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

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

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. 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

POMDP Model Learning for Human Robot Collaboration

Recent years have seen human robot collaboration (HRC) quickly emerged as a hot research area at the intersection of control, robotics, and psychology. While most of the existing work in HRC focused on either low-level human-aware motion planning or HRC interface design, we are particularly interested in a formal design of HRC with respect to high-level complex missions, where it is of critical importance to obtain an accurate and meanwhile tractable human model. Instead of assuming the human model is given, we ask whether it is reasonable to learn human models from observed perception data, such as the gesture, eye movements, head motions of the human in concern. As our initial step, we adopt a partially observable Markov decision process (POMDP) model in this work as mounting evidences have suggested Markovian properties of human behaviors from psychology studies. In addition, POMDP provides a general modeling framework for sequential decision making where states are hidden and actions have stochastic outcomes. Distinct from the majority of POMDP model learning literature, we do not assume that the state, the transition structure or the bound of the number of states in POMDP model is given. Instead, we use a Bayesian non-parametric learning approach to decide the potential human states from data. Then we adopt an approach inspired by probably approximately correct (PAC) learning to obtain not only an estimation of the transition probability but also a confidence interval associated to the estimation. Then, the performance of applying the control policy derived from the estimated model is guaranteed to be sufficiently close to the true model. Finally, data collected from a driver-assistance test-bed are used to train the model, which illustrates the effectiveness of the proposed learning method

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 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

Crystallization and Preliminary X-Ray Analysis of Human Muscle Creatine Kinase

This is the publisher's version, also available electronically from "http://scripts.iucr.org".Creatine kinase is a key enzyme in the energy homeostasis of cells and tissues with high and fluctuating energy demands. Human muscle MM creatine kinase is a dimeric protein with a molecular weight of \sim43 kDa for each subunit. It has been crystallized by the hanging-drop vapor-diffusion method using 2-methyl-2,4-pentanediol as precipitant. The crystals belong to the enantiomorphous space group P6_222 or P6_422 with cell parameters of a=b=89.11 and c=403.97 Å. The asymmetric unit of the crystal contains two subunits. A data set at 3.3 Å resolution has been collected using synchrotron radiation