# Diz 49 en

# Modelling and control of walking robots[edit]

**Autor**: Anderle Milan

This thesis is focused on the design of novel methods for underactuated walking robot control in a way resembling a human walk. The methods are based on partially linear form of Acrobot as the representative of a class of underactuated walking robots. Indeed, Acrobot is the simplest underactuated walking robot theoretically able to walk. Later on, a general method is proposed enabling to extend directly results for Acrobot to any general planar n-link chain underactuated at its pivot point. This technique is referred to as the so-called generalized Acrobot embedding. By virtue of the partial linearization property it is possible to transform the original nonlinear representation of Acrobot into its partially linear form having a one-dimensional nonlinear component only. The newly obtained results include design methods for Acrobot walking, i.e. state feedback controllers, observers and planning of walking-like reference trajectories to be tracked. To be more specific, state feedback controllers are based on the knowledge of time varying entries resulting from approximate linearization of the mentioned nonlinear component along selected Acrobot walking-like reference trajectory. In one particular case of the controller design only bounds of these time varying entries are taken into the account. Alternatively, information about time varying entries including time derivative of the entries up to the order four is used. As already noted, reference trajectory design methods belong to the thesis original results as well. To accommodate the impact effect, the developed reference trajectory is also using the idea that the angular velocities at the end of the previous step and at the beginning of the next step have to be in a ratio determined by the impact properties. Next, due to the absence of the actuator at the pivot point, it is not easy to directly measure all states of Acrobot. Therefore, two algorithms to observe unmeasurable states of Acrobot were developed here based on particular knowledge of angular positions and velocities. Finally, due to its simple geometry, Acrobot is able to walk only theoretically, as it would always hit the ground by its swing leg. Therefore, the results developed for Acrobot are extended to the so-called 4-link using the above mentioned embedding method. As a~matter of fact, 4-link may serve as a~reasonable model of pair of legs with knees thereby providing a more realistic walking model, though without a torso.

**Milan Anderle**, mailto:andermil@fel.cvut.cz