Force control

Foil strain gauge

The trivial approach to force control is the direct measurement of the occurring contact forces via force/torque sensors at the end effector of the machine or at the wrist of the industrial robot. Force/torque sensors measure the occurring forces by measuring the deformation at the sensor. The most common way to measure deformation is by means of strain gauges.

In addition to the widely used strain gauges made of variable electrical resistances, there are also other versions that use piezoelectric, optical or capacitive principles for measurement. In practice, however, they are only used for special applications. Capacitive strain gages, for example, can also be used in the high-temperature range above 1000 °C.[1]

Strain gages are designed to have as linear a relationship as possible between strain and electrical resistance within the working space. In addition, several possibilities exist to reduce measurement errors and interference. To exclude temperature influences and increase measurement reliability, two strain gauges can be arranged in a complementary manner.

Modern force/torque sensors measure both forces and torques in all three spatial directions and are available with almost any value range. The accuracy is usually in the per mil range of the maximum measured value. The sampling rates of the sensors are in the range of about 1 kHz. An extension of the 6-axis force/torque sensors are 12- and 18-axis sensors which, in addition to the six force or torque components, are also capable of measuring six velocity and acceleration components each.

A force/torque sensor with measurement in three force and three torque components.

In modern applications, so-called six-axis force/torque sensors are frequently used. These are mounted between the robot hand and the end effector and can record both forces and torques in all three spatial directions. For this purpose, they are equipped with six or more strain gauges (possibly strain measurement bridges) that record deformations in the micrometer range. These deformations are converted into three force and torque components each via a calibration matrix.

Force/torque sensors contain a digital signal processor that continuously acquires and filters the sensor data (strain) in parallel, calculates the measurement data (forces/torques) and makes it available via the sensor's communication interface.

The measured values correspond to the forces at the sensor and usually still have to be converted into the forces and torques at the end effector or tool via a suitable transformation.

Since force/torque sensors are still relatively expensive (between €4,000 and €15,000) and very sensitive to overloads and disturbances, they - and thus force control - have been reluctantly used in industry.[3] Indirect force measurement or estimation is one solution, allowing force control without costly and disturbance-prone force sensors.

A cost-saving alternative to direct force measurement is force estimation (also known as "indirect force measurement"). This makes it possible to dispense with the use of force/torque sensors. In addition to cost savings, dispensing with these sensors has other advantages: Force sensors are usually the weakest link in the mechanical chain of the machine or robot system, so dispensing with them brings greater stability and less susceptibility to mechanical faults. In addition, dispensing with force/torque sensors brings greater safety, since there is no need for sensor cables to be routed out and protected directly at the manipulator's wrist.[3]

A common method for indirect force measurement or force estimation is the measurement of the motor currents applied for motion control. With some restrictions, these are proportional to the torque applied to the driven robot axis. Adjusted for gravitational, inertial and frictional effects, the motor currents are largely linear to the torques of the individual axes.[7] The contact force at the end effector can be determined via the torques thus known.[8]

During force measurement and force estimation, filtering of the sensor signals may be necessary. Numerous side effects and secondary forces can occur which do not correspond to the measurement of the contact force. This is especially true if a larger load mass is mounted on the manipulator. This interferes with the force measurement when the manipulator moves with high accelerations.

To be able to adjust the measurement for side effects, both an accurate dynamic model of the machine and a model or estimate of the load must be available. This estimate can be determined via reference movements (free movement without object contact). After estimating the load, the measurement or estimate of the forces can be adjusted for Coriolis, centripetal and centrifugal forces, gravitational and frictional effects, and inertia.[9] Adaptive approaches can also be used here to continuously adjust the estimate of the load.

Impedance control, or compliance control, regulates the compliance of the system, i.e., the link between force and position upon object contact. Compliance is defined in the literature as a "measure of the robot's ability to counteract contact forces." There are passive and active approaches to this. Here, the compliance of the robot system is modeled as mechanical impedance, which describes the relationship between applied force and resulting velocity. Here, the robot's machine or manipulator is considered as a mechanical resistance with positional constraints imposed by the environment. Accordingly, the causality of mechanical impedance describes that a movement of the robot results in a force. In mechanical admittance, on the other hand, a force applied to the robot results in a resulting motion.

Remote Center of Compliance yields to rotational and translational deviations during an insertion operation.

Passive compliance control (also known as compliance control) does not require force measurement because there is no explicit force control. Instead, the manipulator and/or end effector is flexibly designed in a way that can minimize contact forces that occur during the task to be performed. Typical applications include insertion and gripping operations. The end effector is designed in such a way that it allows translational and rotational deviations orthogonal to the gripping or insertion direction, but has high stiffness in the gripping or insertion direction. The figure opposite shows a so-called Remote Center of Compliance (RCC) that makes this possible. As an alternative to an RCC, the entire machine can also be made structurally elastic.

Passive impedance control is a very good solution in terms of system dynamics, since there are no latency due to the control. However, passive compliance control is often limited by the mechanical specification of the end effector in the task and cannot be readily applied to different and changing tasks or environmental conditions.[10]

Active compliance control refers to the control of the manipulator based on a deviation of the end effector. This is particularly suitable for guiding robots by an operator, for example as part of a teach-in process.

Active compliance control is based on the idea of representing the system of machine and environment as a spring-damper-mass system. The force ${\displaystyle F}$ and the motion (position ${\displaystyle x(t)\!\,}$, velocity ${\displaystyle {\dot {x}}(t)}$, and acceleration ${\displaystyle {\ddot {x}}(t)}$ are directly related via the spring-damper-mass equation:

${\displaystyle F(t)=c\cdot x(t)+d\cdot {\dot {x}}(t)+m\cdot {\ddot {x}}(t)}$

The compliance or mechanical impedance of the system is determined by the stiffness ${\displaystyle c}$, the damping ${\displaystyle d}$ and the inertia ${\displaystyle m}$ and can be influenced by these three variables. The control is given a mechanical target impedance via these three variables, which is achieved by the machine control.

Block diagram of the active impedance control with specification of the force ${\displaystyle F_{soll}}$ and the position ${\displaystyle X_{soll}}$.

The figure shows the block diagram of a force-based impedance control. The impedance in the block diagram represents the mentioned components L, A and . A position-based impedance control can be designed analogously with internal position or motion control.

Alternatively and analogously, the compliance (admittance) can be controlled instead of the resistance. In contrast to the impedance control, the admittance appears in the control law as the reciprocal of the impedance.

The above concepts are so-called indirect force control, since the contact force is not explicitly specified as a command variable, but is determined indirectly via the controller parameters damping, stiffness and (virtual) mass. Direct force control is presented below.

Direct force control uses the desired force as a setpoint within a closed control loop. It is implemented as a parallel force/position control in the form of a cascade control or as a hybrid force/position control in which switching takes place between position and force control.

One possibility for force control is parallel force/position control. The control is designed as a cascade control and has an external force control loop and an internal position control loop. As shown in the following figure, a corresponding infeed correction is calculated from the difference between the nominal and actual force. This infeed correction is offset against the position command values, whereby in the case of the fusion of ${\displaystyle X_{soll}}$ and ${\displaystyle X_{korr}}$, the position command of force control (${\displaystyle X_{korr}}$ )has a higher priority, i.e. a position error is tolerated in favor of the correct force control. The offset value is the input variable for the inner position control loop.

Block diagram of parallel force/position control with specification of force (${\displaystyle F_{soll}}$) and position (${\displaystyle X_{soll}}$).

Analogous to an inner position control, an inner velocity control can also take place, which has a higher dynamic.[11] In this case, the inner control loop should have a saturation in order not to generate a (theoretically) arbitrarily increasing velocity in the free movement until contact is made.

An improvement over the above concepts is offered by hybrid force/position control, which works with two separate control systems and can also be used with hard, inflexible contact surfaces. In hybrid force/position control, the space is divided into a constrained and an unconstrained space. The constrained space contains restrictions, for example in the form of obstacles, and does not allow free movement; the unconstrained space allows free movement. Each dimension of the space is either constrained or unconstrained.

Block diagram of hybrid force/position control with separation matrix Σ.

In hybrid force control, force control is used for the restricted space, and position control is used for the unrestricted space. The figure shows such a control. The matrix Σ indicates which space directions are restricted and is a diagonal matrix consisting of zeros and ones.

Which spatial direction is restricted and which is unrestricted can, for example, be specified statically. Force and position control is then explicitly specified for each spatial direction; the matrix Σ is then static. Another possibility is to switch the matrix Σ dynamically on the basis of force measurement. In this way, it is possible to switch from position control to force control for individual spatial directions when contact or collision is established. In the case of contact tasks, all spatial directions would be motion-controlled in the case of free movement, and after contact is established, the contact direction would be switched to force control by selecting the appropriate matrix Σ.

The previously mentioned, non-adaptive concepts are based on an exact knowledge of the dynamic process parameters. These are usually determined and adjusted by experiments and calibration. Problems can arise due to measurement errors and variable loads. In adaptive force control, position-dependent and thus time-variable parts of the system are regarded as parameter fluctuations and are constantly adapted in the course of the control by adaptation.

Due to the changing control, no guarantee can be given for dynamic stability of the system. Adaptive control is therefore usually first used offline and the results are intensively tested in simulation before being used on the real system.[3]

A prerequisite for the application of classical design methods is an explicit system model. If this is difficult or impossible to represent, fuzzy controllers or machine learning can be considered. By means of fuzzy logic, knowledge acquired by humans can be converted into a control behavior in the form of fuzzy control specifications. Explicit specification of the controller parameters is thus no longer necessary.

Approaches using machine learning, moreover, no longer require humans to create the control behavior, but use machine learning as the basis for control.

Due to the high complexity of modern robotic systems, such as humanoid robots, a large number of actuated degrees of freedom must be controlled. In addition, such systems are increasingly used in the direct environment of humans. Accordingly, concepts from force and impedance control are specifically used in this area to increase safety, as this allows the robot to interact with the environment and humans in a compliant manner.[12]