Here[.pdf] is my ICRA 2015 paper with an errata (I highlighted the corrections in equation 23 and 30).

This paper was about variable Center-of-Mass height trajectory planning with reactive stepping by using non-linear model predictive control.

Here is an experiment using the proposed approach where a robot walking along a step while also following a variable COM height profile

Usually constant/predefined COM height or models that limit the robot to behaving as if it only has point feet is used when variable COM height is desired because the ZMP equation becomes non-linear when the COM height is a variable. However, it would be desirable to let the COM height be a free variable and let the ZMP move freely within the support polygon without limiting it to the centre of the foot.

In this work, the trajectory planning problem with variable COM height and reactive stepping was formulated as a Quadratically Constrained Quadratic Program (QCQP). This QCQP is then solved using Sequential Quadratic Programming (SQP).

The gradients and Hessian of a quadratic can be found analytically, thus time consuming numerical differentiation is not needed within the SQP solver, this helped to realize realtime performance (about 4 ms compute time on a 3.4 Ghz Quad-core) .

The main trick in this work was to take the linear relationship between the COM states and the COM jerks that is provided by the MPC literature for humanoid robots and substitute this into the expanded ZMP equation, after collecting the terms and cleaning up a little the quadratic ZMP equation was found.

Haptic control usually refers to the bilateral control of the force/position relationship between two robots. One good demonstration of this technology is to have a human move the one robot by hand. In this case the second robot will almost perfectly copy the motion of the first robot and if the second robot collides with something like a wall or a sponge, then the first robot will replicate this collision sensation to the humans hand via the first robot, if the control is done well then the human will feel as if he/she is directly touching the object personally. This video illustrates the concept:

When this technology is combined with humanoid robotics then it could be used in situations where traversing rough terrain is required and human presence is undesirable due to factors such as radiation, explosives, etc.

However one problem here is that Humanoids have underactuated legs, so if the arms apply too large a force on the environment then the robot can fall over. So how is the human to know how much force is too much? We may try indicators but having a software force limit would be more reassuring. What if we used full body haptic control? Giving the human full control may solve all kinds of problems but it introduces some new ones as well, for one the dynamics between the operators body and the humanoid robot will be different so its not clear if the human will be able to control the robot well without at least going  through a training program and then controlling different models of robot may require re-training. So I think that letting the humanoid autonomously limit its arm forces and take corrective action such as changing its trajectory and changing its foot positions is more ideal.

By using model predictive control to regenerate body and feet trajectories online while also considering time changing force/torque values of the wrists, I managed to obtain some experiment results which implement the above mentioned corrective actions.

The interested reader can find more details in my Advanced Robotics 2014 paper (here is a link with 50 free copies while it lasts, I will upload the paper next year once the publishers royalty period expires).

This is a rather innovative 6-axis force sensor in that it uses optical strain gages instead of electrical ones(a bit of info about the theory can be found here). This gives it a advantage in signal to noise ratio’s over conventional electrical strain gage sensors and it also means that the sensor internally requires a digital signal processor to compensate for thermal strain. As a result this sensor also has the rather useful quality of outputting digital data over a serial port running on a RS-422 electrical interface, thus you will need a fast serial port instead of an analog to digital converter. Perhaps the best thing about this force sensor is its price, in terms of Japanese Yen, conventional force sensors that do a similar job cost about 1,000,000 Yen. However this force sensor costs about 300,000 Yen. This is the cheapest I have seen a calibrated force sensor in this force range go for, so kudo’s to Minebea for lowering the cost of robotics(although initially the claimed to be aiming to reduce the cost to 100,000 Yen but it seems they weren’t serious about that). For a small increase in price Minebea can also install stoppers inside the sensor to prevent damage from excessive forces/moments. I have used this force sensor on MARI-3 with reasonable satisfaction however I do have some grievances. Firstly, this sensor has no reverse voltage protection, which I think is a rather big design flaw on such a expensive bit of electronics. Secondly, this sensor has somewhat limited ZMP sensing because the maximum pitch/roll torque (30 nM) is too small. To put it in perspective, a 50Kg robot standing on one leg would be able to sense a ZMP position of up to ±30/9.8*50=±6.1 cm, I would think that the average is 20-30cm long so I would like the sensor to measure a ZMP of ±10-15cm. It would be better if they reduced the maximum downwards force (1 kN) and increased the maximum pitch and roll torques.

So in summary and conclusion:

Pro’s

• Less noise than conventional electrical strain gage sensor’s
• Low cost
• Digital output

Con’s

• No reverse polarity protection
• Limited ZMP measurement due to insufficient torque range.

Elysium Labs Ranking: 3/5  (Decent but has some major flaws)

Here(ForceSensorInterface.c) is a driver to get you started. Note that this driver requires you to implement the serial read, write and serial port initialization routines yourself.

Manufacturers description of this sensor:

http://www.minebea-mcd.com/en/product/6-axial/opft-ch.html

Already know the basics of robot manipulators and want to figure out what makes biped robots tick? Here is a tutorial on the basics of Biped Robots

It might happen that your encoders broke(or someone gave you some questionable encoders), now you need to test if their still kicking. Heres a way to do it with a simple voltmeter, or if you want to be fancy, a oscilloscope.

Some force sensors can literally cost as much as a brand new Mercedes Benz, so you might want to test them while you still have a warranty from your manufacturer. Here is a guide on how to simply test 3 of the force sensors axes without need for special testing/calibration equipment.

Straight from the start I should mention that I am a android fan boy so I may lean to the android side a bit.

Firstly let me introduce my phone, the Sharp 005 SH. If you haven’t heard of it then don’t worry its only sold in Japan. The phone was released at the beginning of 2011.

Heres the features:

• 1 GHz Cpu
• 512 Mb Ram
• Android 2.2 2.3(updated)
• 3-D display(same tech. as the Nintendo 3ds, Sharp makes the screens for Nintendo so go figure)
• One-seg digital tv
• HDMI port
• Irda (infrared data transfer)
• Felica-Keitai based Near Field Communication (Works as a digital wallet in Japan)
• Slide out QWERTY keyboard
• 8 MegaPixel camera
• Support for SDXC(32Gig+ SD cards)
• Bluetooth, Wi-fi, gps, digital compass, the usual goodies

Now for the new iPhone 4S

• 1 GHz Dual core CPU
• 1024 Mb Ram
• iOS 5
• 8 MegaPixel Camera
• Frontal camera
• 64 Gb internal memory
• Bluetooth, Wi-fi, gps, digital compass, the usual goodies

From my point of view there are three big differences between these phones, first the iPhone is faster with double the CPU and RAM but then again my phone is 10 months older so I would expect as much.

Secondly the new iPhone has a frontal camera, that surely would be nice to have for apps like Skype and the hangouts in Google+.

Thirdly , and this is why I think my phone is still batter, the iPhone is lacking several features such as the 3D display, One-Seg tv, HDMI, Felica-Keitai, QWERTY keyboard and Irda. To be fair half of these features aren’t so useful anyway. For instance, I never use Felica-Keitai although one day when I feel like going through all the hassles of the registration process it may be handy to buy drinks from vending machines and get past toll gates at train stations by simply swiping my phone. Irda is somewhat useful in Japan since the majority use it to exchange contact details. The 3D display tires your eyes and its only usable in applications that enable it. On the other hand the 3D screen also provides the “veil view” feature which is indispensable in crowded areas, when I feel like someone next to me is looking on my screen I simply hit a hardware button and voila! I can see the screen but  anyone who looks at it from an angle such as the people next to me see a weird scrambled pattern. Then when I want a clear&easy to view screen I simply disable veil view mode and It becomes a normal screen again. Other features like QWERTY keyboard and one-seg TV are very handy indeed. HDMI is also nice to have because sometimes you want to watch those recorded one-seg programs on a bigger screen or watch some youtube videos through your TV and thanks to the two way communication ability of HDMI I can control the playback process through my TV’s remote control without even touching my phone.

Then there are some fundamental issues I have with iPhone devices.

• Can’t swap batteries
• Can’t use SD cards
• OS not open source

I prefer options and hack-ability. On a side note, open source  represents the minimum bar for software. If your proprietary software is worse than the opensource alternative then you lost. Thats the great thing about open source, its lifting the standard for software & forcing companies to work harder or base their product of the open source alternative while adding value. So if iOS is roughly on the same level as the new android version then I think apple is in hot water.

To round this post up, other than the increased horsepower and frontal camera I can’t see what makes the new iPhone  better than my 10 month old phone. It seems like a average phone, inferior in many ways to its contemporaries such as Samsung’s Galaxy SII and the Google Nexus Prime. Perhaps Apples new strategy(by no means a bad one) is budget smart-phones.

Lastly perhaps Apple should open source iOS ?

This time at RSJ I got to see some interesting research from Mr. Yoshida Yuuki about using the robots null space to move its COM so as to preserve balance while being pushed. I also got to see some interesting robot demonstrations.

embedded by Embedded Video

The tutorial on robot arms is complete! This tutorial will teach you about the modeling and control of robot arms. In particular this tutorial will teach you about

1. Forward Kinematics and Joint parameterization
2. Numeric Calculation of the Kinematic Jacobian
3. Inverse Kinematics
4. Disturbance Observer
5. Position Control