[Paper Review] Model Based Control of Soft Robots: A Survey of the State of the Art and Open Challenges

Cosimo Della Santina, Christian Duriez+1 more|arXiv (Cornell University)|Oct 4, 2021

Soft Robotics and Applications40 citations

TL;DR

This paper surveys finite-dimensional model-based control approaches for soft robots, contrasting infinite-dimensional PDE models with tractable ODE-based approximations, and discusses control strategies, equilibria, actuator dynamics, and simulators.

ABSTRACT

Continuum soft robots are mechanical systems entirely made of continuously deformable elements. This design solution aims to bring robots closer to invertebrate animals and soft appendices of vertebrate animals (e.g., an elephant's trunk, a monkey's tail). This work aims to introduce the control theorist perspective to this novel development in robotics. We aim to remove the barriers to entry into this field by presenting existing results and future challenges using a unified language and within a coherent framework. Indeed, the main difficulty in entering this field is the wide variability of terminology and scientific backgrounds, making it quite hard to acquire a comprehensive view on the topic. Another limiting factor is that it is not obvious where to draw a clear line between the limitations imposed by the technology not being mature yet and the challenges intrinsic to this class of robots. In this work, we argue that the intrinsic effects are the continuum or multi-body dynamics, the presence of a non-negligible elastic potential field, and the variability in sensing and actuation strategies.

Motivation & Objective

• Introduce the control-theoretic perspective to soft robotics and unify terminology.
• Summarize finite-dimensional modeling approaches for soft robot dynamics (PCC, functional parametrizations, FEM).
• Discuss control design for shape regulation and tracking within these models.
• Highlight actuators dynamics integration and modeling choices.
• Identify open challenges and future research directions in model-based soft robot control.

Proposed method

• Review infinite-dimensional rod/Cosserat and PDE models and their role in control.
• Describe finite-dimensional approximations: piecewise constant strain (PCC) and functional parametrizations with M(q)¨q + C(q, q˙)˙q + G(q) = A(q)τ.
• Present Finite Element Methods (FEM) and model order reduction for tractability.
• Explain equilibrium existence via K(q) + G(q) = A(q)τ and discuss monotone/radially unbounded conditions.
• Discuss actuator dynamics with coupled equations if applicable (M, C, D, K, G, Uc).
• Outline control strategies for fully actuated soft robots, including posture regulation and PD-like controllers with feedforward components.

Experimental results

Research questions

• RQ1 What finite-dimensional models can accurately and tractably describe soft robot dynamics for control?
• RQ2 Do equilibria exist for constant actuation in nonlinear soft robot models and under what conditions are they stable?
• RQ3 How can actuator dynamics be integrated into the control design for soft robots?
• RQ4 What control strategies (e.g., feedforward, PD-like feedback) are effective for posture regulation and tracking under these models?
• RQ5 What are suitable simulators and model-reduction techniques to enable practical control development?

Key findings

• Finite-dimensional approximations (PCC, functional parametrizations) provide tractable models that capture essential soft robot dynamics for control.
• Equilibrium configurations exist for any constant actuation due to nonlinear stiffness and gravity, under mild conditions; this contrasts with rigid robots where equilibrium under constant actuation is not guaranteed.
• Actuator dynamics can be incorporated using coupled equations and slow-fast analysis, enabling generalized input mappings in the controller design.
• PD-like nonlinear controllers with feedforward terms can be analyzed in the context of soft robot dynamics, aiding posture regulation and tracking.
• Simulators and model reduction techniques (FEM, PCC, modal analysis) enable practical development and comparison of control strategies.
• The choice of model (PCC, FEM, rigid approximations) significantly affects closed-loop behavior and controller performance.