Научная статья на тему 'Position, force and impedance control in (non-)contact motion'

Position, force and impedance control in (non-)contact motion Текст научной статьи по специальности «Физика»

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Ключевые слова
(non-)contact motion / position / force / impedance / control
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The concept of position, force and impedance control at the process of (non-)contact motion of the systems is proposed.

Текст научной работы на тему «Position, force and impedance control in (non-)contact motion»

YflK 621


V.S. Lovejkin, Doctor of Technical Sciences, Professor, Y.V. Chovnjuk, Candidate of Technical Sciences, Docent, M.G. Dikterjuk, Candidate of Technical Sciences, Docent Kyiv National University of Construction and Architecture

Summary. The concept of position, force and impedance control at the process of (non-)contact motion of the systems is proposed.

Key words: position, force, impedance, control, (non-)contact motion.

This paper shows first position, force and impedance control of mechanical systems during their (non-)contact motion. One may use such approach for design of mechatronics systems (for example, just of the modern building machines).

Positioning is one of the important applications in motion control. There are two kinds of industry requirements to the positioning: 1) PTP path (Point-To-Point Path); 2) CP path (Continuous Path).

The trapezoidal profile of speed reference is used for PTP path tracking. During acceleration and deceleration, the period of constant acceleration is controlled to attain maximum speed.

As to CP tracking, a trajectory of motion is predetermined and it is possible to know the several steps ahead at any time. If the motion reference generator knows two steps ahead, the velocity and the acceleration reference are calculated as well as position reference. The robust motion controller makes the motion system an acceleration controller with unity gain for nominal inertia and torque coefficient [1].

This paper determines an equivalent acceleration to the disturbance, simple way to stabilize the system with the help of state feedback (i.e., position and velocity feedback), the transfer function Pm (5) from acceleration reference to position. One may use special inverse system placed in

front of P (5) in order to recover the delay due to Pm (5).

Since the input of Pm (.v) 1 is position reference

0re/ (parameter of rotational direction), which will have first and second derivatives as the any place of predetermined trajectory, CP tracking control is constructed by the combination of Pm (.v), Pm (s) 1 and state feedback in acceleration controller. The transfers function from 0cmd to 0 be as follows:

0 = 0



where p is an equivalent acceleration to the

disturbance, Kv, Kp - coefficients of transfer of

velocity and position, respectively, 5 - argument of transfers function.

The second term of (1) right side is an error due to disturbance. Most of them is suppressed in robust control part and the little remained error is attenuated by the velocity and position feedback. It is noted that the forward gain from position command to position is unity.

In the industry, the current control feedback has been widely used as a torque control. This loop has only a function to make a power converter to be a controlled current source. The target of



force control is a control of force at the end-effector accurately. The robustness of the force control system is also required. Therefore, acceleration controller is also a basis for force control and there should not be high forward gain to position in order to keep stiffness k as low as possible. If the force sensor is ideal, there would be no forward gain for the position and zero stiffness is attained. However, very small deviation proportional to the imposed force could exist in the force sensor and the robustness will be suffered. There are two categories for force control: 1) noncontact motion; 2) contact motion.

In noncontact motion, a force control is substantially an acceleration control. An end-effector moves along force reference until it collides with a fixed environment.

In contact motion there will be a force sensor between the end-effector and the control object. The sensor will detect very small deviation proportional to the imposed force. Then at that moment, a mechanical loop including environment is set up. The system is oscillatory with natural angular frequency. Once the end-effector touches the environment, a closed loop is completed. Then the system is oscillatory and the end-effector is repulsed from the environment. When the end-effector separates from the environment, the closed loop is eliminated. Again the end-effector is stable and approaches the environment and touches it again. This process repeats over and over.

This hunting phenomenon is overcome by adding damping loop. Generally it is difficult to know the stiffness and the damping of the environment a priori. An inserted forward gain Kf should be chosen so that the total system is


The transfer function from the equivalent disturbance acceleration (- p) to the position is given

in the paper. A virtual stiffness kf is determined

as well. This gives a performance limit of force control due to the very small displacement to measure the force. When the force control approaches to the ideal one by reducing stiffness, the response will be slow.

The stiffness of the system is modified to have a specified mechanical impedance. In this case, position and force signal are used to generate acceleration reference based on the specified impedance. The paper shows an example of such impedance control system. The stiffness corresponding to the virtual spring coefficient, the artificial damping and the equivalent mass realize mechanical impedance.

It is noted that if the gain of the position is zero, the impedance control becomes the force control. The zero gain of the force is the same as the position control. It is possible to turn continuously the motion control to both the position control and the force control by adjusting the control gains in impedance control. In other words, the impedance control is the general form of motion control [2].


1. Luh J., Walker M., Paul R. Resolved-acceleration

control of mechanical manipulators//IEEE Trans. Automat. Contr. - 1980. - Vol. 28. - No. 3. - P. 468-474.

2. Khatib O. A unified approach for motion and force

control of robotic manipulators//IEEE J. Robot., Automat. - 1987. - Vol. RA-3. - No. 1. - P. 43-53.

В.С. Ловейкш, Ю.В. Човнюк, М.Г. Джте-рук


Запропонована концепщя управлшня пози-щюванням, силою та iмпедансом у процес (без-)контактного руху систем.

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