arXiv subjects

Tongjia Zheng

Publications and source records attributed to Tongjia Zheng.

17 recordsLinked to original sources

arXiv2026

Estimating Dynamic Soft Continuum Robot States From Boundaries

State estimation is one of the fundamental problems in robotics. For soft continuum robots, this task is particularly challenging because their states (poses, strains, internal wrenches, and velocities) are inherently \textit{infinite-dimensional} due to continuous deformability, while sensing provides only discrete measurements. Recently, a dynamic state estimation method known as a \textit{boundary observer} was introduced, which uses Cosserat rod theory to recover all states from tip velocity measurements. In this work, we present a dual design that instead relies on measuring the internal wrench at the robot's base. Despite the duality, this approach offers a key practical advantage: it requires only a force/torque (FT) sensor at the base and eliminates the need for external motion capture systems. Both observer types are inspired by energy dissipation principles and can be combined to enhance performance. We conduct a Lyapunov-based analysis to study convergence and reveal a useful property: as observer gains increase, the convergence rate first improves and then degrades. This convex trend enables efficient gain tuning. We also identify cases where linear and angular states are fully determined by each other, further relaxing sensing requirements. In summary, this work achieves dynamic infinite-dimensional state estimation with minimal sensing requirements and systematic parameter tuning, which has not been demonstrated in existing approaches. Simulation and experimental studies using a tendon-driven continuum robot validate convergence under fast dynamic motions, the existence of optimal gains, robustness to external forces, measurement noise, and model uncertainty, and real-time computational performance.

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arXiv2026

Do Rigid-Body Simulators Dream of Soft Robots? Learning Contact-Rich Manipulation for Tendon-Driven Continuum Robots

Learning contact-rich, whole-body manipulation for soft continuum robots is held back by the lack of simulation infrastructure that has accelerated rigid-robot manipulation. Existing soft robot simulators are physically grounded but lack the contact handling, actuation support, or learning integration needed for contact-rich manipulation; rigid-body approximations offer these capabilities but sacrifice physical grounding. We bridge this gap for tendon-driven continuum robots (TDCRs) by deriving a continuum-mechanics-informed discretization that places the soft robot natively inside MuJoCo, unifying tendon forces, body contact, and dynamics in a single physics pipeline. We validate the simulator against a Cosserat rod reference (static and dynamic) and real TDCR hardware. We then train state-based imitation learning policies via teleoperation in simulation and deploy them zero-shot to a physical 3-segment TDCR on a 7-DoF Franka arm across two contact-rich manipulation tasks. To our knowledge, this is the first demonstration of sim-to-real transfer for contact-rich manipulation with continuum robots.

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arXiv2024

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

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. This work focuses on soft robotic manipulators, also known as continuum robots. We design an observer algorithm based on the well-known Cosserat rod theory, which models continuum robots by nonlinear partial differential equations (PDEs) evolving in geometric Lie groups. The observer can estimate all infinite-dimensional continuum robot states, including 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. The distinct advantage of this PDE-based design is that it can be implemented using any existing numerical implementation for Cosserat rod models. All theoretical convergence guarantees will be preserved, regardless of the discretization method. We call this property ``one design for any discretization''. 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.

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arXiv2024

Estimating Infinite-Dimensional Continuum Robot States From the Tip

Knowing the state of a robot is critical for many problems, such as feedback control. For continuum robots, state estimation is an incredible challenge. 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 experimental data recorded from a tendon-driven continuum robot. We feed the recorded tendon force and tip measurements into a numerical solver of the Cosserat rod model based on our 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.

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arXiv2024

Multi-Robot-Guided Crowd Evacuation: Two-Scale Modeling and Control

Emergency evacuation describes a complex situation involving time-critical decision-making by evacuees. Mobile robots are being actively explored as a potential solution to provide timely guidance. In this work, we study a robot-guided crowd evacuation problem where a small group of robots is used to guide a large human crowd to safe locations. The challenge lies in how to use micro-level human-robot interactions to indirectly influence a population that significantly outnumbers the robots to achieve the collective evacuation objective. To address the challenge, we follow a two-scale modeling strategy and explore hydrodynamic models, which consist of a family of microscopic social force models that describe how human movements are locally affected by other humans, the environment, and robots, and associated macroscopic equations for the temporal and spatial evolution of the crowd density and flow velocity. We design controllers for the robots such that they not only automatically explore the environment (with unknown dynamic obstacles) to cover it as much as possible, but also dynamically adjust the directions of their local navigation force fields based on the real-time macrostates of the crowd to guide the crowd to a safe location. We prove the stability of the proposed evacuation algorithm and conduct extensive simulations to investigate the performance of the algorithm with different combinations of human numbers, robot numbers, and obstacle settings.

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arXiv2023

Learning Evacuee Models from Robot-Guided Emergency Evacuation Experiments

Recent research has examined the possibility of using robots to guide evacuees to safe exits during emergencies. Yet, there are many factors that can impact a person's decision to follow a robot. Being able to model how an evacuee follows an emergency robot guide could be crucial for designing robots that effectively guide evacuees during an emergency. This paper presents a method for developing realistic and predictive human evacuee models from physical human evacuation experiments. The paper analyzes the behavior of 14 human subjects during physical robot-guided evacuation. We then use the video data to create evacuee motion models that predict the person's future positions during the emergency. Finally, we validate the resulting models by running a k-fold cross-validation on the data collected during physical human subject experiments. We also present performance results of the model using data from a similar simulated emergency evacuation experiment demonstrating that these models can serve as a tool to predict evacuee behavior in novel evacuation simulations.

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arXiv2023

Stable Real-Time Feedback Control of a Pneumatic Soft Robot

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.

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arXiv2022

Task Space Tracking of Soft Manipulators: Inner-Outer Loop Control Based on Cosserat-Rod Models

Soft robots are robotic systems made of deformable materials and exhibit unique flexibility that can be exploited for complex environments and tasks. However, their control problem has been considered a challenging subject because they are of infinite degrees of freedom and highly under-actuated. Existing studies have mainly relied on simplified and approximated finite-dimensional models. In this work, we exploit infinite-dimensional nonlinear control for soft robots. We adopt the Cosserat-rod theory and employ nonlinear partial differential equations (PDEs) to model the kinematics and dynamics of soft manipulators, including their translational motions (for shear and elongation) and rotational motions (for bending and torsion). The objective is to achieve position tracking of the whole manipulator in a planar task space by controlling the moments (generated by actuators). The control design is inspired by the energy decay property of damped wave equations and has an inner-outer loop structure. In the outer loop, we design desired rotational motions that rotate the translational component into a direction that asymptotically dissipates the energy associated with position tracking errors. In the inner loop, we design inputs for the rotational components to track their desired motions, again by dissipating the rotational energy. We prove that the closed-loop system is exponentially stable and evaluate its performance through simulations.

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arXiv2022

PDE-based Dynamic Control and Estimation of Soft Robotic Arms

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.

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arXiv2022

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

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.

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arXiv2022

Backstepping Mean-Field Density Control for Large-Scale Heterogeneous Nonlinear Stochastic Systems

This work studies the problem of controlling the mean-field density of large-scale stochastic systems, which has applications in various fields such as swarm robotics. Recently, there is a growing amount of literature that employs mean-field partial differential equations (PDEs) to model the density evolution and uses density feedback to design control laws which, by acting on individual systems, stabilize their density towards a target profile. In spite of its stability property and computational efficiency, the success of density feedback relies on assuming the systems to be homogeneous first-order integrators (plus white noise) and ignores higher-order dynamics, making it less applicable in practice. In this work, we present a backstepping design algorithm that extends density control to heterogeneous and higher-order stochastic systems in strict-feedback forms. We show that the strict-feedback form in the individual level corresponds to, in the collective level, a PDE (of densities) distributedly driven by a collection of heterogeneous stochastic systems. The presented backstepping design then starts with a density feedback design for the PDE, followed by a sequence of stabilizing design for the remaining stochastic systems. We present a candidate control law with stability proof and apply it to nonholonomic mobile robots. A simulation is included to verify the effectiveness of the algorithm.

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arXiv2022

Feedback Interconnected Mean-Field Density Estimation and Control

Swarm robotic systems have foreseeable applications in the near future. Recently, there has been an increasing amount of literature that employs mean-field partial differential equations (PDEs) to model the time-evolution of the probability density of swarm robotic systems and uses density feedback to design stabilizing control laws that act on individuals such that their density converges to a target profile. However, it remains largely unexplored considering problems of how to estimate the mean-field density, how the density estimation algorithms affect the control performance, and whether the estimation performance in turn depends on the control algorithms. In this work, we focus on studying the interplay of these algorithms. Specifically, we propose new density control laws which use the mean-field density and its gradient as feedback, and prove that they are globally input-to-state stable (ISS) with respect to estimation errors. Then, we design filtering algorithms to estimate the density and its gradient separately, and prove that these estimates are convergent assuming the control laws are known. Finally, we show that the feedback interconnection of these estimation and control algorithms is still globally ISS, which is attributed to the bilinearity of the PDE system. An agent-based simulation is included to verify the stability of these algorithms and their feedback interconnection.

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arXiv2021

Distributed Mean-Field Density Estimation for Large-Scale Systems

This work studies how to estimate the mean-field density of large-scale systems in a distributed manner. Such problems are motivated by the recent swarm control technique that uses mean-field approximations to represent the collective effect of the swarm, wherein the mean-field density (especially its gradient) is usually used in feedback control design. In the first part, we formulate the density estimation problem as a filtering problem of the associated mean-field partial differential equation (PDE), for which we employ kernel density estimation (KDE) to construct noisy observations and use filtering theory of PDE systems to design an optimal (centralized) density filter. It turns out that the covariance operator of observation noise depends on the unknown density. Hence, we use approximations for the covariance operator to obtain a suboptimal density filter, and prove that both the density estimates and their gradient are convergent and remain close to the optimal one using the notion of input-to-state stability (ISS). In the second part, we continue to study how to decentralize the density filter such that each agent can estimate the mean-field density based on only its own position and local information exchange with neighbors. We prove that the local density filter is also convergent and remains close to the centralized one in the sense of ISS. Simulation results suggest that the centralized suboptimal density filter is able to generate convergent density estimates, and the local density filter is able to converge and remain close to the centralized filter.

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arXiv2021

Distributed Density Filtering for Large-Scale Systems Using Mean-Filed Models

This work studies distributed (probability) density estimation of large-scale systems. Such problems are motivated by many density-based distributed control tasks in which the real-time density of the swarm is used as feedback information, such as sensor deployment and city traffic scheduling. This work is built upon our previous work [1] which presented a (centralized) density filter to estimate the dynamic density of large-scale systems through a novel integration of mean-field models, kernel density estimation (KDE), and infinite-dimensional Kalman filters. In this work, we further study how to decentralize the density filter such that each agent can estimate the global density only based on its local observation and communication with neighbors. This is achieved by noting that the global observation constructed by KDE is an average of the local kernels. Hence, dynamic average consensus algorithms are used for each agent to track the global observation in a distributed way. We present a distributed density filter which requires very little information exchange, and study its stability and optimality using the notion of input-to-state stability. Simulation results suggest that the distributed filter is able to converge to the centralized filter and remain close to it.

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arXiv2021

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

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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arXiv2021

Transporting Robotic Swarms via Mean-Field Feedback Control

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.

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arXiv2020

PDE-based Dynamic Density Estimation for Large-scale Agent Systems

Large-scale agent systems have foreseeable applications in the near future. Estimating their macroscopic density is critical for many density-based optimization and control tasks, such as sensor deployment and city traffic scheduling. In this paper, we study the problem of estimating their dynamically varying probability density, given the agents' individual dynamics (which can be nonlinear and time-varying) and their states observed in real-time. The density evolution is shown to satisfy a linear partial differential equation uniquely determined by the agents' dynamics. We present a density filter which takes advantage of the system dynamics to gradually improve its estimation and is scalable to the agents' population. Specifically, we use kernel density estimators (KDE) to construct a noisy measurement and show that, when the agents' population is large, the measurement noise is approximately ``Gaussian''. With this important property, infinite-dimensional Kalman filters are used to design density filters. It turns out that the covariance of measurement noise depends on the true density. This state-dependence makes it necessary to approximate the covariance in the associated operator Riccati equation, rendering the density filter suboptimal. The notion of input-to-state stability is used to prove that the performance of the suboptimal density filter remains close to the optimal one. Simulation results suggest that the proposed density filter is able to quickly recognize the underlying modes of the unknown density and automatically ignore outliers, and is robust to different choices of kernel bandwidth of KDE.

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