In an age where computers challenge the smartest human beings in cognitive tasks, the
conspicuous discrepancy between robot and animal locomotion appears paradoxical. While
animals can move around autonomously in complex environments, today’s robots struggle
to independently operate in such surroundings. There are many reasons for robots’ inferior
performance, but arguably the most important one is our missing understanding of complexity.
This thesis introduces the notion of discrete actuation for the study of locomotion in
robots and animals. The actuation of a system with discrete actuation is restricted to be
applied at a finite number of instants in time and is impulsive. We find that, despite their
simplicity, such systems can predict various experimental observations and inspire novel
technologies for robot design and control. We further find that, through the study of discrete
actuation, causal relationships between actuation and resulting behaviour are revealed and
become quantifiable, which relates the findings presented in this thesis to the broader concepts
of complexity, self-organisation, and self-stability.
We present four case studies in Chapters 3-6 which demonstrate how the concept of
discrete actuation can be employed to understand the physics of locomotion and to facilitate
novel robot technologies. We first introduce the impulsive eccentric wheel model which is
a discretely actuated system for the study of hopping locomotion. We find that the model
predicts robot hopping trajectories and animal related hopping characteristics by reducing the
dynamics of hopping–usually described by hybrid differential equations–to analytic maps.
The reduction of complexity of the model equations reveals the underlying physics of the
locomotion process, and we identify the importance of robot shape and mass distribution
for the locomotion performance. As a concrete application of the model, we compare the
energetics of hopping and rolling locomotion in environments with obstacles and find when
it is better to hop than to roll, based on the fundamental physical principles we discover in
the model analysis. The theoretical insights of this modelling approach enable new actuation
techniques and design for robots which we display in Robbit; a robot that uses strictly convex
foot shapes and rotational impulses to induce hopping locomotion. We show that such
systems outperform hopping with non-strictly convex shapes in terms of energy effective and robust locomotion. A system with discrete actuation motivates the exploitation of shape
and the environment to improve locomotion dynamics, which reveals advantageous effect
of inelastic impacts between the robot foot and the environment. We support this idea with
experimental results from the robot CaneBot which can change its foot shape to induce timed
impacts with the environment. Even though inelastic impacts are commonly considered
detrimental for locomotion dynamics, we show that their appropriate control improves the
locomotion speed considerably.
The findings presented in this thesis show that discrete actuation for locomotion inspires
novel ways to appreciate locomotion dynamics and facilitates unique control and design
technologies for robots. Furthermore, discrete actuation emphasises the definition of causality
in complex systems which we believe will bring robots closer to the locomotion behaviour of
animals, enabling more agile and energy effective robots