[Paper Review] Using Nonlinear Normal Modes for Execution of Efficient Cyclic Motions in Soft Robots.

Cosimo Della Santina, Dominic Lakatos+2 more|arXiv (Cornell University)|Jun 21, 2018

Cardiomyopathy and Myosin Studies3 citations

TL;DR

This paper proposes a general framework for generating efficient cyclic motions in soft robots by stabilizing nonlinear normal modes—sub-manifolds of the state space that represent natural oscillatory behaviors. By leveraging nonlinear dynamics inspired by the human musculoskeletal system, the method enables energy-efficient, robust oscillations without relying on dynamic cancellation, demonstrated in simulations and experiments on an elastic inverted pendulum and a segmented leg robot.

ABSTRACT

With the aim of getting closer to the performance of the animal muscleskeletal system, elastic elements are purposefully introduced in the mechanical structure of soft robots. Indeed, previous works have extensively shown that elasticity can endow robots with the ability of performing tasks with increased efficiency, peak performances, and mechanical robustness. However, despite the many achievements, a general theory of efficient motions in soft robots is still lacking. Most of the literature focuses on specific examples, or imposes a prescribed behavior through dynamic cancellations, thus defeating the purpose of introducing elasticity in the first place. This paper aims at making a step towards establishing such a general framework. To this end, we leverage on the theory of oscillations in nonlinear dynamical systems, and we take inspiration from state of the art theories about how the human central nervous system manages the muscleskeletal system. We propose to generate regular and efficient motions in soft robots by stabilizing sub-manifolds of the state space on which the system would naturally evolve. We select these sub-manifolds as the nonlinear continuation of linear eigenspaces, called nonlinear normal modes. In such a way, efficient oscillatory behaviors can be excited. We show the effectiveness of the methods in simulations on an elastic inverted pendulum, and experimentally on a segmented elastic leg.

Motivation & Objective

• To develop a general theory for efficient motion generation in soft robots, moving beyond case-specific designs or dynamic cancellation.
• To address the lack of a unified framework for exploiting elasticity in soft robotics to achieve high performance and robustness.
• To draw inspiration from the human central nervous system’s control of the musculoskeletal system for bio-inspired motion planning.
• To identify and stabilize intrinsic oscillatory behaviors in elastic soft robots using nonlinear dynamics theory.
• To enable the execution of regular, efficient, and robust cyclic motions without compromising the benefits of elasticity.

Proposed method

• To model the soft robot as a nonlinear dynamical system and identify its nonlinear normal modes (NNMs), which are the nonlinear continuation of linear eigenspaces.
• To use the theory of nonlinear oscillations to locate sub-manifolds in the state space where the system naturally evolves with periodic behavior.
• To design control laws that stabilize the system on these NNMs, ensuring sustained and efficient oscillatory motion.
• To apply the method to a reduced-order model of an elastic inverted pendulum and a segmented elastic leg for validation.
• To implement the control strategy in simulations and physical experiments, verifying stability and energy efficiency.
• To ensure the control does not rely on dynamic cancellation, preserving the inherent benefits of elasticity.

Experimental results

Research questions

• RQ1 How can nonlinear normal modes be used to generate efficient and stable cyclic motions in soft robots?
• RQ2 What is the role of intrinsic oscillatory behaviors in enabling energy-efficient locomotion in elastic soft robots?
• RQ3 Can a control framework based on nonlinear normal modes outperform conventional methods that rely on dynamic cancellation?
• RQ4 How does the proposed method preserve the advantages of elasticity while achieving desired motion patterns?
• RQ5 To what extent can the human musculoskeletal system’s control principles be transferred to soft robotic systems?

Key findings

• The proposed method successfully generates regular and efficient cyclic motions in soft robots by stabilizing nonlinear normal modes.
• Simulations on an elastic inverted pendulum show that the system achieves stable, self-sustained oscillations without external feedback cancellation.
• Experimental validation on a segmented elastic leg demonstrates the feasibility and robustness of the approach in a real-world soft robotic system.
• The method preserves the benefits of elasticity, such as mechanical robustness and energy efficiency, by avoiding dynamic cancellation.
• The control strategy enables natural, low-energy oscillatory behaviors that emerge from the system’s intrinsic dynamics.
• The results indicate that nonlinear normal modes provide a viable pathway toward a general framework for efficient motion in soft robotics.