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Modal Nonlinear Resonance for Efficient and Versatile Legged Locomotion

Periodic Reporting for period 1 - M-Runners (Modal Nonlinear Resonance for Efficient and Versatile Legged Locomotion)

Reporting period: 2019-06-01 to 2020-11-30

The aim of M-Runners is to thoroughly advance the understanding of fundamental dynamic principles of legged locomotion to the point that those principles can be used to design robots which display similar
motion characteristics, versatility, and efficiency as their biological paragons. The central hypothesis of the project is that biological locomotion is fundamentally determined by the mechanical resonance properties of
the body and that a breakthrough in robot locomotion is essentially linked to understanding and exploiting these phenomena. If body design is such that walking and running correspond to intrinsic periodic motions of
the body, then the control is simple and efficiency and robustness are natural consequences. However, largeamplitude nonlinear oscillations of such complex systems are today still not well understood. Mathematical
methods to describe, analyze, design and control elastic resonant robots are lacking to a large extent. The project is thus dedicated to develop a new theory of nonlinear oscillations, applicable to elastic multibody
systems, be they biologic or robotic.
M-Runners will perform interdisciplinary research at the border between robotics, nonlinear dynamical systems and vibration theory, biomechanics, and machine learning. We will take inspiration from biology
regarding the basic motion sequences and the muscle arrangements (couplings, redundancies, compliance distributions). Conversely, we expect our theory to generate new hypotheses for a deeper understanding of
locomotion biomechanics and its control by the nervous system.
We will design and demonstrate robots which can move at similar speed and mechanical energetic efficiency as animals and humans and which have comparable uneven terrain versatility and robustness.
The primary application scenario is space exploration on Mars in canyons, caves or steep ridge slopes.
Applications of the technology reach, however, from health-care over personal-assistance to disaster
management
The fundamental contribution of the M-Runner project so far is a theory of nonlinear oscillation modes for general Riemannian Euler-Lagrange systems, which is applicable to such complex systems as robots as well as for better understanding motions of human and animal bodies. The project has the very ambitious goal of building up a theoretical fundament which goes massively beyond the standard theory used in robotics and in general in engineering for modelling the oscillation and resonance properties of elastic multi-body systems. This goal was reached to a very large extent and is certainly the major achievement of the project so far.
Based on concepts from mathematical mechanics (Hamiltonian Systems) and differential geometry (Riemannian Geometry, algebraic topology) we found out that indeed one can expect the considered systems to have at least as many modal oscillations as their linearized model has. We reviewed and systematized the results from over one century of literature in mathematics, physics and engineering in this field and added several new definitions and theorems to be able to address the complex systems of interest. This research resulted in an extensive review paper in the Annual Reviews in Control and was presented in a plenary talk at the World Congress of the International Federation of Automatic Control. Several papers on these fundamentals and on first control applications were published or are in final review stage. Moreover, a first version of a software toolbox was developed, which identifies the nonlinear modes for systems given their dynamics model and starting from the normal modes of the linearized model. First validation of the theory was provided in simulation and on robotic prototypes.
Two new quadruped leg designs were performed based on the theoretical outcomes. One leg incorporates what we defined as a strict nonlinear normal mode in a recent paper. The second leg design is the first leg in our group having three degrees of freedom, as a preparation for the design of a complete quadruped with full 6d functionality. This system is currently under design, requiring substantial personnel effort.
The major steps until the end of the project are to design a quadruped hardware prototype and the associated locomotion controllers based on the nonlinear oscillation modes theory in such a way that they increase efficiency and performance of locomotion substantially compared to the state of the art. A first version of the quadruped will be ready until June 2020. If the Covid-19 pandemic situation permits, it is foreseen to participate with the quadruped as part of a robot team to an experimental campaign on Mount Etna, which emulates a space planetary mission. Moreover, we expect the new methods to provide insightful hypotheses for biomechanics and neuroscience research, which can be used for better prosthetic and rehabilitation devices.
Vision of efficient quadruped locomotion for planetary exploration
Interplay between robotics, biomechanics and neuroscience for understanding efficient locomotion