Leimgruber I. , Bacuet Q.

Abstract

How can we control a robot, walking like a human that have an equivalent muscular structure?

In the past, many tasks were tackled in order to provide better tools, like muscle models or controllers, to imitate human’s gait using robots. We want to study the functionality of muscles in walking,  to test whether expressing equations of motion in different spaces simplify the overall complexity of control algorithm. This is an important step as it could critically simplify the calculation of inverse kinematics using calculus in the muscle space. For this purpose, we will first write functions that map the joint space to the prismatic muscle space for single articular muscles and bi-articular muscles, from angles and torque to length and forces. We will then find functions that map the muscle space to muscle tendon unit (MTU), from length and forces to length and activation signals. The next step is to write the equations of motion in three different spaces: the articulated joint space, the prismatic muscle space and the MTU to determine mass matrix and jacobians of the muscle space as a function of those in the joint space and then in a second step we convert the muscle space parameters to MTU units. We will limit ourself to the lower part of the body.

Result

In the first step of this project, we developed equations and functions to be able to pass from joint space to muscle space for single and bi-articular muscle. Then, we did the same to pass from the muscle space to the MTU space.
In the second part of this semester project, we developed the mapping that allowed us to pass the EoM from one space to the other using mostly the formulas that we developed in the first part.
In the last part of this project, we tested our equations to be sure that everything match. We successfully tested the function part and our results are convincing.
 
We can see below our fomulas applied to the case of the GLU muscle.

 

Future Work

For future work, the optimization part is essential to resolve redundancy in muscle space. With this part done, we could have been able to associate part of the mass matrix to corresponding muscle.  Same should be done to the jacobian. We could then have done an analysis of the new matrices, to then answer our initial question.