11 research outputs found

    PDE-based Dynamic Control and Estimation of Soft Robotic Arms

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    Compared with traditional rigid-body robots, soft robots not only exhibit unprecedented adaptation and flexibility but also present novel challenges in their modeling and control because of their infinite degrees of freedom. Most of the existing approaches have mainly relied on approximated models so that the well-developed finite-dimensional control theory can be exploited. However, this may bring in modeling uncertainty and performance degradation. Hence, we propose to exploit infinite-dimensional analysis for soft robotic systems. Our control design is based on the increasingly adopted Cosserat rod model, which describes the kinematics and dynamics of soft robotic arms using nonlinear partial differential equations (PDE). We design infinite-dimensional state feedback control laws for the Cosserat PDE model to achieve trajectory tracking (consisting of position, rotation, linear and angular velocities) and prove their uniform tracking convergence. We also design an infinite-dimensional extended Kalman filter on Lie groups for the PDE system to estimate all the state variables (including position, rotation, strains, curvature, linear and angular velocities) using only position measurements. The proposed algorithms are evaluated using simulations

    Full State Estimation of Continuum Robots From Tip Velocities: A Cosserat-Theoretic Boundary Observer

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    State estimation of robotic systems is essential to implementing feedback controllers which usually provide better robustness to modeling uncertainties than open-loop controllers. However, state estimation of soft robots is very challenging because soft robots have theoretically infinite degrees of freedom while existing sensors only provide a limited number of discrete measurements. In this paper, we design an observer for soft continuum robotic arms based on the well-known Cosserat rod theory which models continuum robotic arms by nonlinear partial differential equations (PDEs). The observer is able to estimate all the continuum (infinite-dimensional) robot states (poses, strains, and velocities) by only sensing the tip velocity of the continuum robot (and hence it is called a ``boundary'' observer). More importantly, the estimation error dynamics is formally proven to be locally input-to-state stable. The key idea is to inject sequential tip velocity measurements into the observer in a way that dissipates the energy of the estimation errors through the boundary. Furthermore, this boundary observer can be implemented by simply changing a boundary condition in any numerical solvers of Cosserat rod models. Extensive numerical studies are included and suggest that the domain of attraction is large and the observer is robust to uncertainties of tip velocity measurements and model parameters

    Transporting Robotic Swarms via Mean-Field Feedback Control

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    With the rapid development of AI and robotics, transporting a large swarm of networked robots has foreseeable applications in the near future. Existing research in swarm robotics has mainly followed a bottom-up philosophy with predefined local coordination and control rules. However, it is arduous to verify the global requirements and analyze their performance. This motivates us to pursue a top-down approach, and develop a provable control strategy for deploying a robotic swarm to achieve a desired global configuration. Specifically, we use mean-field partial differential equations (PDEs) to model the swarm and control its mean-field density (i.e., probability density) over a bounded spatial domain using mean-field feedback. The presented control law uses density estimates as feedback signals and generates corresponding velocity fields that, by acting locally on individual robots, guide their global distribution to a target profile. The design of the velocity field is therefore centralized, but the implementation of the controller can be fully distributed -- individual robots sense the velocity field and derive their own velocity control signals accordingly. The key contribution lies in applying the concept of input-to-state stability (ISS) to show that the perturbed closed-loop system (a nonlinear and time-varying PDE) is locally ISS with respect to density estimation errors. The effectiveness of the proposed control laws is verified using agent-based simulations

    Estimating Infinite-Dimensional Continuum Robot States From the Tip

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    Knowing the state of a robot is critical for many problems, such as feedback control. For continuum robots, state estimation is incredibly challenging. First, the motion of a continuum robot involves many kinematic states, including poses, strains, and velocities. Second, all these states are infinite-dimensional due to the robot's flexible property. It has remained unclear whether these infinite-dimensional states are observable at all using existing sensing techniques. Recently, we presented a solution to this challenge. It was a mechanics-based dynamic state estimation algorithm, called a Cosserat theoretic boundary observer, which could recover all the infinite-dimensional robot states by only measuring the velocity twist of the tip. In this work, we generalize the algorithm to incorporate tip pose measurements for more tuning freedom. We also validate this algorithm offline using recorded experimental data of a tendon-driven continuum robot. Specifically, we feed the recorded tension of the tendon and the recorded tip measurements into a numerical solver of the Cosserat rod model based on our continuum robot. It is observed that, even with purposely deviated initialization, the state estimates by our algorithm quickly converge to the recorded ground truth states and closely follow the robot's actual motion

    Stable Real-Time Feedback Control of a Pneumatic Soft Robot

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    Soft actuators offer compliant and safe interaction with an unstructured environment compared to their rigid counterparts. However, control of these systems is often challenging because they are inherently under-actuated, have infinite degrees of freedom (DoF), and their mechanical properties can change by unknown external loads. Existing works mainly relied on discretization and reduction, suffering from either low accuracy or high computational cost for real-time control purposes. Recently, we presented an infinite-dimensional feedback controller for soft manipulators modeled by partial differential equations (PDEs) based on the Cosserat rod theory. In this study, we examine how to implement this controller in real-time using only a limited number of actuators. To do so, we formulate a convex quadratic programming problem that tunes the feedback gains of the controller in real time such that it becomes realizable by the actuators. We evaluated the controller's performance through experiments on a physical soft robot capable of planar motions and show that the actual controller implemented by the finite-dimensional actuators still preserves the stabilizing property of the desired infinite-dimensional controller. This research fills the gap between the infinite-dimensional control design and finite-dimensional actuation in practice and suggests a promising direction for exploring PDE-based control design for soft robots

    Multi-Robot-Assisted Human Crowd Evacuation using Navigation Velocity Fields

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    This work studies a robot-assisted crowd evacuation problem where we control a small group of robots to guide a large human crowd to safe locations. The challenge lies in how to model human-robot interactions and design robot controls to indirectly control a human population that significantly outnumbers the robots. To address the challenge, we treat the crowd as a continuum and formulate the evacuation objective as driving the crowd density to target locations. We propose a novel mean-field model which consists of a family of microscopic equations that explicitly model how human motions are locally guided by the robots and an associated macroscopic equation that describes how the crowd density is controlled by the navigation velocity fields generated by all robots. Then, we design density feedback controllers for the robots to dynamically adjust their states such that the generated navigation velocity fields drive the crowd density to a target density. Stability guarantees of the proposed controllers are proven. Agent-based simulations are included to evaluate the proposed evacuation algorithms

    Field Estimation using Robotic Swarms through Bayesian Regression and Mean-Field Feedback

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    Recent years have seen an increased interest in using mean-field density based modelling and control strategy for deploying robotic swarms. In this paper, we study how to dynamically deploy the robots subject to their physical constraints to efficiently measure and reconstruct certain unknown spatial field (e.g. the air pollution index over a city). Specifically, the evolution of the robots' density is modelled by mean-field partial differential equations (PDEs) which are uniquely determined by the robots' individual dynamics. Bayesian regression models are used to obtain predictions and return a variance function that represents the confidence of the prediction. We formulate a PDE constrained optimization problem based on this variance function to dynamically generate a reference density signal which guides the robots to uncertain areas to collect new data, and design mean-field feedback-based control laws such that the robots' density converges to this reference signal. We also show that the proposed feedback law is robust to density estimation errors in the sense of input-to-state stability. Simulations are included to verify the effectiveness of the algorithms
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