Reducing kinematic errors

Abstract

A method for reducing the kinematic error of a joint (5j) between a distal portion and a proximal portion of a manipulator (1), the joint (5j) being connected with: a motor (9j) for driving the joint in rotation; a measuring device (8j) for measuring the rotation angle of the motor (9j); a joint controller (12j) connected to the motor (9j) and to the measuring device (8j) for controlling at least the angle of rotation of the motor based on an input position command (qmot, j); and a trajectory generator (11) for outputting a position command (qmot, j), the method comprising the steps of: a. Providing an acceleration sensor (7) in the distal portion, b. Selecting a trajectory to be followed by the acceleration sensor (7), c. Estimating an expected acceleration value to which the sensor (7) is expected to be subjected along the trajectory, d. Outputting, by the trajectory generator (11), an initial command (qmot, j, qmot, j) for moving the sensor (7) along the trajectory, and e. Determining a position command (qmot, j) for moving the sensor (7) along the trajectory. E. Obtaining a correction command by adding a kinematic error correction (beta) to a specified parameter in the initial command (alpha) and inputting the correction command (gamma) into the joint controller (12j), f. Recording the acceleration value (a) experienced by the sensor (7) when moved in accordance with the correction command (gamma), and f. Determining the acceleration value (a). G. Determining if the deviation (Lambda) between the expected acceleration value and the recorded acceleration value exceeds a predetermined threshold, and h. If it is determined that the deviation (Lambda) exceeds the threshold, modifying the kinematic error correction (Beta) to reduce the deviation.

Description

Technical Field

[0001] The present invention relates to methods and apparatus for reducing kinematic errors when controlling the movement of joints within a robotic manipulator. Background Art

[0002] The robotic manipulator includes a plurality of links that are coupled to each other, to a base, or to an end effector through rotatable joints. The rotation of such joints is driven by a motor, and usually via a reduction gear. The play and inaccuracies generated during the manufacturing process of the motor and gears affect the control accuracy of the position and speed of the end effector at the distal end of the robotic arm. Because harmonic drive gears are virtually play-free, they are widely used as reduction gears in robots, but unavoidable inaccuracies (such as eccentricity of gears or splines) can still cause fluctuations in the rotation speed of the joint, even when the motor can be driven at a completely constant speed, so that the position of the joint may deviate from the expected position based on the known motor position and the transmission ratio of the reduction gear. This deviation is usually referred to as kinematic error or transmission error. Summary of the invention

[0003] The object of the present invention is to provide a simple and cost-effective way of reducing kinematic errors of robot joints.

[0004] According to one aspect of the present invention, the object is achieved by a method for reducing the kinematic error of a j-th joint between a distal portion and a proximal portion of a manipulator, the joint being connected with: a motor for driving the joint to rotate; a measuring device for measuring the rotation angle of the motor; a controller connected to the motor and the measuring device for controlling at least the rotation angle of the motor based on an input position command; and a trajectory generator for outputting a position command, the method comprising the following steps:

[0005] a. Arrange an acceleration sensor in the distal portion,

[0006] b. Select the trajectory to be followed by the acceleration sensor,

[0007] c. Estimate the expected acceleration values ​​that the sensor is expected to experience along the trajectory,

[0008] d. The initial command for moving the sensor along the trajectory is output by the trajectory generator,

[0009] e. Obtaining a correction command by adding the kinematic error correction to the specified parameters in the initial command, and inputting the correction position command into the controller,

[0010] f. record the acceleration value experienced by the sensor when it moves according to the correction position command,

[0011] g. Determine whether the deviation between the expected acceleration value and the recorded acceleration value exceeds a predetermined threshold, and

[0012] h. If the deviation is determined to exceed a threshold, the kinematic error correction is modified to reduce the deviation.

[0013] Since the kinematic errors reflect the inaccuracy of a given joint, their correction should be determined individually for each joint based on the characteristics of each joint. However, precisely because the kinematic errors reflect the individual characteristics of each joint, the trajectory generator and controller can be the same for all joints of manipulators manufactured in the same series. Therefore, it is convenient to manufacture robot systems in which the method of the present invention is applied in a series; by implementing appropriate kinematic error corrections in each joint of each sample robot system, the inaccuracies specific to each individual sample in the series can be compensated. Therefore, once the kinematic error corrections are known, they can be compensated easily and cost-effectively. The determination and implementation of the kinematic error corrections can be completed after the manufacturer assembles each sample robot system, or at the time of each joint repair or maintenance.

[0014] The acceleration sensor does not have to be permanently installed; since it is only needed when determining the kinematic errors, it can be removed after this operation and can be reused for a different manipulator. The method is therefore very cost-effective when applied to manipulators manufactured in series; it can also be applied when performing maintenance or repair work on conventional manipulators that do not have such sensors.

[0015] When the acceleration sensor is installed, it can be used to find the kinematic error correction of all joints between the acceleration sensor and the fixed base of the manipulator. Therefore, it is best to place the acceleration sensor at the distal end of the manipulator. In the case where the distal end includes a holder, the holder can be used to hold the acceleration sensor while performing the method.

[0016] When step e. is performed for the first time and the kinematic error is still unknown, the position commands received by the controller are those output by the trajectory generator, so the deviation of the measured acceleration from its expected value represents the overall kinematic error. When step e. is repeated with a non-zero correction, the residual deviation allows to judge whether the correction quality is sufficient and, if necessary, to improve it.

[0017] The above-mentioned command may be a position command in which the designated parameter is a position, and a speed command in which the designated parameter is a speed.

[0018] There is no specific restriction on the trajectory selected in step b., however, it is advantageous to find the kinematic error correction for the jth joint if the trajectory does not involve movements of other joints ≠ j of the manipulator, but rather involves movements of the joint to which the kinematic error correction is to be associated.

[0019] Estimating the expected acceleration can be very simple; indeed, when the selected trajectory is a constant speed rotation about an axis, the expected acceleration may be constant, or will have a component proportional to a circular function of the joint angle due to gravity. It is therefore preferred that at least part of the trajectory is a constant speed rotation; when the range of rotation of the joint is limited, several rotations in alternating directions may be combined into a trajectory defining an oscillating motion. Indeed, it is not even necessary to calculate the expected acceleration in advance; when the motor of the joint is controlled to rotate at a constant speed, the acceleration experienced by the sensor at any particular moment can be expected to be the average of the accelerations experienced before and after; that is, by calculating a moving average of the measured accelerations, the expected acceleration can be determined while moving the sensor along the selected trajectory.

[0020] It has been observed that the kinematic errors of the motor and reduction gear assembly can be accurately approximated by the sum of a small number of circular functions of different frequencies. The contributions from the motor and from the reduction gear input shaft (rotating at the same frequency as the motor) can be expressed as the motor's rotation angle q mot,j It can be described by a circular function (i.e. sine or cosine function) that is an integer multiple of n.

[0021] When the reduction gear is a harmonic drive gear (with i c The number of teeth on the gear is i f (slightly less than i c ) of the flexible wheel), the orientation of the wave generator and the flexible wheel driven by the motor is in each i f / i c After rotation, it becomes the same, so that the motor rotation frequency mi f / i c times, where m is a small integer.

[0022] While trajectories that require the motor to operate at the resonant frequency of the robot arm are usually avoided in normal operation of the robot to avoid exciting vibrations, in the method of the present invention, the speed of the trajectory is preferably selected so that the motor frequency or a harmonic thereof is the resonant frequency of the manipulator, preferably the lowest resonant frequency, because vibrations of the manipulator thus excited will produce a clearly detectable deviation between the expected acceleration value and the actual acceleration value. Preferably, the speed is selected so that the second harmonic of the motor frequency coincides with the resonant frequency.

[0023] Accelerometers are typically sensitive to acceleration in space in all three directions. Since vibrations can occur in any direction, the amount of data to be processed can be reduced by combining the three components of the recorded or estimated acceleration vector into a single scalar. This combining step can involve calculating the sum of the squares of the three components of the vector to obtain a scalar that is invariant under sensor rotation.

[0024] By performing a spectrum analysis, such as Fourier transformation, on the recorded acceleration values ​​(preferably, with respect to the rotation angle q of the motor mot,j ), which can facilitate the determination step. Here, if any spectral component of the Fourier transform exceeds a predetermined threshold, the deviation can be considered to be too large. The determination can be based on only one such spectral component, preferably a component whose frequency is twice the motor frequency, because this component may be the strongest component in the Fourier transform.

[0025] After the kinematic error correction has been modified in step h., steps d. to g. are repeated to find out whether the new kinematic error correction meets the threshold in step g., or at least whether the deviation of the new kinematic error correction is smaller than the deviation of the original kinematic error correction.

[0026] In theory, the kinematic error function can be modified in step h. according to a simple trial and error scheme, but in this case, finding a satisfactory kinematic error function may take a long time. The processing time can be shortened by estimating the gradient of the deviation with respect to the weighting coefficients of the kinematic error function and then adding this gradient multiplied by a scalar factor to the vector formed by the weighting coefficients of the kinematic error function.

[0027] When the vector formed by weighting is close to the optimum, it can be expected that the direction of the gradient obtained in the consecutive iterations of step 1) changes more strongly from one iteration to the next than when the vector is far from the optimum. Therefore, by increasing the scalar factor when the change in direction is below a given lower threshold and reducing the scalar factor when the change in direction is above a given upper threshold, the number of iterations required to reach this optimum can be reduced.

[0028] The change in direction may be considered to have not reached the lower threshold when there is no sign change between components of consecutive gradients, and may be considered to have exceeded the upper threshold when at least one component changes sign from one gradient to the next.

[0029] According to one aspect of the present invention, the object is achieved by a robot system, the robot system comprising:

[0030] - a manipulator having a proximal portion, a distal portion, a joint connecting the proximal portion and the distal portion, and a motor for driving the joint to rotate;

[0031] - a measuring device for measuring the rotation angle of the motor;

[0032] - a controller connected to the motor and the measuring device for controlling at least the rotation angle of the motor based on an input position command;

[0033] - a trajectory generator, the trajectory generator being used to output a position command;

[0034] - An acceleration sensor, preferably removably mounted in the distal part of the robot arm.

[0035] According to another aspect, the object is achieved by a computer-readable storage medium storing a plurality of instructions, which, when executed by a processor, cause the processor to perform at least steps d. to h. of the above method. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Other features and advantages of the present invention will become apparent from the following description of embodiments with reference to the accompanying drawings.

[0037] Figure 1 is a block diagram of a robot system implementing the present invention;

[0038] Figure 2 yes Figure 1 a perspective view of a manipulator of the illustrated system;

[0039] Figure 3 is the cross section of the harmonic drive gear;

[0040] Figure 4 is the pose assumed by the manipulator when the above method is performed on one of its joints; and

[0041] Figure 5 is the pose the manipulator takes when the above method is executed on its other joint. DETAILED DESCRIPTION

[0042] Figure 1 is a schematic diagram of a robot system in which the method of the present invention can be applied, the robot system comprising an articulated robot arm 1 and a controller 2. Figure 2 The robot arm 1 shown in more detail in FIG. 1 has a fixed base 3 fixed to a support and a joint 5 connected to the support. j A plurality of links 4 rotatably connected to each other and to the base 3 j , where j = 1, ..., 6. The joint 55 connecting the links 44 and 45 is hidden behind the link 45. Each joint 5 j Make the connecting rod 4 j It can be located at its distal end around the axis 6 jRotation. Axis 61 is vertical, axes 62 and 63 are horizontal; the orientation of the other axes may vary. Each joint 5 j Has a motor associated therewith for driving the joint in rotation; the motor may be disposed in a member on the proximal side of the joint and connected to a member on the distal side of the joint, or vice versa. Figure 2 In the robot arm shown, joints 51, 52, 53 each have a motor located in the components on their proximal side (i.e., base 3 and links 41, 45). Joints 53, 54 and 55 each have a motor located on their distal side (i.e., in links 43, 44 and 45).

[0043] The most distal link 46 has a tool replaceably mounted thereto. The tool may be a three-dimensional acceleration sensor 7, or may be a holder for holding such a sensor 7.

[0044] Figure 1 The motors 92, 93, 94 associated with the joints 52, 53, 54 are shown, as well as the harmonic drive gears 102, 103, 104 connecting these motors to the connecting rods 42, 42 and 43, each motor 9 j With associated therewith a rotary transformer 8 j , as a measure of the rotation angle of its output shaft Measuring device.

[0045] The controller 2 includes a trajectory generator 11 for generating a trajectory corresponding to a specific joint 5 at an appropriate time. j Associated joint controller 12 j Output position and velocity commands, as required by the sensor 7 assuming that the joint has no kinematic errors and follows the predetermined trajectory. Each joint controller 12 j Also has a kinematic error calculator 13 associated therewith j , for superimposing corrections on the commands output by the trajectory generator 11, as will be explained in detail below.

[0046] Figure 3 It is harmonic drive gear 10 j The wave generator 14 is rigidly coupled to the motor 9. j The output shaft 15 rotates in the flexible wheel 16 and makes the teeth of the flexible wheel engage with the rigid wheel 17 around it. When the number of teeth of the rigid wheel 17 is i c And the number of teeth of the flexible wheel 16 is i f When gear 10 j Transmission ratio Since the rotation direction of the flexible wheel 16 is opposite to that of the wave generator 14, after the wave generator 14 rotates 2πi f / i cAfterwards, the two points that are currently touching will meet again.

[0047] In order to find out the kinematic errors of the joints 51 or 54, the manipulator 1 is placed as follows: Figure 4 The posture shown, in which the axis 61 or 64 associated with the joint in question is vertical and the gravitational acceleration detected by the sensor 7 does not change during the rotation around the axis at a constant speed. Therefore, in step b. of the method of the invention, this rotation is selected as the trajectory for measuring the acceleration of the sensor 7. Figure 4 In the posture of the joint 51 or 54, several rotations can be performed without stopping, while recording the acceleration detected by the sensor 7. In the laboratory coordinates, the direction of the centrifugal acceleration experienced by the sensor should be changing, but since the sensor 7 itself also rotates, the acceleration is constant in the reference system of the sensor. Therefore, any fluctuations in the acceleration detected by the sensor 7 can be attributed to defects of the motor 91 or 94 and its corresponding reduction gear 101 or 104.

[0048] Axes 62 and 63 are always horizontal, so when the sensor 7 is rotated about one of these axes, the direction of the gravitational acceleration will inevitably change in the reference frame of the sensor 7. Since the harmonic drive gears 102 and 103 will have a reduction much less than 1, it can be expected that acceleration fluctuations with a frequency of only a small integer multiple or R times the motor rotation frequency are due to imperfections in the motor and the reduction gears. To measure these parameters, the manipulator can be placed as follows Figure 5 The posture shown in FIG. 1 and, while avoiding collisions between the links of the manipulator 1 and each other or with the support, swing back and forth around the axis 62 or 63 at a constant motor speed as much as possible, as shown in FIG. Figure 5 As shown by the double-headed arrow in .

[0049] To determine, for example, joint 5 j The trajectory generator 11 outputs a trajectory in which the motor 9 has a kinematic error of j Controlled to a constant speed rotates while all other motors remain stationary. In this section, motor 9 j The rotation frequency is chosen to be equal to the resonant frequency of the manipulator 1, so that if the motor 9 j Or the harmonic drive gear 10 driven thereby j If there are fluctuations in the velocity of the vehicle, then these fluctuations can be expected to excite vibrations and thus produce acceleration fluctuations that can be clearly and easily detected.

[0050] At least in the constant velocity section of the trajectory, the acceleration detected by the sensor 7 is recorded. Although it is possible to record all three components of the acceleration vector a x、a y 、a z Record them separately, but only their size This is convenient because there is no need to worry about the orientation of the sensor 7 relative to the distal link 46 on which it is located.

[0051] When the trajectory is executed for the first time and joint 5 j When the final defect is unknown, the kinematic error calculator 13 j The output of can be constant to zero, so that the command output by the trajectory generator 11 reaches the controller 12 without modification. j , and the joint angles are not exactly equal without considering the motor 9 j and gear 10 j The expected defect is q arm，j =Rq mot，j , but you can write

[0052]

[0053] k is an integer or i f / i c That is, if the kinematic error calculator 13 j The correction applied totals

[0054]

[0055] Then the ideal relationship q is satisfied arm，j＝ R mot，j .

[0056] Typically, the maximum contribution to the sum is k1 = 2l f / i c and k2=2, that is, and At a frequency of . We can assume that there are only these two summands, so we get the approximate δq ke Alternatively, a spectral analysis may be performed on the collected acceleration data to identify the frequencies making the largest contribution.

[0057] In the absence of kinematic errors, when joint 51 or joint 54 is Figure 4 When the posture starts to rotate at a constant speed, the acceleration measured by the sensor 7 should be constant, or when one of the joints 52 and 53 is Figure 5 When the oscillation is shown, it should be consistent with the arm angle q arm，j The sine or cosine of a voltage changes proportionally, that is, at a rate that is practically negligible.

[0058] As a measure of the mass of the control manipulator, the magnitude of the acceleration a(t) or a(q mot,j ) and the expected acceleration at that time or location, which can be measured when the sensor is moving at a constant motor speed. Average or integrate over the moving part of the trajectory:

[0059]

[0060] or

[0061]

[0062] Among them, it can be based on the motor speed Transmission ratio and sensor 7 relative to axis 6 j The radius is used to calculate the expected acceleration a exp , or they can be respectively low-pass filtered a(q mot,j ) or a(t), or by obtaining start ,q end ] or [t start , t end ] are derived from some other forms of moving averages on intervals of .

[0063] Alternatively, when the acceleration data a(q mot,j ) the sum of the amplitudes of the most important spectral components of the acceleration may be used for the same purpose. This analysis may be restricted to the range of the spectrum where these components are expected to exist. When there is reasonable certainty, for example based on experimental evidence obtained from several harmonic drive gears of the same design, it is reasonable to conclude that the acceleration is not the same as the speed of the gear. and The contribution at the frequency of is negligible, then the spectral analysis can be restricted to the frequency range [k1-ε, k2+ε].

[0064] In the above equation (1), the mass Λ is the adaptable parameter A i，j ,θ i，j To optimize this quality, its gradient is determined by making a small change δA to each of these parameters in turn. i，j or δθ i，j , so that the trajectory generator 11 outputs the trajectory again, and at the same time the kinematic error calculator 13 j Apply a correction δq to the trajectory obtained by changing the parameter ke , The acceleration is remeasured and from the data obtained therefrom the mass Λ (A i，j ,θi，j +δA i，j ) or result. Therefore, A i，j The gradient in the direction is approximated as

[0065] When changing the amplitude parameter A i，j When calculating φ(R) , it must be noted that these parameters should be positive, but small enough not to cause potentially harmful vibrations of the manipulator 1.

[0066] When all parameters A i，j ,θ i，j After the gradient of is determined, the parameter value is updated according to the following formula:

[0067]

[0068] The step length ΔA i，j , Δθ i，j The step size δA can be different from those used to determine the gradient i，j .

[0069] Based on the use of the parameter A modified according to equation (3) i，j ,θ i，j The acceleration measurements are obtained and the mass Λ is recalculated.

[0070] This process is repeated until Λ drops below a predetermined threshold, a maximum number of iterations have been performed, or no significant change in Λ is observed over a certain number of iterations.

[0071] In this iterative process, the spectral composition of the acceleration measurement may change. If for each iteration, the spectral composition of the acceleration measurement is determined and the most important component k is selected i , i=1,...,M for compensation, then component k i The set of can change from one iteration to the next, and during the iterations, compensation will proceed from more important components to less important components, allowing compensation of a large number of parameters with limited effort.

[0072] For a given spectral component k i , by adjusting the step width ΔA i，j , Δθ i，j To improve the convergence speed of the process. For a given parameter A i，j or θ i，j Component, if the gradient sign or symbol The sign of is the same in two consecutive iterations, then the step width is increased according to the following formula:

[0073]

[0074] Otherwise, reduce the step width according to the following formula:

[0075]

[0076] When one of the above conditions for terminating the process is met, the kinematic error calculator 13 j Load the A obtained in the process i，j ,θ i，j and further applies the kinematic error correction obtained by applying equation (1) to the output of trajectory generator 11 to its associated joint controller 12 j Any position command.

[0077] By applying the above process successively to each joint 5 of the manipulator 1 j To compensate the entire manipulator 1.

[0078] After all joints have been compensated, the sensor 7 is removed for use on another manipulator.

[0079] Reference numerals

[0080] 1 Manipulator

[0081] 2 Controller

[0082] 3 Base

[0083] 4 Connecting rod

[0084] 5 Joints

[0085] 6 Axis

[0086] 7 Accelerometer

[0087] 8. Resolver

[0088] 9 Motor

[0089] 10 Harmonic Drive Gear

[0090] 11. Trajectory Generator

[0091] 12 Joint Controller

[0092] 13 Kinematic Error Calculator

[0093] 14 Wave Generator

[0094] 15 Output shaft

[0095] 16 Flexspline

[0096] 17 Steel Wheel

Claims

1. A method for reducing the joint (5) between the distal part and the proximal part of a manipulator (1) j ) of the kinematic error method, the joint (5 j ) connected with: motor (9 j ), the motor is used to drive the joint to rotate; the measuring device (8 j ), the measuring device is used to measure the motor (9 j )'s rotation angle; joint controller (12 j ), the joint controller is connected to the motor (9 j ) and the measuring device (8 j ), for input position-based commands (q mot,j ) controls at least the rotation angle of the motor; and a trajectory generator (11), the trajectory generator being used to output a position command (q mot,j ), the method The following steps are involved: a. an acceleration sensor (7) is arranged in the distal portion, b. selecting the trajectory to be followed by the acceleration sensor (7), c. estimating the expected acceleration value to which the sensor (7) is expected to be subjected along the trajectory, d. The trajectory generator (11) outputs an initial command for moving the sensor (7) along the trajectory e. By correcting the kinematic error Add to initial command The specified parameters in the above table are used to obtain the correction command and the correction command is sent to Input to the joint controller (12 j )middle, f. Recording the sensor (7) according to the calibration command The acceleration experienced during movement (a), g. Determine whether the deviation (Λ) between the expected acceleration value and the recorded acceleration value exceeds a predetermined threshold, and h. If it is determined that the deviation (Λ) exceeds the threshold, modify the kinematic error correction to reduce the deviation. 2 . The method of claim 1 , wherein the command is at least one of a position command and a speed command, wherein the position command the specified parameter is a position, and wherein the speed command the specified parameter is a speed.

3. A method according to claim 1 or 2, wherein in step b), the trajectory is selected so that the expected acceleration value or the magnitude of the expected acceleration is constant along at least a portion of the trajectory, and optionally, wherein the trajectory defines an oscillating motion.

4. The method according to any one of the preceding claims, wherein the kinematic error correction (δq ke ) is the motor (9 j ) of the rotation angle (q mot,j ) is a weighted sum of circular functions that are at least integer multiples of ).

5. The method according to claim 4, wherein the joint (5 j ) also includes a harmonic drive gear (10 j ), where the kinematic error correction (δq ke ) or an integer multiple of the rotation angle multiplied by i f / i c The weighted sum of circular functions of f It is a harmonic drive gear (10 j ) of the flexible wheel (16), and i c It is a harmonic drive gear (10 j ) has the number of teeth of the rigid wheel (17).

6. Method according to any of the preceding claims, wherein in step b) the speed of the trajectory is selected such that the motor frequency or a harmonic thereof is a resonant frequency, preferably the lowest resonant frequency, of the manipulator (1).

7. The method according to any one of the preceding claims, wherein the expected acceleration value in step c. and / or the recorded acceleration value in step f. is a vector (a x 、a y 、a z ), and the determination in step g. includes combining all three components of each vector into a single scalar (a).

8. Method according to any one of the preceding claims, wherein the determination in step g. is based on a spectral analysis of the recorded acceleration values.

9. A method according to any one of the preceding claims, wherein the determination in step g. is based on spectral components of the recorded acceleration values, the frequency of the recorded acceleration values ​​being twice the motor frequency.

10. The method according to any of the preceding claims, wherein steps d. to g. are repeated when the kinematic error correction has been modified in step h.

11. The method according to any one of the preceding claims, wherein modifying the kinematic error function in step h. comprises the following sub-steps: correcting (δq ke ) weighting coefficient (A i，j ) estimates the gradient of the deviation and multiplies it by a scalar factor (ΔA i，j , Δθ i，j ) is added to the vector formed by the weighting coefficients of the kinematic error correction.

12. The method according to claim 10 and 11, wherein if the change in direction of the gradient between consecutive iterations in step 1) is below a given lower threshold, the scalar factor (ΔA i，j , Δθ i，j ), and if the direction change is above a given upper threshold, the scalar factor (ΔA i，j , Δθ i，j ).

13. A robot system comprising - a manipulator (1) comprising a proximal portion, a distal portion, a joint (5) connecting the proximal portion and the distal portion j ) and for driving the joint (5 j ) Rotating motor (9 j ); - Measuring device (8 j ), the measuring device is used to measure the motor (9 j )’s rotation angle; -Controller(12 j ), the controller is connected to the motor (9 j ) and the measuring device (8 j ), for controlling at least the motor (9) based on an input position command j )’s rotation angle; - a trajectory generator (11) for outputting position commands, - an acceleration sensor (7) which is preferably removably mounted in the distal part of the manipulator (1).

14. A computer-readable storage medium on which a plurality of instructions are stored, which, when executed by a processor (13), cause the processor to perform at least steps d. to h. of the method according to any one of claims 1 to 12.

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