### Abstract

This semester project focused on exotendons spanning one or more joints to provide passive assistance in walking. These exotendons would have the same behavior as traction springs and create an exoskeleton for the human body legs, in order to reduce the required moment/power at the joints during the gait cycle. Four configurations were considered:

Each exotendon is attached with pulleys to one (configuration A), three (configuration B) or six leg joints (configuration C and D). The configurations A, B and C are composed of two exotendons and the configuration D of four exotendons.

Thus, when the angles of the joints change, the lenght of the exotendons also and therefore, the forces created by the exotendons vary. Below the situation is represented for the configuration A (in blue the exotendon and in red the pulley attached to the ankle) for one leg.

A main goal of the project was to optimize, thanks to the PSO algorithm, these exoskeletons in order to reproduce the same results obtained in the literature (“Exotendons for assistance of human locomotion” by Antonie van den Bogert ). At the end of the project, an implementation in Webots was done to see the behavior of the body in a dynamical situation with the exosqueletons. More details are available in my report, attached below.

### PSO algorithm

Particle swarm optimization is a computation technique inspired by social behavior and movement dynamics of insects, birds and fish. It is a global gradient-less, stochastic search method. Several particles which represent possible solutions of the problem are initialized through the whole space of the parameters (slack lengths of the exotendons and radii of the pulleys of the joints), and each one has random position and velocity. At each run of the algorithm the particles move and each of them try to find a better position taking its best performance and the best performance among all the particles into account.

The graphs below represent the average residual moment for the configuration A, as a function of the two parameters, the slack length of the exotendon and radius of the pulley of the ankle (on the left) and the contour of this function with the minimum average residual moment represented by a red circle (on the right).

Below you have the videos recorded of the movement of some particles initialized in different areas, thus you can see their behavior according to their initial position. If the function has no clear gradient, it will be hard for the particles to reach the minimum of the function.

### Simulation using Webots

In order to see if such exosqueleton had the expected effect, different optimizations were implemented in Webots. The person has to provide a specific moment (feedback moment) to do his gait cycle, it means to follow the reference positions of the joints. A moment is intrinsically applied at the joints, the passive moment, which come from the ligamentous system of the legs. The active moment provided by the exotendons were computed and added to the final moment applied at the joints.

Below you can see the moments at the joints without contribution of the exotendons (top figure) and the ones with assistance of the exotendons (bottom figure), for the right leg and the configuration A, during one gait cycle.

We see that the position of the ankle is correctly followed and the moment provided by the exotendon reduces the feedback moment.