameters.

According to some embodiments, the method includes measuring the at least one robot parameter indicating an inclination of the robot with an accelerometer and/or an inclinometer mounted at a known position and orientation with respect to the internal reference system of the robot. According to some embodiments, the dynamic model includes a predefined mounting orientation of the robot in relation to a mounting surface.

According to a second aspect, the disclosure propose a robot system including a robot with at least one axis and an actuator arranged for driving the at least axis, and a control system arranged for controlling motion of the robot. The control system includes a dynamic model of the robot and a kinematic model of the robot. The robot system is further arranged to provide at least one robot parameter indicating a torque of the actuator, or includes a measuring device for measuring at least one robot parameter indicating an inclination of the robot. The control system is configured to obtain the robot parameter and to automatically adjust a gravity vector of the dynamic model of the robot based on the at least one robot parameter. According to some embodiments, the robot system is configured to estimate the at least one robot parameter indicating a torque r_actuator of the actuator on the basis of an output torque of a controller of the control system.

According to some embodiments, the robot system is arranged to measure the at least one robot parameter indicating a torque r_actuator of the actuator.

According to some embodiments, the control system is configured to perform an optimization of the dynamic model with respect to an estimated robot orientation with respect to gravity of the robot as optimization parameter in order to minimize an error between a calculated torque r_model of the dynamic model and a torque ^Tactuai to the actuator determined based on the at least one robot parameter indicating the torque to the actuator, and to adjust the gravity vector of the dynamic model based on the optimization. According to some embodiments, the robot includes a plurality of axes and a respective actuator arranged for driving each axis, and wherein the control system is configured to obtain for a plurality of actuators robot parameters indicating torques of the actuators, and wherein the control system is configured to adjust the gravity vector of the dynamic model of the robot based on the obtained robot parameters. According to some embodiments, the measuring device includes an

accelerometer and/or an inclinometer mounted at a known position and orientation with respect to the internal reference system of the robot. According to some embodiments the measuring device is mounted to a base of the robot. Brief description of the drawings

Figs. 1 A-1 D illustrate a robot mounted in different angles according to some embodiments.

Fig. 2 illustrates a system according to some embodiments of the disclosure. Fig. 3 illustrates how an optimization is performed according to some

embodiments.

Fig. 4 illustrates a flowchart of a general method according to some embodiments of the disclosure.

Fig. 5 illustrates a flowchart of a method according to some embodiments of the disclosure.

Detailed description

In the following a system and a method will be explained that automatically finds the true orientation of a robot with respect to gravity, irrespective of how the robot is mounted to a surface. The orientation of the robot with respect to gravity is thus adjusted to correctly reflect the actual orientation, without any need for operator intervention. The system and method are particularly useful for robots that often change their orientations.

In this disclosure, the robot can have an arbitrary orientation. Figs. 1A to 1 D shows examples of a robot 1 with different orientations, that is, mounted to surfaces 2 with different inclinations with respect to gravity. In Fig. 1 A, the robot 1 is mounted to a regular floor surface 2a, e.g. a factory floor. In Fig. 1 B the robot 1 is mounted to a ceiling surface 2b, thus approximately up-side-down with the respect to the mounting in Fig. 1A. In Fig. 1 C the robot 1 is mounted to a wall surface 2c, and in Fig. 1 D the robot 1 is mounted to a support surface 3a of a wedge-shaped support 3. The wedge-shaped support 3 is mounted to the regular floor surface 2a. The support surface 3a is inclined with an angle a with respect to the floor surface 2a.

In Fig. 2 a robot system 6 including a general industrial robot 1 is illustrated representing any of the robots 1 of the Figs. 1 A to 1 D. The robot 1 is a

programmable robot with six axes and six degrees of freedom (DOF). This robot 1 is however only an example, and the invention is applicable to industrial robots having more or less than six axes, and more or less than 6 DOF. An industrial robot is here defined to be a robot that can be automatically controlled, that is reprogrammable, that can adopt to a multitude of tasks and has a plurality of axes. The robot 1 includes an arm including a plurality of links interconnected with joints. A joint is arranged to be actuated with an actuator, typically a servo- controlled motor, which apply torques (or linear forces, in the case of a linear actuator) at the joint of the robot in order to move the link interconnected to the joint. The actuator is controlled by a reference position q_ref and applies a corresponding torque to the joint. A joint and a thereto interconnected link is referred to as an axis 4. In other words, an actuator 5 is arranged for driving a respective of the axes 4. The depicted robot 1 has six axes 4, and thus six actuators 5. The robot system 6 further includes a control system 7 configured for controlling motions of the robot 1 . The control system 7 comprises a robot controller 8 with a first processor 8a and a first memory 8b. In some embodiments the control system 7 also includes another control entity 9, e.g. a control unit or a computer. The control entity 9 comprises a second processor 9a and a second memory 9b. The first and second processors 8a, 9a may include one or several central processing units, CPUs. The first and second memories 8b, 9b may include one or several memory units, e.g. a read-only memory, ROM, and a random access memory, RAM. The robot 1 also comprises an internal sensor used for measuring a position q of the actuator 5 during normal operation in order to provide feedback of the position of the actuator 5 to the control system 7.

The control system 7 includes and stores a dynamic model and a kinematic model of the robot 1 . The kinematic model in included in the controller 8. The dynamic model may be included in the controller 8, or included in the control entity 9. The dynamic model describes how the robot 1 moves in response to actuator forces or torques. The kinematic model of the robot 1 describes how the motion of the joints of the robot 1 is related to the motion of the end effector in Cartesian space. In this disclosure it is generally assumed that the kinematic and dynamic model parameters except gravitational direction are known. Thus, the kinematic model is calibrated, and the dynamic model is at least partly calibrated. However, as will be explained later, if a measurement device 10 (Fig. 2) is mounted to the base of the robot 1 , the kinematic model does not have to be calibrated in order for the method to be performed accurately as the orientation and position of the base is known prior to calibration. The dynamics of the robot 1 may be described using a set of nonlinear, second-order, ordinary differential equations which depend on the kinematic and inertial properties of the robot. The dynamic model is a corner stone in modern robot control and can be used for a multitude of tasks, e.g. time optimal trajectory generation, accurate servo control, or supervision.

The dynamic model of the robot 1 includes a gravity vector G . The true orientation of the robot 1 is defined in three dimensions with angles a_x, a_y, a_z of coordinate axes x, y, z of an internal reference system of the robot 1 in relation to the gravity vector G . The gravity vector G is typically defined with the assumption that the robot 1 is horizontally mounted in an upright position as in Fig. 1A. This may be problematic in situations when the robot 1 is not horizontally mounted in an upright position on a horizontal surface, e.g. as in Fig. 1 B, 1 C and 1 D. Fig. 1 D is illustrating a special situation where the robot 1 is mounted in a predefined angle a for example with a wedge-shape support 3. The angle a may be input to the control system 7 by an operator and the gravity vector updated accordingly, thus assuming that the floor surface 2a the wedge-shape support 3 is mounted to is truly horizontal. However, this assumption might be incorrect, and the operator may unknowingly input a false angle a to the control system 7. By using an automatic estimation method to find the true orientation of the robot 1 with respect to gravity as will be explained in the following, it will be easier for the operator to set up the robot system 6 and the likelihood of utilizing the optimal performance of the robot 1 is increased. In the following two different

embodiments will be explained that each can be used in isolation, or combined to further increase the accuracy. Generally, the control system 7 is arranged to obtain a robot parameter and to automatically adjust the gravity vector of the dynamic model of the robot 1 based on the at least one robot parameter.

In a first embodiment, the robot 1 includes a measuring device 10 for measuring at least one robot parameter indicating an inclination of the robot 1 , for example an inclination of a surface of the robot with a known position and orientation with respect to an internal reference system of the robot 1 . The orientation of the measuring device 10 in relation to a base 1 1 of the robot 1 may thus be known. The measuring device 10 may in beforehand be calibrated or reset e.g. relative to a surface with known orientation, such that its readout can be trusted. According to some embodiments, the measuring device 10 is arranged directly to the base 1 1 . Then, the output from the measuring device 10 shows the orientation of the robot 1 with respect to gravity directly. This because the base 1 1 often defines the internal reference system of the robot 1 . If the measuring device 10 is located at any other place on the robot 1 , e.g. on any of the other links or joints, the position and orientation of the measuring device 10 and thus the output of the measuring device 10 should be related to the orientation of the base 1 1 via the calibrated kinematic relation included in the calibrated kinematic model of the robot 1 . The measuring device 10 comprises e.g. an accelerometer and/or an inclinometer mounted at a known position and orientation with respect to the internal reference system of the robot 1 . The measuring device 10 is attached, built-in or mounted to the robot 1 at a known position and orientation. For example, the measuring device 10 may be integrated on an already existing electric board on the robot 1 . During e.g. the production of the robot 1 the measuring device 10 could be calibrated. In Fig. 2 two different measuring devices 10 are illustrated and arranged to a base 1 1 of the robot 1 . The measuring device 10 is arranged to measure the at least one robot parameter and send the at least one robot parameter to the control system 7. The control system 7 then obtains the at least one robot parameter and automatically adjusts the gravity vector of the dynamic model of the robot 1 based on the at least one robot parameter. As the measuring device 10 is arranged to a known surface of the robot 1 , thus a surface with a known orientation with respect to an internal reference system of the robot 1 , and the measuring device 10 has been calibrated e.g. during manufacturing, the measured values from the measuring device 10 can be directly used for adjusting the orientation of the gravity vector G of the dynamic model. In a second embodiment, an actuator torque, r_actuator, is estimated or measured. The actuator torque can be estimated by using the output torque of the controller 8. It is here assumed that the actuator 5 has an accurate torque control. When standing still, a proper controller 8 outputs an estimated torque which should essentially equal a measured torque of the actuator 5. If the joint friction is significant compared to the gravity torque of each joint, a small back and forth movement could be used to improve the estimation of the torque. The actuator torque may instead be measured by an internal measuring device configured for measuring the torque of the actuator. In other embodiments, an external force/torque measuring device 12 may be arranged to a link or joint of the robot 1 for measuring torque or force of the link or joint, typically a multi-axis force/torque measuring device. For example, the external force/torque measuring device 12 may be attached to an end flange of the robot 1 . In some embodiments, where the robot 1 includes a plurality of axes 4 and a respective actuator 5 arranged for driving each axis, the control system 7 is configured to obtain for a plurality of actuators 5 robot parameters indicating the respective actuator torques. The control system 7 is then configured to adjust the gravity vector of the dynamic model of the robot 1 based on the obtained robot parameters. According to the second embodiment, the control system 7 is configured to perform an optimization of the dynamic model. It is a prerequisite for the second embodiment that the kinematic model of the robot 1 is calibrated, and thus that the positions of the axes 4 and thus the joints and links of the robot 1 are known. Also, if the robot 1 is arranged with an extra weight, e.g. an end effector, this has to be specified to the control system 7 in beforehand as it affects the optimization. The control system 7 is configured to perform the optimization with an optimizing parameter being an estimated robot orientation with respect to the gravity field of the Earth, in order to minimize an error between a calculated torque Tmodei of the dynamic model and an actuator torque T_actuator . The gravity vector of the dynamic model is then adjusted based on the optimization. In Fig. 3 the principle of the optimization is illustrated. The dynamic model "M" is schematically shown as included in the control system 7. The dynamic model may for example be included in the controller 8 or in the control entity 9. During normal use of the robot 1 , the controller 8 sends an actuator torque r_actuator to an actuator 5 of the robot 1 , and the actuator 5 moves the joint accordingly. The position q of the actuator 5, or of the joint, is measured and sent as feedback to the controller 8. The controller 8 calculates the actuator torque r_actuator based on the measured position q and reference position q_ref . In order to find the true orientation of the robot system 6, it is desired to perform an optimization in order to minimize the error between the actuator torque r_actuator and the calculated torque r_model , when either the measured actual position q or the reference position q_ref is input to the dynamic model which calculates the calculated torque T_model for each joint. Here it is assumed that only the gravity part of the dynamic model is calculated, otherwise speed and acceleration may be required. In the optimization, the orientation of the gravity vector G of the robot 1 is adjusted in order to minimize the error, and the true orientation of the robot 1 is thus inherently determined. The optimization of the gravity vector G is then finished and the gravity vector G of the robot 1 is considered calibrated. The torques r_actuator, T_model for the optimization can be obtained in either one specific position or if necessary during a movement scheme.

As understood, the optimization may be made based on actuator torques r_actuator and positions q for a plurality of actuators and joints. Thus, the orientation is estimated based on the forces exerted on the robot structure due to gravity and the actuator torque or actuator torques which arise due to these forces. Since the robot 1 is calibrated, the positions of the robot axes 4 are known and the orientation could be calculated.

In some embodiments, the dynamic model includes a predefined mounting position and orientation of the robot 1 in relation to a mounting surface 2. This predefined mounting orientation is determined by e.g. a wedge-shaped support 3 as a predefined angle a (including a_x, a_y, a_z ) and may be input to the control system 7 and thus to the dynamic model by the operator via a conventional user interface. However, the mounting surface 2 may not be totally horizontal and/or the predefined angle a specified by the operator might actually be incorrect, which may yield an incorrect designation of the orientation with respect to gravity of the robot 1 if only the predefined angle a e.g. specified by the operator is used to adjust the gravity vector G of the dynamic model. With the described system, it is not necessary that the operator specifies any details of a mounting orientation. However, if the operator does, the control system 7 will anyway determine the true orientation of the robot 1 and a corrected adjusted gravity vector G of the dynamic model automatically, and thus override the operators setting. Alternatively, the operator may be presented with an option to use the described functionality and actively choose to use it or not by making an input to the control system 7.

The disclosure also relates to one or several methods for automatically adjusting a gravity vector of a robot 1 . The one or several methods may be implemented as a computer program P. The computer program P comprises a computer program code to cause a control system 7, or a computer connected to the control system 7, to perform the one or several methods according to any of the steps explained herein. According to some embodiments, the one or several methods may be included on a computer program product comprising a computer program code stored on a computer-readable medium to perform the method according to any of the steps explained herein, when the computer program code is executed by a control system 7 or a computer connected to the control system 7.

In Fig. 4 a flowchart of a general method is illustrated, which will now be explained with reference to this figure. The method includes in a first step S1 : obtaining at least one robot parameter indicating an actuator torque, or measuring at least one robot parameter indicating an inclination of the robot 1 . The measuring may include measuring at least one parameter indicating an inclination of a surface of the robot 1 with a known position and orientation with respect to an internal reference system of the robot 1 . The step S1 may be performed with the previously described system 6. In a further step S2, the method includes adjusting a gravity vector of a dynamic model of the robot 1 based on the at least one robot parameter. The general method thus implements either the first or the second embodiments. When performing the method for implementing the first

embodiment, the measuring device 10 has to be fed with power, but the actual robot 1 does not have to be powered or driven yet in order to adjust the gravity vector according to the first embodiment.

In Fig. 5 a method implementing the second embodiment is illustrated in a flowchart. In this method, the step S1 includes obtaining at least one robot parameter indicating an actuator torque. For example, the at least one robot parameter indicating an actuator torque is estimated by a controller 8 or is measured with an internal or external sensor of the robot 1 . Further, the step S2 includes adjusting the gravity vector including performing an optimization of the dynamic model with an estimated robot orientation with respect to gravity of the robot 1 as optimization parameter in order to minimize an error between a calculated torque r_model of the dynamic model and an actuator torque r_actuator determined based on the at least one robot parameter indicating the actuator torque. When implementing the second embodiment, power has to be fed to the actuators 5 of the robot 1 . In some cases the robot 1 does not have to perform any certain movement scheme in order to correctly adjust the gravity vector, it is enough that the robot 1 e.g. tries to hold an initial certain position. In other cases a small movement may be performed around a certain position, and in some cases a certain movement scheme may be required. As previously described, the robot 1 may include a plurality of axes 4 and a respective actuator 5 is then arranged for driving each axis 4. The method may thus include obtaining for a plurality of actuators 5 robot parameters indicating actuator torques, and adjusting the gravity vector of the dynamic model of the robot 1 based on the obtained robot

parameters.

As previously mentioned, the robot 1 needs to be calibrated in order to be able to implement some of the described methods. Thus, a step SO may precede the step S1 , where the step SO includes to perform a calibration where the correct parameters of the kinematic model of the robot 1 are determined.

Claims

1 . A method for automatically adjusting a gravity vector of a robot (1 ), wherein the robot (1 ) includes at least one axis (4), an actuator (5) arranged for driving the at least one axis (4), and a kinematic model of the robot (1 ), wherein the method includes:

- obtaining at least one robot parameter indicating an actuator torque r_actuator, or measuring at least one robot parameter indicating an inclination of the robot (1 );

- adjusting a gravity vector of a dynamic model of the robot (1 ) based on the at least one robot parameter.

2. The method according to claim 1 , wherein the kinematic model is a calibrated kinematic model.

3. The method according to claim 1 or 2, including estimating the at least one robot parameter indicating an actuator torque r_actuator on the basis of the output torque of the controller (8).

4. The method according to claim 1 or 2, including measuring the at least at one robot parameter indicating an actuator torque r_actuator .

5. The method according to any of the preceding claims, wherein

adjusting the gravity vector includes performing an optimization of the dynamic model with an estimated robot orientation with respect to gravity of the robot (1 ) as optimization parameter in order to minimize an error between a calculated torque T_modeiof the dynamic model and an actuator torque Tactuator determined based on the at least one robot parameter indicating the actuator torque.

6. The method according to claim 5, wherein the robot (1 ) includes a plurality of axes (4) and a respective actuator (5) arranged for driving each axis (4), wherein the method includes obtaining for a plurality of actuators (5) robot parameters indicating actuator torques, and adjusting the gravity vector of the dynamic model of the robot (1 ) based on the obtained robot

parameters.

7. The method according to claim 1 or 2, including measuring the at least one robot parameter indicating the inclination with an accelerometer and/or an inclinometer mounted at a known position and orientation with respect to the internal reference system of the robot (1 ).

8. The method according to any of the preceding claims, wherein the dynamic model includes a predefined mounting orientation of the robot (1 ) in relation to a mounting surface (2).

9. A robot system (6) including:

- a robot (1 ) with at least one axis (4) and an actuator (5) arranged for driving the at least one axis (4);

- a control system (7) arranged for controlling motion of the robot (1 ) and including a dynamic model of the robot (1 ) and a kinematic model of the robot (1 ), c h a ra ct e r i z e d i n t h a t the robot system (6) further is arranged to provide at least one robot parameter indicating an actuator torque, or includes a measuring device (10) for measuring at least one robot parameter indicating an inclination of the robot (1 ); and wherein the control system (7) is configured to obtain the at least one robot parameter and to automatically adjust a gravity vector of the dynamic model of the robot (1 ) based on the at least one robot parameter.

10. The robot system (6) according to claim 9, wherein the kinematic model is a calibrated kinematic model.

1 1 . The robot system (6) according to claim 10, configured to estimate the at least one robot parameter indicating an actuator torque T_actuator on the basis of an output torque of a controller (8) of the control system (7).

12. The robot system (6) according to claim 9 or 10, arranged to measure the at least one robot parameter indicating an actuator torque r_actuator .

13. The robot system (6) according to any of the claims 9 to 12, wherein the control system (7) is configured to perform an optimization of the dynamic model with respect to an estimated robot orientation with respect to gravity of the robot (1 ) as optimization parameter in order to minimize an error between a calculated torque r_model of the dynamic model and an actuator torque ^actuator determined based on the at least one robot parameter indicating the actuator torque and to adjust the gravity vector of the dynamic model based on the optimization.

14. The robot system (6) according to any of the claims 9 to 13, wherein the robot (1 ) includes a plurality of axes (4) and a respective actuator (5) arranged for driving each axis (4), and wherein the control system (7) is configured to obtain for a plurality of actuators (5) robot parameters indicating actuator torques, and wherein the control system (7) is configured to adjust the gravity vector of the dynamic model of the robot (1 ) based on the obtained robot parameters.

15. The robot system (6) according to claim 9 or 10, wherein the

measuring device (10) includes an accelerometer and/or an inclinometer mounted at a known position and orientation with respect to the internal reference system of the robot (1 ).

16. The robot system (6) according to claims 9, 10 or 15, wherein the measuring device (10) is mounted to a base (1 1 ) of the robot (1 ).

17. The robot system (6) according to any of the claims 9 to 15, wherein the dynamic model includes a predefined mounting orientation of the robot (1 ) in relation to a mounting surface (2).