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

2004 Student Estuarine Research Project

This report describes the results of the second education and bird-monitoring program conducted by sixth grade students, teachers, and volunteers at Portsmouth Middle School. The program combined classroom lessons with field trips to monitor bird populations in South Mill Pond, a tidal pond-like estuary in front of the school. The Pond has suffered over the years from a variety of environmental problems as the City of Portsmouth developed, including major watershed changes, combined sewer overflows, runoff from city streets and parking lots, and fill projects. Several years ago, the City initiated a long-term project to re-direct sewage away from the Pond to the City\u27s wastewater treatment plant. In 2001, scientists from the University of New Hampshire joined with the City, eighth grade students and teachers from Portsmouth Middle School, and local volunteers to construct experimental shellfish reefs and salt marsh habitat in the Pond. Our project was designed to allow sixth grade students to participate in the overall community-wide program of restoring South Mill Pond. It had the dual goal of education and monitoring an ongoing habitat restoration project, and it involved approximately 175 students during Spring 2004 and 162 students during Fall 2004. The education component consisted of teaching lessons on the ecology of coastal waters, how scientists study nature, and several biology topics, including identification and ecology of birds. The bird-monitoring component of the project involved observing, identifying and recording data on birds in and around the Pond. Each observation team consisted of four to six students and one or two adult volunteers, who in most cases were parents of students in the classes. The data collected in 2004 were compared to the 2003 (year of the first bird monitoring project) data, and represented the beginning of what is anticipated as a long-term monitoring project for South Mill Pond. Similar numbers of birds and major bird types were observed in Spring 2004 compared to Spring 2003. However, during Fall 2004 many more ducks were observed compared to the Spring monitoring periods, perhaps reflecting waterfowl migratory patterns in general. This suggests that South Mill Pond may be an important feeding area for migratory ducks. The observation site that included restored shellfish reefs had the highest numbers of birds during Fall 2004. Otherwise, similar numbers and types of birds were observed in all four observation sites of the Pond both years. Future bird monitoring efforts will be able to use these data to assess long-term recovery of South Mill Pond. Both goals of the project were accomplished in substantial ways. Sixth grade students participated in an extraordinary, hands-on science project and were given the opportunity to work with professionals. The unique curriculum and lesson plans included a student handbook on the ecology of the Pond. For nearly all of the science topics covered – including photosynthesis, food webs, pollution, habitats, and others - the focus was on how they related to South Mill Pond. This made all of the lessons much more interesting and relevant

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

Restricted Discrete Invariance and Self-Synchronization For Stable Walking of Bipedal Robots

Models of bipedal locomotion are hybrid, with a continuous component often generated by a Lagrangian plus actuators, and a discrete component where leg transfer takes place. The discrete component typically consists of a locally embedded co-dimension one submanifold in the continuous state space of the robot, called the switching surface, and a reset map that provides a new initial condition when a solution of the continuous component intersects the switching surface. The aim of this paper is to identify a low-dimensional submanifold of the switching surface, which, when it can be rendered invariant by the closed-loop dynamics, leads to asymptotically stable periodic gaits. The paper begins this process by studying the well-known 3D Linear Inverted Pendulum (LIP) model, where analytical results are much easier to obtain. A key contribution here is the notion of \textit{self-synchronization}, which refers to the periods of the pendular motions in the sagittal and frontal planes tending to a common period. The notion of invariance resulting from the study of the 3D LIP model is then extended to a 9-DOF 3D biped. A numerical study is performed to illustrate that asymptotically stable walking may be obtained.Comment: Conferenc

Torque Saturation in Bipedal Robotic Walking through Control Lyapunov Function Based Quadratic Programs

This paper presents a novel method for directly incorporating user-defined control input saturations into the calculation of a control Lyapunov function (CLF)-based walking controller for a biped robot. Previous work by the authors has demonstrated the effectiveness of CLF controllers for stabilizing periodic gaits for biped walkers, and the current work expands on those results by providing a more effective means for handling control saturations. The new approach, based on a convex optimization routine running at a 1 kHz control update rate, is useful not only for handling torque saturations but also for incorporating a whole family of user-defined constraints into the online computation of a CLF controller. The paper concludes with an experimental implementation of the main results on the bipedal robot MABEL

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

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