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Model Based Control of Soft Robots: A Survey of the State of the Art and Open Challenges

Cosimo Della Santina, Christian Duriez, Daniela Rus

arXiv:2110.01358v2eess.SYcs.RO

TL;DR

Actuator dynamics shape soft-robot behavior, yet few controller designs explicitly account for them. This survey organizes model-based control in a common framework, revealing similarities with other robot types and open control challenges.

  • Problem

    Actuator dynamics shape soft-robot behavior, but few controller designs explicitly account for their dynamics.

    Source: Actuators dynamics and constraints · p. 23

  • Method

    The survey organizes model-based soft-robot control strategies using common terminology inspired by classical robotics and control.

    Source: Conclusions · p. 33

  • Results

    The shared framework makes similarities among rigid, flexible, and soft robots apparent while pinpointing fundamental differences from related fields.

    Source: Conclusions · p. 33

  • Takeaways & Limitations

    Connections with established robotics results allow controllers to be ported from rigid robots to soft continuum robots.

    Source: Conclusions · p. 33

    Designing a provably stable task-space dynamic controller that ensures full-state convergence under underactuation remains an open problem.

    Source: Task space regulation and tracking · p. 26

Abstract

from arXiv · show

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.

Finite Dimensional Models for Control Purposes … Finite dimensional approximations

Soft-robot control models must reduce continuum dynamics to finite-dimensional forms that are tractable while retaining the dynamics needed for control analysis. The section surveys rod-based representations, infinite-dimensional models, and finite-dimensional approximations.

Finite Dimensional Models for Control Purposes

  • Finite-dimensional ODE approximations can describe soft-robot behavior with sufficient precision, while control-design models must be lower-dimensional and structurally analyzable than simulation models.Model development is integral to soft-robot control design: simulation models prioritize accuracy, whereas algorithm-design models may neglect fine details to support analysis of structural properties and closed-loop behavior.Source: Finite Dimensional Models for Control… · pp. 2–3

When the rigid part is dominant

  • When rigid dynamics dominate, standard rigid-body multibody models can represent the rigid portion while a nonlinear lumped impedance accounts for the soft part.Examples include a soft neck on a rigid humanoid, and soft muscles actuating rigid links –.Source: When the rigid part is dominant · p. 3

Rod Models

  • Rod models approximate slender robots by neglecting volumetric deformation and describing a deformable backbone; local strains encode curvature, twist, elongation, and shear, whose integration recovers posture.When cross-sectional changes are negligible, their contribution can be represented through an infinitesimal rotational inertia along the rod.Source: Rod Models · pp. 3–4, Figure 2 · p. 5

Infinite Dimensional Models

  • Kirchhoff-Clebsch-Love and Cosserat rod theories – describe rod-like robots, but their infinite-dimensional PDE states impede direct control despite their use for steady-state solutions.Tendon-actuated statics and dynamics have been derived and experimentally validated –; coupled Cosserat rods model parallel robots,, and a dynamic-model tutorial is available.Source: Infinite Dimensional Models · pp. 5–6

Finite dimensional approximations

  • Finite-dimensional approximations restrict strains to piecewise-constant or functionally parametrized spaces, representing strain by configuration q ∈ R^n and enabling continuum forward kinematics.The forward-kinematics map h(s, q) connects q(t) to backbone posture x(s, t), with J the Jacobian of h; piecewise constant curvature is used as a widespread illustrative model.Source: Rod Models · p. 5, Finite dimensional approximations · p. 6
  • Lagrangian mechanics yields finite-dimensional ODEs with multi-body inertia, Coriolis and centrifugal, gravity, elastic, and dissipative forces, with (q, q̇) as the robot state.The inertia matrix M(q) may be singular in some configurations, but suitable configuration-space parametrization can avoid this.Source: Finite dimensional approximations · p. 6
  • Elastic and gravitational actions derive from integrated potential energies; the elastic force field is positive definite, while its stiffness may be only semipositive definite in corner cases such as a floating base.Friction losses are modeled as possibly nonlinear damping with D ≻ 0, and gravitational forces are bounded.Source: Finite dimensional approximations · p. 7
  • The actuation field A(q) maps applied forces into configuration space, often noncollocated with the states; the formulation assumes A has full-rank columns.Representative actuation matrices are shown in Fig. 3.Source: Finite dimensional approximations · p. 7

Piecewise Constant Strain Approximations

Piecewise constant strain discretizations reduce a continuum rod to finite-dimensional segments, with piecewise constant curvature (PCC) as the simplest case. The section also describes 3D and elongating PCC variants, rigid-link approximations, and models that include all six strains.

Piecewise Constant Strain Approximations

  • PCC models assume curvature is constant within each segment, representing a planar robot as differentiable arcs whose configuration has one curvature coordinate per segment.The segment curvature distributes the bending angle along the segment rather than localizing it at a joint.Source: Piecewise Constant Strain Approximations · p. 7
  • In 3D, PCC segments retain arc geometry but allow their bending planes to change, introducing two degrees of freedom per segment; optional elongation adds another coordinate per segment.The usual relative-plane orientation representation introduces singularities and discontinuities, which alternative parameterizations can avoid –.Source: Piecewise Constant Strain Approximations · p. 9
  • Rigid-link approximations model a rod as links with independent joints and parallel lumped springs, yielding a rigid robot with elasticity described by ordinary differential equations [46],.In the strain view, deformation is zero except at a finite set of points, where it is represented by Dirac delta values.Source: Piecewise Constant Strain Approximations · p. 9
  • Piecewise constant strain models add shear deformation and twist to PCC, representing six strains per segment and enabling descriptions of soft parallel structures,,.Their inertia matrix couples the six strains fully, while elastic potential forces are usually diagonal or block diagonal.Source: Piecewise Constant Strain Approximations · p. 9

How Fine Should the Discretization Be? … Model order reduction

The section compares ways to represent soft-robot deformation, from choosing piecewise-constant segments to functional and finite-element models. It also describes reducing model dimension while retaining dynamics relevant to the intended application.

How Fine Should the Discretization Be?

  • Segment count must respect actuated-module mechanics, balance simulation accuracy against cost, and can be chosen to make control models fully actuated.For simulation, cost grows as O(n_s^2) as n_s increases; in planar PCC models with tip torques, A(q) = I.Source: How Fine Should the Discretization Be? · p. 10

Functional Parametrizations

  • Functional parametrizations project deformation onto basis functions, with truncated regular bases ensuring convergence and constant functions extending constant-curvature or constant-strain models.For inextensible planar robots, polynomial curvature bases π_i(s) = s^(i−1) meet these conditions.Source: Functional Parametrizations · p. 10
  • Functional-coordinate dynamics retain the general model form but generally couple all degrees of freedom; piecewise and functional strategies can be combined as piecewise variable-strain models.In the combined strategy, transformation matrices are parametrized functionally.Source: Functional Parametrizations · p. 11

Finite Element Models

  • Finite-element models are preferred when three-dimensional shape changes are significant relative to the virtual backbone, and can also discretize rod models and multiphysics systems.The framework extends to continuous behaviors such as magnetic, thermal, and fluid effects.Source: Finite Element Models · pp. 11–12
  • FEM configuration uses node positions, and its dynamics simplify to M q̈ + G with diagonal M under nodal mass assumptions, but K(q) is usually nonlinear.The configuration dimension is generally three times the node count; FEM converges as node count grows, while several thousand nodes can yield high accuracy at substantial dimensional cost.Source: Finite Element Models · p. 12

Model order reduction

  • Model reduction projects high-dimensional FEM configurations onto a few dozen directions, with modal analysis selecting slow modes to capture a chosen vibration-frequency range.An alternative builds the projection directions by singular value decomposition of representative system evolutions.Source: Model order reduction · pp. 12–13
  • For detailed geometries, condensation reduces FEM size by separating directly actuated from unloaded variables and imposing loading conditions as holonomic constraints.X-FEM can address geometric details but does not radically reduce model size; condensation has also been used to connect FEM and rod models.Source: Model order reduction · p. 13

Existence of Equilibria · Actuators dynamics · Simulators

Soft-robot equilibria can exist under constant actuation, with existence conditions depending on stiffness and actuation; actuator dynamics can be modeled through potential-field coupling, while simulators remain important tools whose selection has no clear solution.

Existence of Equilibria

  • Several equilibrium solutions may exist; when K + G is monotone and A is configuration independent, the equilibrium equation has a closed-form solution.In general, nonlinearities prevent closed-form solutions; radial unboundedness of K is also given as a condition under which existence is expected when monotonicity or configuration independence fails.Source: Existence of Equilibria · pp. 13–14
  • If K(q) is radially unbounded and G(q) is limited, at least one equilibrium exists for any constant actuation, unlike rigid robots unless gravity is involved.The passage sketches this result using the continuity and radial unboundedness of (K + G)/A.Source: Existence of Equilibria · p. 14

Actuators dynamics

  • Although actuator dynamics have received relatively little attention in control models, classic robotics formulations, apply when the actuators’ main components are mechanical.Examples include tendons driven by electric motors and fluids pressurized through pistons.Source: Actuators dynamics · p. 14
  • The actuator and robot dynamics are coupled through the potential field Uc, which can represent tendon elasticity, molecular interactions in compressible fluids, or electromagnetic fields.The supplied model omits dissipation in the actuation system for simplicity.Source: Actuators dynamics · p. 14
  • When actuator dynamics are fast and robustly globally stable, their steady state can approximate the input field; singular perturbation theory can instead separate fast actuator and slow robot dynamics.The steady-state substitution is η ≃ ¯η(q, τ), with ∂Uc(q, ¯η(q, τ))/∂q generalizing A(q)τ.Source: Actuators dynamics · p. 14

Simulators

  • Open-source simulators span volumetric FEM tools SOFA, and ChainQueen and rod-mode tools Elastica, TMTDyn, SimSOFT, and SoRoSim [95].Implementing a simulator has been a bottleneck because simulation models are typically more sophisticated than control models.Source: Simulators · p. 15
  • Choosing among soft-robot simulators has no clear solution, though experimental comparisons, can help with selection.Further simulator details are referenced in [96, Sec. VII].Source: Simulators · p. 15

Shape Control in the Fully Actuated Approximation

The section examines whole-shape control under a fully actuated approximation, where model choice affects closed-loop behavior. It shows how posture regulation can exploit the robot’s elastic and gravitational fields, then considers tracking strategies that limit reliance on direct model cancellation.

Shape Control in the Fully Actuated Approximation

  • The fully actuated approximation offers useful control insight, but the chosen model matters because applying the same controller with different models can substantially change transient and steady-state behavior.Shape control may target configuration, curvature, strain, or volume.Source: Shape Control in the Fully Actuated… · p. 15

Posture regulation

  • A constant feedforward action makes the desired posture asymptotically stable when total potential energy is locally convex and the equilibrium is isolated; elastic stiffness can stabilize while gravity may stabilize or destabilize.The elastic field can simplify control through self-stabilization,.Source: Posture regulation · pp. 15–18
  • Adding proportional and derivative feedback preserves local posture stability under stated damping and potential conditions; nonnegative derivative gain injects damping, while large proportional gains can stiffen the robot and amplify noise or neglected dynamics.Nonlinear integral actions may compensate steady-state error and achieve global stabilization.Source: Posture regulation · pp. 18–19

Trajectory tracking

  • For slowly varying references, posture controllers can keep the state near the desired trajectory, with higher gains and slower references shrinking the steady-state neighborhood.Zero steady-state tracking error requires explicit dynamic-force compensation; the section gives a feedforward controller and states local exponential stabilization conditions for its feedback-augmented form.Source: Trajectory tracking · pp. 19–20
  • For generic trajectories, feedforward dynamic compensation plus feedback achieves local exponential stabilization under gain conditions that tighten with gravity-gradient magnitude, reference speed, and acceleration; state-based PD+ can track perfectly even with zero gains.A robust variant without direct velocity measurement is also proposed and tested.Source: Trajectory tracking · p. 20

Underactuation, Actuators Dynamics, and Task Execution

The section identifies underactuation, actuator dynamics and constraints, task-space control, and environmental interaction as challenges for model-based soft-robot control. It presents control approaches alongside assumptions and stability or modeling problems that remain unresolved.

Dealing with undearctuation in shape control

  • Underactuation can make generic shapes and states unattainable; local stabilization requires actuation aligned with directions where effective stiffness loses rank, while repulsive unactuated directions may require dynamic coupling.Stabilizing unstable equilibria through non-collocated feedback is largely unexplored; analyzes a soft inverted pendulum and identifies a range of low stiffnesses where such feedback can stabilize it.Source: Dealing with undearctuation in shape… · pp. 21–22
  • Underactuated shape control becomes more complex for configuration-dependent actuation, whose local changes may destabilize the system; extending feedback results to trajectory tracking remains a substantial challenge.Linearized models around an equilibrium or desired trajectory are described as practical alternatives,.Source: Dealing with undearctuation in shape… · p. 21

Actuators dynamics and constraints

  • Actuator dynamics strongly shape soft-robot behavior but are rarely modeled; singular perturbation or backstepping can address them, while bounds and unilateral inputs motivate model-based allocation or MPC.The cited soft-robot backstepping example uses a single segment with linear robot and airflow models.Source: Actuators dynamics and constraints · p. 23

Task space regulation and tracking

  • Underactuated task-space kinematic control requires fast actuator-side regulation, stable equilibria under constant actuation, and a one-to-one actuator-to-configuration map.When these assumptions hold, control can operate from actuator space to task space; the resulting task Jacobian can have full row rank when task dimension is no greater than the number of actuators.Source: Task space regulation and tracking · p. 25
  • Operational-space control can generate fully actuated task-space dynamics under a full-rank condition, but provable convergence of the full state under underactuation remains open.The formulation supports strong underactuation, including m << n, but task-space behavior alone does not ensure convergence of (q, ˙q).Source: Task space regulation and tracking · p. 26

Interaction with the environment

  • Environmental contact is sparsely studied in model-based control, yet external wrenches can help overcome underactuation and input saturation or enlarge the accessible space.Soft-robot bracing is demonstrated in, and a vine-robot planner sequences interactions to reach desired locations. Interaction control also trades open-loop stability against compliance, motivating stiffness adjustment.Source: Interaction with the environment · pp. 27–28

leveraging data and machine learning in model-based control

This section surveys ways to integrate data and learning into model-based soft-robot control, motivated by incomplete models and inherent uncertainty.

leveraging data and machine learning in model-based control

  • Model incompleteness and inherent uncertainty make integrating data into model-based soft-robot control important.Challenges include models that are difficult or computationally expensive to obtain, unknown environments, unreliable sensors and actuators, and changing physical parameters.Source: leveraging data and machine learning… · pp. 29–30

Using models to drive learning

Adaptive control

  • Adaptive control updates unknown parameters online within a model-based feedback controller; when they describe the real system, updates stop and standard model-based control results.Soft-robot applications include adaptive visual servoing, single-actuator control, adaptive MPC,, and disturbance estimation or compensation,.Source: Adaptive control · pp. 30–31

Iterative Learning Control

  • Iterative learning control uses a nominal model to update feedforward actions across repeated task attempts, aiming for zero error; it is robust to model uncertainty and inherently stable if the robot is not too soft.Pure feedforward actions do not disrupt physical softness; applications include learning optimal-trajectory actuation patterns and improving soft-worm crawling,.Source: Iterative Learning Control · p. 31

Simulators as virtual environments

  • First-principles models can create virtual environments for robots to evolve or learn skills; differentiable simulators enable gradient-based supervised learning and behavior optimization.Source: Simulators as virtual environments · p. 32

Control loops based on learned models

  • End-to-end controller learning can limit explainability and make closed-loop performance, stability, and learning difficult; learning a model instead enables model-based control.Source: Control loops based on learned models · p. 32

Learning the model, by using the model

  • First-principles models can warm-start black-box model learning, while model-driven data acquisition can target nonlinear stiffness or robot geometry.Examples include pre-training a neural network with a pneumatic-actuator linear model before experimental fine-tuning, and using a finite-element model to guide stiffness-data acquisition.Source: Learning the model, by using the model · p. 32

Closing the loop

  • Learned kinematic and dynamic models support model-based control, including inverse-kinematics solutions, open-loop actions, MPC, LQR, and linear MPC.A learned forward-kinematics model resolves redundancy when solving the inverse problem; learned dynamics support linear MPC, and Koopman-based LQR [242] or linear MPC.Source: Closing the loop · pp. 32–33

Conclusions

The survey organizes model-based soft-robot control in a common framework, showing both connections to established robotics and intrinsic control challenges. It concludes that open theoretical questions must ultimately support real robots’ motor capabilities.

Conclusions

  • A common framework and terminology reveal links to rigid-robot control and enable controllers to be ported to soft continua after discretization.The survey also clarifies differences from related fields, especially the many degrees of freedom that make soft robots intrinsically underactuated.Source: Conclusions · p. 33
  • Many degrees of freedom make soft robots intrinsically underactuated, but positive-definite elastic potential and strictly dissipative forces simplify control across discretizations.Without these simplifying effects, the control challenge would be too complex except in straightforward cases.Source: Conclusions · p. 33
  • Despite progress, model-based soft-robotics research remains nascent, with open questions on underactuation, neglected non-actuated dynamics, unstable equilibria, and compliant, fast, precise motion.The challenges also include controlled movement during continuous interaction with unstructured environments and integrating embodied intelligence with control design.Source: Conclusions · p. 33
  • Theoretical advances should contribute to soft robotics’ experimental vision by endowing real robots with unmatched motor capabilities.The conclusion frames this vision as the discipline’s aim to revolutionize how robots enter people’s lives.Source: Conclusions · pp. 33–34

Sidebar: Dynamics of a Constant Curvature Segment

The sidebar derives the geometry and scalar dynamics of a planar constant-curvature segment as an accessible model of a soft robot. It shows how the segment resembles a lumped rigid-link model structurally while differing in geometry and dynamic expressions.

Sidebar: Dynamics of a Constant Curvature Segment

  • A fixed-length planar constant-curvature segment is fully described by scalar curvature q, also its bending angle, and extends a revolute joint connecting two rigid links.The segment’s shape is defined for q = 0, though division by zero in the expressions can cause numerical instability; the rigid-link and segment shapes increasingly diverge as |q| grows.Source: Sidebar: Dynamics of a Constant… · p. 35, Figure 11 · p. 38
  • The segment’s inertia decreases toward zero as |q| increases, while at q = 0 it exceeds the rigid approximation’s mL2/24 because that model neglects motion of the robot’s lower half.The segment and rigid approximation are perfectly superimposed in the straight configuration, despite their different inertias.Source: Sidebar: Dynamics of a Constant… · p. 36
  • When qdot is nonzero, the centrifugal action −C(q, qdot)qdot tends to increase |q|.The centrifugal term arises because the segment’s inertia M varies with curvature.Source: Sidebar: Dynamics of a Constant… · p. 36
  • Gravity produces a curvature-dependent torque with symmetries G(q, ϕ) = −G(q, ϕ + π) and G(q, ϕ) = −G(−q, −ϕ).The sidebar’s plotted gravity case aligns the gravity field with the segment’s straight configuration.Source: Sidebar: Dynamics of a Constant… · p. 37
  • Under the constant-curvature assumptions, elastic and damping forces are linear, with elasticity proportional to q and damping mapped from local curvature variation.The local stiffness is assumed nearly constant along the segment; local damping is proportional to curvature variation.Source: Sidebar: Dynamics of a Constant… · p. 37
  • The resulting scalar second-order dynamics has the same structural properties as a lumped joint with parallel impedance, but more complex expressions; CC and R-PEA evolutions are qualitatively similar and both differ from R.The examples compare the constant-curvature segment with rigid-link approximations with and without parallel springs under three torque and gravity settings.Source: Sidebar: Dynamics of a Constant… · pp. 37, 40, Figure 13 · p. 40

Better than Rigid Robots: Exploiting Softness in Model-Based Control

Soft-body impedance provides distributed physical feedback, while elasticity can support dynamic behaviors beyond rigid-robot capabilities; control-ready descriptions for some of these behaviors remain an open challenge.

Better than Rigid Robots: Exploiting Softness in Model-Based Control

Sidebar: Model-based Perception of Shape and Forces

Models can infer continuum configuration from sparse sensor measurements, while the persistent potential field links robot shape and forces, supporting perception in both directions.

Sidebar: Model-based Perception of Shape and Forces

  • Because sensors rarely measure configuration q directly, perception must infer q from measured h(q), a problem formally equivalent to task-space regulation.Constant-curvature models, constrained optimization, and dynamics-informed observers provide alternative inversion approaches.Source: Sidebar: Model-based Perception of… · p. 42
  • Closed-form inverse kinematics recovers constant-curvature configurations, constrained optimization handles lumped-joint robots, and Extended Kalman observers use dynamics,.Source: Sidebar: Model-based Perception of… · p. 42
  • At steady state, static models connect shape and forces: base six-axis force/torque measurements infer posture, while posture estimates end-effector wrench for lightweight robots,.Source: Sidebar: Model-based Perception of… · p. 42
  • With sufficient shape information, piecewise-constant-curvature and modal models regress external-force location and intensity, while static Cosserat inversion estimates force distribution.Source: Sidebar: Model-based Perception of… · p. 42
  • Disturbance observers detect interactions when robot mass is non-negligible, and static FEM inversion with capacitive and pneumatic sensing detects and characterizes contacts.The contact-detection method can also be applied to soft surfaces.Source: Sidebar: Model-based Perception of… · p. 42
  • Tip forces and robot shape can be estimated together by combining base-load measurements with a static Cosserat model.Source: Sidebar: Model-based Perception of… · p. 42

Sidebar: Robust control

Soft-robot models remain uncertain because material and manufacturing variability and state discretization leave dynamics imperfectly represented. Controllers can accommodate this uncertainty through learning or robust design, including techniques used in existing soft-robot controllers.

Sidebar: Robust control

  • Material and manufacturing variability, together with dynamics ignored by state discretization, make uncertainty unavoidable in soft-robot models.Advances in materials and modeling may mitigate but are unlikely to eliminate the issue, so model-based strategies must account for it.Source: Sidebar: Robust control · p. 43
  • Many soft-robot control techniques are implicitly robust by avoiding strong reliance on feedback model cancellations or high gains.Learning loops are another way to account for model uncertainty.Source: Sidebar: Robust control · p. 43
  • Explicit approaches include linear robust H∞ control,, interval-arithmetic tracking control, robust sliding-model control,,, and fractional-order control,.The H∞ examples control a single segment and a planar soft robot, respectively; interval arithmetic is used to achieve prescribed tracking performance in the presence of uncertainties.Source: Sidebar: Robust control · p. 43

Sidebar: Infinite Dimensional Control

Finite-dimensional approximations simplify controller design but do not resolve mathematical issues of convergence and well-definiteness; infinite-dimensional analysis can rule out control spillover and yield more compact, interpretable solutions, although PDE control has focused mainly on linear systems,,,, –.

Sidebar: Infinite Dimensional Control

  • Finite-dimensional models simplify feedback design and can capture dynamics to desired precision, but their practical equivalence to continuum models is not mathematically rigorous,.The argument requires keeping controller discretization fixed as model discretization increases. Approximation error can shift the equilibrium, and local convergence then requires a condition centered on that new equilibrium; analysis grows more complex with nontrivial feedback,.Source: Sidebar: Infinite Dimensional Control · p. 44
  • Infinite-dimensional analysis can exclude control spillover and provide more compact, interpretable solutions, but nonlinear PDE control remains an active research area,, –.Control spillover occurs when controllers designed from finite-dimensional approximations excite high-order, otherwise stable dynamics, degrading performance and potentially causing instability.Source: Sidebar: Infinite Dimensional Control · p. 44
  • Most PDE-control applications to continuum mechanics use linear Euler–Bernoulli or Timoshenko beams as small-displacement approximations of nonlinear rod dynamics [287, Secs. 4,5],.For Euler–Bernoulli beams, boundary feedback suppresses vibrations,, with extensions for output constraints and disturbances and input constraints. Timoshenko-beam work uses damping injection for vibration absorption,, combines it with energy shaping for configuration control, or regulates contact force assuming dissipative environmental damping.Source: Sidebar: Infinite Dimensional Control · pp. 44–45
  • Nonlinear beam studies address large deformations through passivity-based stabilization, practically stable boundary regulation, and boundary feedback for large deflections and rotations with small strains.The boundary-feedback result uses a mapping to a one-dimensional first-order semilinear hyperbolic system.Source: Sidebar: Infinite Dimensional Control · p. 45
  • Kirchhoff-rod and Cosserat-theory work examines open-loop stability, experimental kinematic control, quasi-static soft-object manipulation, and soft-robot posture regulation [303],.The quasi-static strategy proves that equilibria under changes in boundary position and orientation form a smooth manifold parametrizable with one chart; posture-regulation convergence is discussed under finite-element approximation.Source: Sidebar: Infinite Dimensional Control · p. 45

Authors Biography

The authors bring expertise spanning soft-robot control, deformable-object simulation, robotics, AI, and data science. Their biographies also describe academic leadership, research appointments, and professional recognition.

Authors Biography

  • Cosimo Della Santina studies model-based control of soft robots and elastic systems, combining machine learning and model-based strategies for mechanical systems, grasping, and manipulation.He is an Assistant Professor at TU Delft and Research Scientist at DLR, and received his robotics Ph.D. from the University of Pisa in 2019.Source: Authors Biography · p. 46
  • Christian Duriez researches soft-robot models and control, finite-element methods, contact response, and mechanical interactions, developing results in the SOFA framework.He leads INRIA’s DEFROST team and was one of the founders of InSimo.Source: Authors Biography · p. 46
  • Daniela Rus’s research interests are robotics, artificial intelligence, and data science; she directs MIT CSAIL and the Toyota-CSAIL Joint Research Center.She is a MacArthur Fellow, a fellow of ACM, AAAI, and IEEE, and a member of the National Academy of Engineering and the American Academy of Arts and Sciences.Source: Authors Biography · p. 46

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