Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot

This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3D (spatial) bipedal robot consisting of a torso, two legs, and passive (unactuated) point feet. The contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and 6 actuators. The interest of studying robots with point feet is that the robot's natural dynamics must be explicitly taken into account to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit. This method allows the computations to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincar\'e map of the hybrid zero dynamics. Three strategies are explored. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an event-based controller. In the third approach, the effect of output selection is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller

RF sensing for real-time monitoring of plasma processing

A novel sensing system based on the microwave resonance probe is compared to standard RF metrology. The system uses an antenna in the glow discharge to excite the bulk plasma at a frequency range of 30 MHz to 1 GHz. Standard RF metrology is implemented by measuring the fundamental and five harmonics of the RF power signal. An experiment varying power, pressure, CF4CF4 and O2O2 is constructed. Using a subset of the data to regress a model, standard RF sensing reconstructs the experimental variables with a best average R2R2 of 0.586 at a high model coefficient variance (σb2),(σb2), whereas the novel sensing system results in a best average R2R2 of 0.804 and an order of magnitude lower σb2.σb2. © 1998 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87554/2/442_1.pd

Control Barrier Function Based Quadratic Programs for Safety Critical Systems

Safety critical systems involve the tight coupling between potentially conflicting control objectives and safety constraints. As a means of creating a formal framework for controlling systems of this form, and with a view toward automotive applications, this paper develops a methodology that allows safety conditions -- expressed as control barrier functions -- to be unified with performance objectives -- expressed as control Lyapunov functions -- in the context of real-time optimization-based controllers. Safety conditions are specified in terms of forward invariance of a set, and are verified via two novel generalizations of barrier functions; in each case, the existence of a barrier function satisfying Lyapunov-like conditions implies forward invariance of the set, and the relationship between these two classes of barrier functions is characterized. In addition, each of these formulations yields a notion of control barrier function (CBF), providing inequality constraints in the control input that, when satisfied, again imply forward invariance of the set. Through these constructions, CBFs can naturally be unified with control Lyapunov functions (CLFs) in the context of a quadratic program (QP); this allows for the achievement of control objectives (represented by CLFs) subject to conditions on the admissible states of the system (represented by CBFs). The mediation of safety and performance through a QP is demonstrated on adaptive cruise control and lane keeping, two automotive control problems that present both safety and performance considerations coupled with actuator bounds

Contact-Aided Invariant Extended Kalman Filtering for Legged Robot State Estimation

This paper derives a contact-aided inertial navigation observer for a 3D bipedal robot using the theory of invariant observer design. Aided inertial navigation is fundamentally a nonlinear observer design problem; thus, current solutions are based on approximations of the system dynamics, such as an Extended Kalman Filter (EKF), which uses a system's Jacobian linearization along the current best estimate of its trajectory. On the basis of the theory of invariant observer design by Barrau and Bonnabel, and in particular, the Invariant EKF (InEKF), we show that the error dynamics of the point contact-inertial system follows a log-linear autonomous differential equation; hence, the observable state variables can be rendered convergent with a domain of attraction that is independent of the system's trajectory. Due to the log-linear form of the error dynamics, it is not necessary to perform a nonlinear observability analysis to show that when using an Inertial Measurement Unit (IMU) and contact sensors, the absolute position of the robot and a rotation about the gravity vector (yaw) are unobservable. We further augment the state of the developed InEKF with IMU biases, as the online estimation of these parameters has a crucial impact on system performance. We evaluate the convergence of the proposed system with the commonly used quaternion-based EKF observer using a Monte-Carlo simulation. In addition, our experimental evaluation using a Cassie-series bipedal robot shows that the contact-aided InEKF provides better performance in comparison with the quaternion-based EKF as a result of exploiting symmetries present in the system dynamics.Comment: Published in the proceedings of Robotics: Science and Systems 201

Fall Prediction for Bipedal Robots: The Standing Phase

This paper presents a novel approach to fall prediction for bipedal robots, specifically targeting the detection of potential falls while standing caused by abrupt, incipient, and intermittent faults. Leveraging a 1D convolutional neural network (CNN), our method aims to maximize lead time for fall prediction while minimizing false positive rates. The proposed algorithm uniquely integrates the detection of various fault types and estimates the lead time for potential falls. Our contributions include the development of an algorithm capable of detecting abrupt, incipient, and intermittent faults in full-sized robots, its implementation using both simulation and hardware data for a humanoid robot, and a method for estimating lead time. Evaluation metrics, including false positive rate, lead time, and response time, demonstrate the efficacy of our approach. Particularly, our model achieves impressive lead times and response times across different fault scenarios with a false positive rate of 0. The findings of this study hold significant implications for enhancing the safety and reliability of bipedal robotic systems.Comment: Submitted to ICRA 2024. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Exploring Kinodynamic Fabrics for Reactive Whole-Body Control of Underactuated Humanoid Robots

For bipedal humanoid robots to successfully operate in the real world, they must be competent at simultaneously executing multiple motion tasks while reacting to unforeseen external disturbances in real-time. We propose Kinodynamic Fabrics as an approach for the specification, solution and simultaneous execution of multiple motion tasks in real-time while being reactive to dynamism in the environment. Kinodynamic Fabrics allows for the specification of prioritized motion tasks as forced spectral semi-sprays and solves for desired robot joint accelerations at real-time frequencies. We evaluate the capabilities of Kinodynamic fabrics on diverse physically challenging whole-body control tasks with a bipedal humanoid robot both in simulation and in the real-world. Kinodynamic Fabrics outperforms the state-of-the-art Quadratic Program based whole-body controller on a variety of whole-body control tasks on run-time and reactivity metrics in our experiments. Our open-source implementation of Kinodynamic Fabrics as well as robot demonstration videos can be found at this url: https://adubredu.github.io/kinofabs

Sampling, infinite zeros and decoupling of linear systems,

In order to understand more fully some of the trade-offs involved in using a sampled-data representation of a continuous-time system, the effects of time-sampling on the ability to achieve disturbance decoupling and input-output decoupling for linear systems are investigated. It is shown that disturbance decouplability is lost through sampling whereas row-by-row dynamic input-output decouplability is preserved in a very strong way. These results are obtained by analyzing the structure at infinity of a sampled-data system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27318/1/0000340.pd