# Why non-backdrivability is a problem for Force Control

In previous posts we have discussed about the causes of the non-backdrivability in robotic actuators, the efficiency of most common reducers and the conditions under which a ballscrew becomes backdrivable. Here we will take a closer look into the effects of the non-backdrivability into the force control.

We can distinguish two types of non-backdrivability:

A.) Inherent non-backdrivability

B.) High friction/inertia/gear ratio caused backdrivability

The best example of inherent non-backdrivability is the worm gear mechanism although there are many. In this case, the movement can only be produced in one sense but not in the opposite. The worm can displace the worm wheel but the opposite is not possible due to mechanical constraints.

The second case is more subtle. A transmission with high friction could make the backdriving force very high and create a non-backdrivable mechanism. This could be the case of very inefficient transmissions that require excessive force to be actuated. Excessive actuator’s inertia is also an issue as the backdriving force needs to fight against that inertia when accelerating the mechanism. Finally, the gear ratio, which is tightly coupled with the inertia. The inertia of the load as seen by the motor corresponds to the following formula:

JTotal_motor = ( JLoad / N2 ) + JMotor

It is obvious that the higher the gear ratio (N), the lower the perceived inertia for the motor. However, for the sake of analysing the backdrivability we are interested on the opposite, i.e. the motor inertia as seen by the load which is where the backdriving force is applied. In this case, the term N2 changes and multiplies the JMotor as per this:

Following this, the inertia on the load is proportional to the motor inertia times the square of the gear ratio, then, increasing the gear ratio is very detrimental for the backdrivability. As a rule of thumb a gear ratio higher than 10:1 is considered non-backdrivable.

However, in this post I wanted to focus on the effects of friction on the force control. Friction models are very complex, but a widely used approximation is given by this model that considers stiction, coulomb friction and viscous friction.

Whenever we want to maximise the backdrivability we should consider minimising the stiction as it is the cause of frequent control issues.

On the graph below we can see the effect of the stiction on the output force of a mechanism. The stiction acts as a dead zone of the actuators torque by eating up all the torque produced without causing any output force until the stiction is overcome. F[N] is here the output force of the mechanism whereas T[Nm] is the motor torque.

There are two problems caused by the stiction and both related to the difficulty of model such effect. It is never possible to achieve a 100% accurate model of the actuator’s friction, and even if a long time is invested on obtaining such a perfect model, things may change, temperature may change causing the grease to vary its state, and hence affect the friction, calibration may change, wearing of the mechanism can influence your model, etc.. In the case of an inaccurate model and high stiction, a high motor torque is required to produce very low force, and hence, any model errors would be amplified and cause high output force errors. In addition to that, in the proximity of zero force, a constant switching of high torque would be produced, causing undesirable behaviour on the actuator.

It is certain that this curve could be smoothed out, obtaining something like this:

However, this does not solve all of our problems as small torque errors would cause high force errors, deteriorating our control performance at the output. We can then consider that the range of output forces where the stiction is present, limits the resolution of our force controlled application.

The sticion is not only present when low forces are applied. What governs the stiction is the speed as shown in the first graph. Everytime the speed is close to zero, the stiction enters into the game. Even controlling our output force at high forces, if this is done at very low speed, we have a problem. Our force control resolution gets deteriorated by the stiction band.

Then, by minimising the stiction we would be improving the performance of our force controlled application. We can do this by designing conveniently our mechanism, reducing the number of elements that cause friction, ensuring the correct alignment of the mechanical components, adding lubricant to the system, etc.

# Backdrivability on ball screws

This article complements previous entry on general backdrivability exploring the conditions under which a ball screw is backdrivable.

Power transmission screws—ball screws and lead screws—are typically used for converting rotary motion to linear motion. But when a load is applied axially to the nut, they do the opposite and convert linear motion to rotary motion. This is known as back driving. Depending on the application, backdrivability in ball screws could be an unwanted effect or a desired mode of operation. When using a ball screw as a mechanism to lift something we are probably interested on not having any backdrivability, however for some applications such as robotics mechanisms, grippers and so on, it could be interesting to have some backdrivability. For example on a gripper mechanism using a left-right ballscrew.

#### What determines whether a screw will back drive?

Efficiency is the primary indicator of whether a screw will back drive or not—the higher the efficiency, the more likely the screw is to back drive when an axial force is applied. Two main factors play a part in determining a screw’s efficiency: the lead angle of the screw and the amount of friction in the screw assembly,

Lead angle—labeled “B” in the image below—is the angle between the helix of the screw thread and a line perpendicular to the axis of rotation.

The chart below shows that the larger the lead angle, the higher the screw efficiency. In other words, screws with a higher lead (20 mm vs. 5 mm, for example) have a higher efficiency and, therefore, are more likely to back drive.

Friction in a screw assembly comes from seals, end support bearings, and drag torque from the nut itself. Although seals aren’t typically used on lead screws, lead screws do have higher drag torque than ball screws due to the fact that they rely on sliding (rather than rolling) contact. This means lead screws often have lower efficiencies, and as a result, are less likely to back drive than ball screw assemblies.

#### When does back driving matter?

In vertical applications, most drive mechanisms—such as belts, rack and pinion drives, and linear motors—will let the load “crash” or fall if power is lost to the motor. Screws, on the other hand, are less likely to allow the load to drop, and if they do (that is, if the screw is back driven by the load), it will occur at a somewhat controlled rate, since the friction in the assembly, the lead angle, and the inefficiency of the screw all must be overcome.

Determining if a screw will back drive is relatively simple: compare the back driving torque to the friction in the screw assembly. Back driving torque is based on the axial load, the screw lead, and the screw’s efficiency.

$\Large T_b = \frac{(F \cdot P \cdot \eta2)} {(2\cdot pi)}$

Where:

Tb = back driving torque (Nm)

η2 = reverse efficiency*

*Efficiency when back driving is typically less than the efficiency for normal operation. Be sure to check the manufacturer’s specification for the back driving efficiency.

To determine the friction in the screw assembly, add the friction torque of the nut, seals, and end bearings—all of which can usually be found in the screw manufacturer’s catalog specifications. If the back driving torque is lower than the friction torque of the assembly, the screw is unlikely to back drive.

A rule of thumb for lead screws: if the lead is less than one-third the diameter of the screw, the screw is not likely to back drive.

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# The most important elements of a robot

A beginner roboticist should learn the basics of a few type of technologies and components before embarking himself in the design and construction of his own robot. I would say that the main areas one should be familiar with are:

• Electric motors: it is important to distinguish the types and to know the basics of operation of the most used motors, e.g. DC brushed, DC brushless, PMSM, steppers, servos, etc. In a typical project, very frequently, one has to select the proper motor for an application and possibly the combination of motor and gearbox. I have published a very useful guide to select an electric motor for a simple robotic application. (https://enriquedelsol.com/2017/11/19/motor-selection-for-robots-i/).

Brushless motor

• Motor controllers: the motors need to be powered and controlled with the right hardware, typically based on a H bridge made of transistors. It is important to understand the very basics of motor control to avoid spending a considerable amount of money in unnecessary hardware.

H bridge

• Sensors: in robotics, it is a must to know the different sensors that can provide positional feedback, such as encoders, resolvers, potentiometers. Some of them will be needed depending on the motor we select for our application. In the simpler scenario of choosing servomotors, position sensors will only be needed as a backup sensing method. Other types of sensors very common are: temperature sensors, force sensors, velocity sensors (tachometers), linear displacement, light sensors, etc. It is very important to measure distance, in order to map the environment or to avoid obstacles. The most common sensors to measure distance are: infrared sensors (relatively inexpensive), ultrasonic sensors (inexpensive as well), lasers and depth cameras. These can measure the distance on a large interval to which they have been calibrated for. For an accurate distance detection, there are switches based on capacitive and inductive technology, very reliable but only available for fixed distances. Other common sensors that are used during the electronic control are current sensors and voltage meters.
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# The most common places to shop for robotics components

This time I would like to review the most used online shops to buy components for a robotic design. Some of them are more focused on the professional market and some others pay attention to the hobbyist.

The two main companies that distribute components for the robotics industry and other engineering projects are RS (https://uk.rs-online.com/web/) and Farnell (https://www.farnell.com/). They are generalist companies oriented to the professional market with a very good client service, lead time and stock. Their search engines are very powerful and one can practically find everything they need. They are very well known in the European market and also established in the American market under other names: https://americas.rsdelivers.com/ , and https://www.newark.com/ . They usually offer free or very competitively priced next day delivery.

More focused on the hobbyist market, one can find RobotShop (https://www.robotshop.com) which has a deep and very well priced stock. It sells internationally. In this shop, the robotics enthusiast can find everything, from ready to assemble kits, to motors, sensors, cables, fixings, electronics, etc.

Another important reference in the hobbyist market is SparkFun (https://www.sparkfun.com/). Almost everything you may need can be found in this online shop, with special focus on electronic components.

If we need specialised hardware like wheels, structural elements, aluminium profiles, etc, a good online shop to buy from is Active Robots (https://www.active-robots.com/)

For an additional stock in electronics and mechanical components, I recommend to check Pololu (https://www.pololu.com), with a good range of components at a very competitive price.

Mouser (https://www.mouser.com/) and DigiKey (https://www.digikey.com/ ) are also two reference shops that work internationally, delivering plenty of products specially for the professional or the engineer. They are more focused in electronic components.

If we are looking for servos or ready to mount kits, we should check out Trossen Robotics, with a wide catalogue for the robotics enthusiast (https://www.trossenrobotics.com).

In addition to previous websites, the engineer or enthusiast should not forget the official distributor of Arduino (https://www.arduino.cc/) and the RaspberryPI official website (https://www.raspberrypi.org/), with tons of information about how to program their widely used development boards.

Depending on the desired component we are after, we can also review the website of the main manufacturers. For example, if there is plenty of budget available and we are looking for a motor, I would recommend checking out Maxon motors (https://www.maxongroup.com), with almost an infinite catalogue of electric motors of all types, electric drives and gearboxes. Other famous brands for the professional markets are Infranor (http://www.infranor.com/) and Yaskawa (https://www.yaskawa.com).

And this is all for now. Enjoy your shopping!

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Posted in Robotics

# Best blogs and podcasts to stay tuned on the Robotics Industry

Hi, I would like to come back to my blog by commenting on very useful resources for the roboticist.

• IEEE Spectrum: https://spectrum.ieee.org/ .The first one on the list. The IEEE is the world largest technical professional organization. They organise conferences, publish standards, and serve as a repository for an enormous amount of technical papers. Normally, when a researcher or just a curious person tries to access the papers in its brother website (ieee.org), they need to either pay a monthly/annual fee, or one-off payment to access the information. If the need is for professional use, your research centre or company should cover the expenses of the consultation or subscription. However, the IEEE Spectrum website can be enjoyed for free and it contains probably the best summary of new discoveries, advances and new trends in robotics and related industries. It is however, biased towards the American research.
• Robohub: https://robohub.org/ .Robohub is a non-profit organisation that as its name says, it is a hub for sharing stories, news, research, articles and interviews about robotics. It brings together experts in robotics to make sure the contents meet the highest editorial standards. They claim that their information is original and does not appear anywhere else. It is a good source of educational resources. It also has a very good podcast at: https://robohub.org/podcast-episodes/.
• org: The Robotic Industries Association posts daily news, case studies, technical papers, job openings and much more. It has a very good section about news in emerging markets and industry standards ( https://www.robotics.org/).
• Robotics Business Review: The Robotics Business Review claims to be “The Largest, Most Comprehensive Online Robotics News and Information Resource“. It regularly posts about all aspects of the business of robotics. However, most of its posts are only short abstracts and you must pay a yearly membership fee to access the complete article ( https://www.roboticsbusinessreview.com/).
• The Robot Report: The Robot Report is written by roboticist, Frank Tobe, cofounder of Robo-Stox, a tracking index for the robotics industry, now RoboGlobal. Through the blog he aims to follow the business of robotics and regularly reports on developments from all areas of the robotics industry.( https://www.therobotreport.com/)
• Machine Design: (machinedesign.com/). The technical quality of this blog / website is impressive. They provide a general knowledge of different fields in robotics, automation and engineering. It is a good source of technical articles and also news about the industry. If anyone is looking to explore more in-depth the technical issues behind robotics this is the place to go.

For the people interested in attending to conferences, workshops or looking for jobs in the robotics industry, there are two mail lists where every event is published. These are:⅞

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# Magnetic Encoders VS Optical Encoders

Encoders, whether rotary or linear, absolute or incremental, typically use one of two measuring principles—optical or magnetic. While optical encoders were, in the past, the primary choice for high resolution applications, improvements in magnetic encoder technology now allow them to achieve resolutions down to one micron, competing with optical technology in many applications. Magnetic technology is also, in many ways, more robust than optical technology, making magnetic encoders a popular choice in industrial environments.

 Parameter Optical Sensor Characteristics Magnetic Hall Sensor Characteristics Principle coded disc/scale, through beam arrangement magnet/tape/polewheel opposed to sensor Incremental accuracy of target 100 nm – 1 μm (lithography process) 5 μm – 30 μm (magnetisation process) Energising by external LED (20 mW) by target (Br>220 mT) Signal Frequency > 1 MHz possible < 50 kHz Benefits high code density, high code accuracy robust Disadvantages sensitive to contamination, high alignment requirements raw code density, medium code accuracy
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# Complementary Encoder Signals to mitigate the electrical noise

Electrical noise is a common problem that occurs during the transmission of an incremental encoder’s signal to the receiving electronics, especially when the cable lengths are very long. Stray electromagnetic fields or currents induce unwanted voltages into the signal. These voltages can cause the receiver to make false counts, producing errors in the position or velocity feedback.

The primary way to alleviate electrical encoder noise is to use TTL output – also known as differential line driver output. This output format provides not only the standard A and B square wave signals and a Z reference signal, it also includes their complementary signals, /A, /B, /Z (sometimes written as A’, B’, and Z’). These complementary signals are produced by splitting the output of each channel (A, B, and Z) into two signals that are 180 degrees out of phase (complements) with each other. In other words, when the A signal is high (logic state 1) the A’ signal will be low (logic state 0). The receiving electronics take the state of that channel as the difference between the two signals.

In order for the complementary signals to be read, however, the receiving electronics must have a circuit that is designed for differential input – known as line receiver input. In addition, the wires for each channel (A and A’, for example) should be a twisted pair. In this twisted pair of wires, any electrical encoder noise that is induced will be the same on each signal. The receiving electronics recognise only the difference between the two signals, and because the signals are complements (equal in magnitude, with 180 degree phase lag) but the noise is common mode (equal on each signal, with no phase lag), the noise is cancelled out on the receiving end.

Incremental quadrature encoder for noise rejection

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# Optical Encoders in Brushless Servo Motors

The trend towards wide scale use of Brushless Motors is being driven by manufacturing
cost reductions, improved efficiencies, greater reliability, availability of improved drive
electronics, and the availability of improved sensors for motor control.

The brushless motors, independently whether they are PMSM or BLDC motors, require to know the relative position of the windings with respect the motor poles. To do this, a set of Hall Effect sensors are typically employed and placed between windings. An alternative option is to use the positional feedback from more accurate sensors to determine the presence of the magnetic field without using Hall Effect sensors. However, an intelligent drive is required to perform this count and issue the signal that conmutates the phases. This action is performed automatically with the bipolar Hall-Effect sensors.

Hall Effect sensor

For the majority of applications in the US and Japan, the trend in brushless motor sensor designs is moving away from Hall boards and feedback elements to integrated devices. For resolver applications, it can be handled by adding a dedicated set of 2, 3, or 4 speed windings for commutation, or it can be handled with a single speed winding and an intelligent drive.

The elimination of the Hall sensors from the BLDC motor eliminates many of the potential problems which can occur in a motor application. Hall devices are sensitive to acoustic noise, current spikes, temperature, EM fields, and can be difficult to align, which results in torque ripple. When a BLDC motor is used in a servo application with a high resolution feedback sensor, Hall sensors are redundant and consume space. They also add to motor length, assembly costs, cable harnessing complexity, and decrease overall reliability. The use of an encoder or resolver to eliminate Hall sensors in this situation is not only cost effective, but also improves the overall system performance.

Drive with Hall board, Encoder or Resolver for Commutation and Feedback a caption

Drive with Commutating Encoder

Encoder Types.

When an encoder is used as the feedback element, there are a variety of types to choose from. The following is a short summary of the predominant types currently available.

1. Incremental, (TTL)
Readily available from a wide variety of Suppliers. Almost unlimited line count availability up to 5000 cycles per revolution. Special line counts and output options
are easily obtained.

2. Incremental with Commutation, (TTL)
Becoming more common in the US and Japan, availability is somewhat constrained by lack of industry standards. Mounting configuration, signal conditioning, and power supplies vary widely. Available in line counts up to 8000 for 2, 4, 6, and 8 pole motors. They are being developed in both hollow-shaft and modular versions by a variety of encoder suppliers.

3. Incremental with Commutation, (Sine wave)
More common in Europe, this type of encoder generally has sinusoidal quadrature
outputs, with a 1 volt pk-pk amplitude. Commutation is accomplished using a quadrature one cycle per revolution output.

4. Absolute Single Turn, (TTL/Parallel)
Less common for drive applications, these are usually found in 10 to 12 bit versions. Larger word sizes are available, but costs become a real issue and make them unsuitable for all but the most specialized applications.

5. Absolute Multi-turn, (Sine wave Incremental, Serial Absolute)
These encoders are generally based upon a 12 or 13 bit single turn absolute encoder, with a 12 bit turn counter yielding 24 or 25 bits of position information. Although these have been available for some time, they have been too costly for widespread applications. Recent developments in Europe, however, are making these more available, and costs are starting to come down. These encoders contain an incremental output with A, B, and Reference pulse, a serial absolute interface, and commutation outputs. Commutation output is derived from the MSB of the single-turn absolute. The Incremental tracks are derived from the LSB of the absolute encoder, and generally result in a 2048 or 4096 cycles per revolution incremental signal that is suitable for use in high-speed servo controls.

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# A good robotic blog

One of my mates is developing several projects related to robotics which are worth mentioning.  In his blog,  one of his last projects is the construction of an humanoid robot based on steppers.

Posted in Robotics

# Backdrivability

There is a trend in robotics towards the use of backdrivable actuators due to multiple reasons. One of them, is the need of sharing the environment with humans. Such a robot needs flexibility to adapt the differences between real environmental condition and assumed environmental condition. The robot´s joints may need to be articulated by a human and that would require high backdrivable actuators with low friction.
There are many other applications where a backdrivable actuator is needed, for example, in teleoperation, when Position-Position control is implemented. In teleoperation, a master device is controlled by a human operator and a slave device placed in a safe area mimics the movements of the master device. Position-Position uses the difference in position between master and slave to calculate the feedback forces to the operator. The more the positional error, the greater the forces. This positional error would be much more reduced with non-backdrivable actuators, and then, more difficult to provide feedback to the operator. At the end of the day, what you want in your slave device is to behave like a human, to react to the external forces as a human would do. If having a very stiff slave, the positional error would be minimum in normal tasks and the operator would not feel anything.

In any circumstance where the estimation of the external forces is needed, a backdrivable actuator is preferred. This could also be the case of walking robots, where it is important to feel the impact between the leg and the ground and react accordingly with a determined compliance.

Backdrivability is essential for safe robotic-arm operation around people; operating in unstructured environments; for stable control of contact forces; and for exploiting Jacobian-Transpose safely to enable Cartesian control of forces, haptic objects, and direct Cartesian control of trajectories.

Backdrivability is the ability for interactive transmission of force between input axis and output axis. To get high backdrivability, we have to reduce friction of power transmission considerably. Backdrivability provide actuators with high force sensitivity and high impact resistance which adapts to quick external force mechanically.

In rehabilitation robotics, particularly in upper limbrobotics, the drives must be able to deliver high torques at low velocity. Therefore, many rehabilitation robots are driven by motor-gearbox combinations. In contrast to direct-drive motors, the backdrivability of geared drives is poor due to friction in the gearbox. The back-driving torque sb can be defined as the amount of torque the human must apply to the robotic joint in order to perform a user-driven movement. Perfect backdrivability is achieved if sb = 0.

In [1] it is suggested that a reduction ratio over 60 in harmonic drives creates non-backdrivable actuators.

The backdrivability of a gearbox is highly correlated with the friction and the efficiency. Hence, let us have a look to the efficiency of different types of gears to get a initial impression of the backdrivaility of them.

In [2] a comparison between Harmonic drives and Cycloid drives is shown. In their research, Cycloid drives fitted into the same package diameter as harmonic drives with equal torque-generating capabilities. In their research, they demonstrated many advantages over harmonic drives, including substantially greater efficiency (especially at low torques) and lower reflected inertia, and often provided a thinner profile. These benefits were offset, however, by substantial disadvantages, including significant backlash and gear ratio ripple.

They conclude that, neither Cycloid nor harmonic drives are universally superior for all applications and conditions. However, Cycloid drives should be considered for applications in anthropomorphic robots and prostheses, especially those in which size, inertia, and efficiency take precedence over backlash and torque ripple.

## Gear Efficiency Comparison Table

 No Type Normal Ratio Range Efficiency Range 1 Spur 1:1 to 6:1 94-98% 2 Straight Bevel 3:2 to 5:1 93-97% 3 Spiral Bevel 3:2 to 4:1 95-99% 4 Worm 5:1 to 75:1 50-90% 5 Hypoid 10:1 to 200:1 80-95% 6 Helical 3:2 to 10:1 94-98% 7 Cycloid 10:1 to 100:1 75% to 85%

Double helical gear drives are considered to be more efficient than single helical gears.

Spur Gears

Straight Bevel Gears

Spiral Bevel Gears

Hypoid Gears.

Cycloid Gear.

Double Helical Gears.

Helical Gears

Worm Gears.

### Backdrivability of ball screws

Check out my article on backdrivability of ball screws to discover the main parameters that make them backdrivable.

[1] Instrumented Harmonic Drives for Robotic Compliant Maneouvres. H. Kazerooni.
[2] Cycloid vs. Harmonic Drives for use in High Ratio, Single Stage
Robotic Transmissions. Jonathon W. Sensinger, Member, IEEE and James H. Lipsey.2012 IEEE International Conference on Robotics and Automation
RiverCentre, Saint Paul, Minnesota, USA

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