Mechanical Impedance Compliance Adjuster for Humanoid Joints

The current design of the University of Calgary robot does not have compliance implemented in its joints. A small-scale version of the robot was tested in pediatric care, and reduced the time it took for children to be vaccinated by 62% (from 32 mins to 12 mins); however, in order to keep the children safe, it had to be powered off first, and many complained about it being lifeless or not being able to interact with it. Additionally, the goal of the Robotarium lab is to use the robot in search and rescue in locations inaccessible by humans. In the first three months of 2021 alone, the Kananaskis search-and-rescue team responded to 63 calls; however, it is often very difficult and expensive to accurately sense and maneuver rough terrain.

Our design to implement compliance in the robot solves these two issues. Not only will it allow for children to interact with the robot more realistically when it is powered off because the joints will flex under force (e.g. giving the robot a high five), but it will also make it safer to be left on, as the joints will bend and absorb force should they run into patients, doctors, or family. Additionally, compliance allows for a robot to maneuver rough terrain more easily and the robot does not have to perfectly sense and predict the ground, but rather can flex to unexpected changes in elevation. This is closer to how a human navigates uneven surfaces: getting a general idea through the sense, and flexing the ankles and knees to fit the ground as they step.

Our design is innovative because it allows for adjustable compliance. Implementing compliance is easy, but creating a device that can change how stiff or loose a robotic joint is is much more challenging. It is important, however, because different situations call for different amount of compliance. For example, if the robot is running, the compliance in the knee must be very stiff (minimal compliance) otherwise the knee will buckle when the foot strikes the ground, whereas if the terrain is very uneven, the compliance in the knee must be very loose (large compliance).

Our device works by an internal motor moving a slider up and down the cantilevered beam, which can be controlled by external software. By moving this slider, the effective length of the beam is changed, meaning that the stiffness of this beam can change. Because the input motor (thigh) and external shaft (shin) are connected through this beam, the compliance can be altered easily. Additionally, the cantilever beam is designed to easily be replaced, meaning that if compliance needs to be drastically altered, a different material beam can be selected.

Our design is effective for many reasons:

• It fits with the current motor and design of the current robot, with a small modification to the robot joint agreed upon by the Robotarium team.
• The total weight of the device is 335.44g (not including the chosen customized stepper motor to move the slider), meaning that every joint could contain a device like this with minimal impact on the robots overall weight.
• The device can be easily machined (confirmed by the U of C machine shop) with simple materials and common fasteners, bringing the total cost of the device to $202.49, under the project limit of $250 (excluding additional parts, like microcontroller, motor, and motor driver).
• It is a very small device, filling a total cylindrical volumetric space of approximately 440cm³ (radius = 47.25mm, width = 62.6mm). It is so small, in fact, that because it is designed to be placed within the robot’s pre-existing joint cavities, the joints are only extruded from the robot by 43.2mm, meaning that it does not affect the overall robot design.
• All aspects of the design meet the predetermined engineering specifications of strength, fatigue, failure, and compliance (see “Validation” and “Feasibility”).

Compliance

• One goal was to match human compliance ranges. Initial research was completed; however, very limited data is currently available, so we conducted a study on our own
  • The maximum bound was found by analyzing Olympic runners at max speed. It was hypothesized that knee compliance would be near its minimum (stiffest), as a stiff knee joint is a sign of efficient form. Therefore, elite sprinters will have some of the lowest possible human knee compliance when running. By analyzing these sprinters in slow motion (to capture the angular deflection of their knee joints), corresponding force plate data, and known physical dimensions of the runners, the total moment around the runners knee was calculated done for a variety of runners and strides, and averaged to get a max human torsional spring constant in the knee of 1623 Nm/rad or 28.32 Nm/deg.
  • The minimum bound was more difficult, as humans can technically have infinite compliance (0 N/m spring constant), so a practical situation that may demand a low spring constant in the robot’s knee must be analyzed to find the minimum spring constant it would conceivably need. This was found by analyzing a situation the robot could be in, where human compliance would likely be the highest: miscalculating their footing. The project sponsor hoped that our device would allow the robot would be able to walk up stairs normally, so by researching city residential and commercial buildings codes, it was determined that the max difference in possible step heights was 75mm. Assuming the robot sensed the step to be at the smallest possible height and it was actually at the highest, compliance needs to adjust for this miscalculation before significant weight has been shifted to the upper foot, otherwise the miscalculation will throw the robot off balance. The maximum amount of weight that can be shifted on an incorrect leg position (i.e. before the leg must be fully complied to the correct position to maintain balance) was approximated as less than or equal to 5% of the body weight, as found through testing our own human balance limits. Assuming an approximate limb position for the robot and knowing the total weight of the robot is 50kg, the minimum applicable human torsional spring constant in the knee was found (through testing all possible stair widths) to be 17.68Nm/rad or 0.3086Nm/deg.

Failure

• Another goal used to validate the design was a factor of safety of at least 1.2 for every part of the device
  • Solidworks/Ansys simulations were run on over 20+ potential materials and beam geometries to determine cantilever deflection and stress throughout the cantilevered spring under a 135N load (the max possible applied force to the device, based on the robot joint motor’s max input torque of 7N).
  • Material selection of the cantilever spring was based on its ability to meet this criteria (as well as provide an range accurate to human compliance).
  • All test to find an acceptable material were performed on just the cantilever beam at the max effective length (68.93 mm) and input force (135N). Once Aluminum 7068-T6 was chosen, more rigorous Ansys testing with finer meshes, at all effective lengths and force locations, and including all connecting parts like the slider and outer shell was completed to ensure there was no stress concentrators or unexpected externalities that could cause failure.

The design was measured to be feasible based on all the predetermined parameters:

Cost – The project came in $47.51 under budget, with a total cost of $202.49 for raw materials, manufacturing, and fasteners

Compliance – The device can create compliance for a range of 21.06 Nm/rad to 151 Nm/rad, which is within desired range, and encompasses all practical applications. If human compliance extrema is desired the material of the cantilever can be changed to achieve this

Failure – The parts experiencing maximum stress, the cantilever spring, the outer shell, and the slider, all have factors of safety greater than 1.2 (1.44, 1.32 and 3.20, respectively).