STRANGER Robot alu metallic

Even though many of the newly emerging humanoid robot start-ups have high hopes, the functionality, cost-effectiveness, safety, and autonomy of humanoid robots have yet to be tested—a process that, as with the full autonomy of self-driving electric cars, could take 5 to 10 years. So we still have some time; nothing is certain yet.

We may well find that it is far more cost-effective to pay a worker—who can easily withstand several billion load cycles over the course of his working life—60,000 dollars a year than to employ a robot, which is cumbersome compared to a human, costs 60,000 dollars or more per year in maintenance and depreciation, and is capable of doing much less. And who certainly won’t be buying the products they manufacture. This is where macroeconomics comes into play. So we still need to figure out which applications are truly useful and cost-effective.

With the STRANGER ROBOT project, we are essentially working on technologies that foreshadow artificial muscles. That is why we should strive to a better understand the biomechanics of elastically pretensioned robots and, above all, to implement them experimentally, since physical simulations alone are not sufficient for this purpose–and, due to the nonlinear behavior of rubber muscles, are also hardly practical.

This includes the effects of muscle loops spanning multiple joints, the optimal configuration and placement of the muscle-tendon actuators, and an anatomical or structural design of the knee and hip joints that ensures the robot consumes virtually no energy while standing, without losing its passive responsiveness.

Artificial muscles and applications for humanoid robots are still in the development stage, in part because, until now, there has been no cost-effective skeletal structure (i.e., standard platform) available for experiments that could be equipped relatively quickly with artificial muscles and thus with morphological intelligence–a need that can now be met by the STRANGER ROBOT R&D CHASSIS. 

An initial rough assessment of whether the required specifications can be met under the most extreme load condition–standing up from a squatting position against the body weight of STRANGER. Assuming 480 N = 48 kg (106 lbs) weight, without the weight of foot & lower leg, and using a rubber-muscle-tendon system driven by ordinary e-motors:

1) What pretensions are generated in the rubber cords passively by lowering into a squat?

2) How work the muscle groups in the lower leg and thigh together? Are the hip and back muscles involved?

3) What contribution makes the rotation of the pelvis around the hip joints, caused by activated spline muscles and hip drives, the torso's inclination, and the position of the arms to shorten the the load-lever arms?

4) How much tension force must be generated in the thigh and calf muscles, the hip joint drives, and the spline muscles, in addition to the pre-tension, for a brief moment to initiate the rise from the squat?

5) What is the required torque of the electric motor(s), and what is its mass?

6) What is the optimal muscle-tendon-motor design configuration?

In bio-inspired humanoid robot design, there is still plenty to explore, invent, and improve.

See also the animation videos "Biomechanik Bein passiv B" and "STRANGER ROBOT biomechanics–standing up from a squat" (below)

RE 1) If the weight of the humanoid robot STRANGER is 48 kg or approximately 480 N (excluding the feet and lower legs) and the load lever arm is 0.2 to 0.27 m long, this results in a torque of 48 to 65 Nm per knee. It follows that: With a force lever arm of 60 mm at the knee, a tensile force of 1,200 N must be applied to the lower leg extensor to achieve equilibrium. This theoretically generates a torque of 72 Nm in the knee (i.e., slightly more than 65 Nm). 

RE 2) The lower leg extensor muscles are located on the front of the thigh. Their tendons are routed around the knee and pull on the shinbone. They work together with the calf muscles to form a functional muscle loop. Together, they hold the knee joint in position.

Since the sole of the foot is in contact with the ground, the calf muscles act as extensors of the lower leg at this moment: they pull the lower leg backward with the knee—against the applied load. This is the reverse of plantar flexion (during which the calf muscles normally extend the foot). Reverse plantar flexion thus helps reduce the tensile stress in the thigh muscle through its counteracting force.

RE 3) When lowering into a squat, the work is essentially performed passively by the robot’s own weight—that is, by gravity. The lower leg extensors are stretched further and further, causing the tensile stress on the muscles to increase steadily. On the one hand, they slow the downward movement; on the other, they store potential energy. With skillful control, the pre-tension of the muscles can be increased while they are relaxed or before lowering, so that the motors that tension the muscle-tendon system rarely have to work against the full passive tension. Clear is that the movement of other body parts, such as the pelvis, arms, and chest, can influence the length of the load lever and thus the position of the center of gravity. The extent to which this is relevant during a squat has yet to be determined.

RE 4) When squatting, the lower leg extensors must generate enough tension to support the body’s main weight while maintaining pseudostatic balance. In this squat case study, each lower leg extensor of the STRANGER ROBOT, located at the front of the thigh, consists of eight STRANGER RUBBER MUSCLES that exhibit an exceptional force-strain curve. Each was stretched by 115%, thereby exerting a tensile force of approximately 150 N. Together, they generate 1,200 N, which produces a torque of 65 Nm - up to 72 Nm - at the knee (130 Nm up to 144 Nm at both knees). So, theoretically, this amounts to 1200 N per leg in the static equilibrium of the squat. However, the extensor muscle loop also includes the calf muscles (and others), which reduce the theoretically required tension in the thigh–possibly by as much as one-third. Whether this assumption is correct still needs to be verified through physics simulations and experiments.

Since there may still be a payload, we'll stick with the assumption of 1,200 N for now. Once these 1,200 N have been passively generated, only a small additional amount of force needs to be applied to initiate the rise from a squatting position. Incidentally, this could also be achieved by moving limbs such as the arms or the pelvis in a way that shortens the load-bearing lever arms. When fully tensed in static equilibrium, only the inertia of the upper body needs to be overcome to stand up. Since the system is “suspended” under tension in equilibrium, impulses of only a few Newton are sufficient for this. These impulses consist of additional tensile forces, which are ideally applied by a separate “control or initiation muscle” that had previously been under little or no tension. Only minimal motor forces are required for this. This principle is explained and illustrated in even greater detail to licensees. As the humanoid robot stands up, the load levers continue to shorten, resulting in less and less tensile stress in the rubber cords, which consequently shorten until they reach their basic tension.

RE 5) Let’s assume we need a standard electric motor that is supposed to apply a tensile force of 150 N to a rubber cord. To do this, the motor winds the tendon—a 2-mm Dyneema cord or a fishing line—directly onto its shaft, which has a diameter of 3 mm. This determines the lever arm and the required torque: r = 1.5 mm + 1 mm (half the diameter of the Dyneema cord) = r = 2.5 mm = 0.0025 m × 150 N = 0.375 Nm. The motor would therefore need to have a torque of 375 Ncm. If the diameter of the motor shaft can be made smaller, the torque can also be reduced further.

To protect the motor shaft from bending stresses, we position the tendon string so that it pulls on the shaft from both sides and both sides are wound in opposite directions simultaneously. Winding the cord on both sides tensions the rubber muscle more quickly and also neutralizes the tensile forces acting on the motor shaft when the rubber cord is fully tensioned. In this state, the motor is not powered but can detect passively induced torques and thus function as a sensor (more details and corresponding drawings are provided to licensees).

Since the motor runs for only a very short time—the maximum possible string length is wound up on both sides after about 6-25 revolutions—the motor can presumably be designed for the stall torque, which is significantly greater than the effective torque. This means that the motor can be even smaller, operates in start-stop mode, and could therefore also be a standard, inexpensive DC brush motor. The weight of such a motor can only be specified once the exact specifications are available, but it will likely be between 250 g (target) - 450 g (maximum).

Torque Density at the knee joint
If the lower leg extensor muscles on the front of the thigh, including the motors, weigh a total of 4 kg, the torque density at the knee joint would be 18 Nm/kg (72 Nm/4 kg). If we could reduce the weight of this muscle group by half through optimal design and fine-tuning, the torque density would double to 36 Nm/kg (72/2)—which would currently be among the highest values achievable. Once the design of the artificial muscles and their various applications have been clarified, we will seek expert advice from selected manufacturers regarding the design of the respective electric motors. We also need to determine whether it makes sense to group four muscle-tendon units in the thigh into a single unit that can be driven by just one motor, so that we only need two motors per leg for the quadriceps muscle group—that is, the lower leg extensors.

RE 6) Some considerations have already been mentioned. The detailed rubber muscle design will be made available exclusively to licensees. Licensees are, of course, free to develop their own, improved solutions. But even in this case, the proposed design of the STRANGER ROBOT’s artificial muscles can serve as a template, since the geometry and mass ratios remain essentially the same.

The artificial muscles of the STRANGER ROBOT are made of natural rubber, which has a stress-strain curve that is particularly well-suited for this purpose:

1.  In the main operating range of 40 to 90 N (considering a single rubbber muscle cord), the STRANGER ROBOT muscles behave in a virtually linear manner, while they exhibit steep increases in the range of muscle pre-tension (basic muscle tone) and maximum elongation.

2. In the range of baseline tension, they exhibit a steep, likewise nearly linear increase from 0.2 N to 20 N at an elongation of 0.2 to 2.5 mm. The knee joint driven by the muscle is thus relatively stiff at the onset of force application, without losing its sensitivity to reaction forces.

3. In the range of 2.5 to 7 mm of elongation, the tensile stress increases to 30 N, then transitions into the linear behavior range at 25 mm of elongation and a stress of 45 N. The knee joint becomes more compliant and responds in a nearly ideally elastic manner over a wide range of forces.

4. If the strain exceeds 90%, the stress doubles nonlinearly from 90 N to 180 N over the next 50 mm of strain—and rises even more steeply once the strain exceeds 110%. The stiffness of the knee joint thus increases significantly without losing its responsiveness.

Conclusions
Re 1)
 The wide linear operating range is likely to prove advantageous for dynamic simulation in the physics engine. 

Re 2)
The behavior in the range of basic tensions suggests excellent force sensitivity. Reaction forces are detected as low as 0.2 N. At the same time, disturbances are strongly damped, which implies passive self-stabilization.  

Re 3)
It remains to be clarified whether the active control range—which in this artificial muscle design is achieved via electric motors—can be limited to the linear range, while higher stresses are generated purely passively through pre-stretching as the robot assumes appropriate postures. Consider, for example, athletes who use this method to ensure maximum force development in the respective muscle groups. 

Force-strain diagrams, detailed specifications, and sources of supply will, of course, be made available to licensees.