Virtual Constraints Research Articles

A Piecewise Monotonic Smooth Phase Variable for Speed-Adaptation Control of Powered Knee-Ankle Prostheses

Researchers are currently making progress in unifying the entire gait cycle of powered prostheses by using a human-inspired phase variable, but constructing a robust phase variable to more accurately estimate the gait phase and desired joint trajectories of prostheses during varying walking speeds remains an open problem. Firstly, this study proposed a piecewise monotonic and smooth phase variable to predict the gait phase from only the measured thigh angle. Compared to the two most widely used methods, thigh angle integral vs. thigh angle and thigh angular rate vs. thigh angle, the proposed method addressed the drift problem of the integral-based method and the noise problem of the angular rate-based. Then a predictive tuning-free model that represents gait kinematics as a continuous function of proposed phase variable and walking speed was constructed to generate desired joint virtual constraints for speed-adaptation control of powered knee-ankle prosthesis during continuously varying walking speeds. Experiments were conducted with six able-bodied participants wearing inertial measurement units and performing periodic and non-periodic (quick start and stop) tasks, and one transfemoral amputee wearing a powered knee-ankle prosthesis walking on a treadmill. Experimental results illustrated that the root mean squared error of the gait phase estimated by the proposed approach was 75% lower than the integral-based and angular rate-based methods, and the proposed approach performed well in the continuous phase control of a powered knee-ankle prosthesis during varying walking speeds.

The impact of mentoring on early career faculty: Assessment of a virtual mentoring program.

11039 Background: Participation in mentorship programs for early career physicians may be crucial to developing key skills and professional networks to navigate racial, ethnic and gender leadership disparities in medicine. A 6-month virtual facilitated peer mentorship program was developed and piloted through the Society for Neuro-Oncology (SNO) Women & Diversity Committee. The evaluation of the program’s feasibility to positively impact early career physicians, investigators and trainees is presented here. Methods: We designed and conducted a virtual mentoring program pilot open to SNO’s multidisciplinary members in residency, fellowship, or early career phase, leveraging peer-mentoring sessions with mid-to late-career physician mentors. A curriculum with online resources was provided recommending groups meet for 6 sessions: 3 involving the mentor and 3 dedicated to peer-mentoring. Group assignments were based on time-zones and interests. Pre- and post-participation surveys assessed mentee experience. Descriptive statistics were used to assess participant demographics and survey results. Results: Our call for participation was broad; all 20 mentee applicants participated in 5 groups. Mentees were 90% women and 60% were from diverse racial and ethnic backgrounds. Most were aged 31-40 (75%) and junior faculty (50%) in neuro-oncology (65%). The 5 senior mentors (3 men and 3 of diverse race and ethnic backgrounds) practiced either neuro-oncology (3), neurosurgery (1) or radiation oncology (1). The proportion who reporting having a signature lecture increased from 15% to 62% during the pilot. A large majority reported their participation was worthwhile (85%), that they would participate again (92%) and would recommend it to others (92%). Feedback themes included positive personal growth, peer support, networking and job opportunities, access to CV reviews, lack of and desire for late career female mentors, and virtual scheduling constraints. While the pilot was limited by several variables, it was timely to connect participants in Q3 of 2020 early in the COVID-19 global pandemic. The virtual meeting environment created a venue to share and discuss topics such as work-life balance, burnout, leading through change and social connection. Despite not achieving 100% professional concordance, participants found the experience worthwhile. The tools and curriculum of topics provided was implemented differently across groups, leading to varied experiences. Finally, we did not have 100% post pilot follow up despite multiple attempts limiting our complete understanding of the pilot. Conclusions: This virtual mentorship pilot program proved feasible and of value in development of early career women and diverse individuals. A resource toolkit has been designed to scale and diffuse.

A Topological Approach to Gait Generation for Biped Robots

This article describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2-D and 3-D biped walkers subject to configuration inequality constraints, physical holonomic constraints (e.g., closed-loop linkages), and virtual holonomic constraints (user-defined constraints enforced through feedback control). Our method constructs implicitly defined manifolds of feasible periodic gaits within a state-time-control space that parameterizes the biped’s hybrid trajectories. Since equilibrium configurations of the biped often belong to such manifolds, we use equilibria as “templates” from which to grow the gait families. Equilibria are reliable seeds for the construction of gait families, eliminating the need for random, intuited, or bio-inspired initial guesses at feasible trajectories in an optimization framework. We demonstrate the approach on several 2-D and 3-D biped walkers.

Orbital synchronization of homogeneous mechanical systems with one degree of underactuation

AbstractA methodology for asymptotic orbital synchronization of a set of homogeneous mechanical systems with one degree of underactuation is proposed. A reference model generating a reference orbit is first constructed under the virtual holonomic constraints approach. Then, the synthesis is designed to, first, estimate the state vector of the homogeneous systems, provided that only position measurements are available, and second, to drive the state of the systems to that of the reference model. Due to the synthesis properties, the homogeneous systems converge asymptotically to the reference orbit when there are no disturbances affecting the systems nor the measurements. When disturbances are present, robustness is guaranteed provided that the gain of the closed‐loop systems remains lower than an attenuation level . Numerical results for a set of underactuated cart‐pendulums corroborate the proposed methodology.

Asymmetric integral BLF based state‐constrained flight control using NN and DOB

AbstractThis article proposes an adaptive back‐stepping flight controller under angle of attack (AOA) constraints. Taking the hypersonic flight vehicle (HFV) for example, considering the AOA constraints caused by the scramjet intake requirements, the asymmetric integral barrier Lyapunov function is used to design the controller, while the AOA is directly limited to a predefined interval without setting the tracking error and virtual control constraints separately. Furthermore, the neural networks and disturbance observer are applied in the controller to deal with the model uncertainty and external disturbance. The system stability and the AOA constraints are proved via Lyapunov analysis. Simulation tests on HFV longitudinal dynamics present that the proposed controller can prevent the AOA from exceeding the given bounds while altitude and velocity tracking.

Boundary Stabilization of Underground Multirobot System with Virtual String Constraints

The manipulation of multiple physical connected objects can be described by virtual connected string system. We proposed a Lyapunov‐based stabilization control approach for virtual connected string with midway discontinue vertical force. The system is with Riemannian boundary. We use the backstepping method to transform the system into a stable system with Dirichlet boundary. In this way, we get the controller to make sure the closed‐loop system converge to the zero point exponentially. Then, we construct a Lyapunov function to analyze the stability for the closed‐loop system. We also show the system is well‐posedness. Also, we use the active disturbance rejection control (ADRC) to reject the disturbance when disturbance is present. Some numerical stimulations show that the control law is the effective.

Virtual control strategy and conditioning technique for tracking and learning controls under input restrictions

The virtual control strategy for mechanical systems has been recently proposed (Gnucci and Marino, 2021) in the context of under-actuated mechanical systems. Such a strategy views and represents an under-actuated mechanical system as a fully actuated system with virtually added inputs and outputs having to satisfy, through a suitable choice of the virtual output reference signals, the virtual input zero-equality constraint: the related adaptive tracking control problem is then solved through standard design techniques. This paper exhibits a twofold aim. The first one is: to enlarge the concept of zero-input constraint and thus naturally adapt the virtual control approach to the case in which an actuator fault can occur. The second aim is: to show how the application and transposition of such an adaptation to two well-known classes of nonlinear systems (special systems in multi-variable tracking form with two inputs and outputs under actuator faults; one-relative-degree, single-input, single-output systems in output feedback form under input saturation) not only own strong connections with the conditioning technique, originally conceived in the context of anti-windup problems under input constraints, but they also gain original results.

Robust Stabilization of Periodic Gaits for Quadrupedal Locomotion via QP-Based Virtual Constraint Controllers

This letter develops, theoretically justifies, and experimentally implements an optimization-based nonlinear control methodology for stabilizing quadrupedal locomotion. This framework utilizes virtual constraints and control Lyapunov functions (CLFs) in the context of quadratic programs (QPs) to robustly stabilize periodic orbits for hybrid models of quadrupedal robots. Properties of the proposed QP are studied wherein sufficient conditions for the continuous differentiability of the controller are presented. Additionally, this letter addresses the robust stabilization problem of the orbits based on the Poincaré sections analysis and input-to-state stability (ISS). The proposed controller is numerically and experimentally validated on the A1 quadrupedal robot with 18 degrees of freedom to demonstrate the robust stability of trotting gaits against external disturbances and unknown payloads.

Cooperative Locomotion Via Supervisory Predictive Control and Distributed Nonlinear Controllers

Abstract This paper presents a hierarchical nonlinear control algorithm for the real-time planning and control of cooperative locomotion of legged robots that collaboratively carry objects. An innovative network of reduced-order models subject to holonomic constraints, referred to as interconnected linear inverted pendulum (LIP) dynamics, is presented to study cooperative locomotion. The higher level of the proposed algorithm employs a supervisory controller, based on event-based model predictive control (MPC), to effectively compute the optimal reduced-order trajectories for the interconnected LIP dynamics. The lower level of the proposed algorithm employs distributed nonlinear controllers to reduce the gap between reduced- and full-order complex models of cooperative locomotion. In particular, the distributed controllers are developed based on quadratic programing (QP) and virtual constraints to impose the full-order dynamical models of each agent to asymptotically track the reduced-order trajectories while having feasible contact forces at the leg ends. The paper numerically investigates the effectiveness of the proposed control algorithm via full-order simulations of a team of collaborative quadrupedal robots, each with a total of 22 degrees-of-freedom. The paper finally investigates the robustness of the proposed control algorithm against uncertainties in the payload mass and changes in the ground height profile. Numerical studies show that the cooperative agents can transport unknown payloads whose masses are up to 57%, 97%, and 137% of a single agent's mass with a team of two, three, and four legged robots.

Virtual constraint control of Knee-Ankle prosthesis using an improved estimate of the thigh phase-variable

In the human gait cycle, virtual constraints enforce a robust relationship between the thigh phase-variable and the knee/ankle angle. These constraints enable an accurate estimation and control of angular trajectory when the input phase-variable profile is low in gait aperiodicity and sensor noise. In this work, we present discrete Fourier transform (DFT) based virtual constraint schemes for estimating the knee/ankle trajectories using an improved monotonic and linear trajectory of the thigh phase-variable. To minimize the likely aberrations in the desired trajectory of the phase-variable, the contour of the thigh angle and its integral is amplitude scaled, time shifted, and interpolated over the complete stride. The processed contour is then refitted to an ideal circle using polynomial optimization via two different schemes. For both proposed schemes, estimated knee/ankle trajectories are compared with the benchmark gait kinematics of healthy persons and an amputee wearing three commercial prostheses. Simulation results, based on realistic prosthesis actuator parameters, show a 2.18 ± 0.83 times reduction in the mean trajectory tracking error for three contrasting walking speeds, validating the efficacy of proposed schemes.

Block Partitioning Structure in the VVC Standard

Versatile Video Coding (VVC) is the latest video coding standard jointly developed by ITU-T VCEG and ISO/IEC MPEG. In this paper, technical details and experimental results for the VVC block partitioning structure are provided. Among all the new technical aspects of VVC, the block partitioning structure is identified as one of the most substantial changes relative to the previous video coding standards and provides the most significant coding gains. The new partitioning structure is designed using a more flexible scheme. Each coding tree unit (CTU) is either treated as one coding unit or split into multiple coding units by one or more recursive quaternary tree partitions followed by one or more recursive multi-type tree splits. The latter can be horizontal binary tree split, vertical binary tree split, horizontal ternary tree split, or vertical ternary tree split. A CTU dual tree for intra-coded slices is described on top of the new block partitioning structure, allowing separate coding trees for luma and chroma. Also, a new way of handling picture boundaries is presented. Additionally, to reduce hardware decoder complexity, virtual pipeline data unit constraints are introduced, which forbid certain multi-type tree splits. Finally, a local dual tree is described, which reduces the number of small chroma intra blocks.

Online Learning of Unknown Dynamics for Model-Based Controllers in Legged Locomotion

The performance of a model-based controller can severely suffer when its model inaccurately represents the real world dynamics. We propose to learn a time-varying, locally linear residual model along the robot's current trajectory, to compensate for the prediction errors of the controller's model. Supervised learning is performed online, as the robot is running in the unknown environment, using data collected from its immediate past. We theoretically investigate our method in its general formulation, then apply it to a bipedal controller derived from the full-order dynamics of virtual constraints, and a quadrupedal controller derived from a simplified model of contact forces. For a biped in simulation, our method consistently outperforms the baseline and a recent learning-based method. We also experiment with a 12 kg quadruped in simulation and real world, where the baseline fails to walk with 10 kg of payload but our method succeeds.

Tube-model predictive control based on sum of squares for hypersonic vehicle with state-dependent input constraints

In this paper, tube-model predictive control based on the sum of squares technique is developed for hypersonic vehicles with state-dependent input constraints. Firstly, the longitudinal non-linear model in the presence of uncertain parameters is transformed into the polytopic linear parameter varying model with bounded disturbance by feedback linearization. Then the actual input constraints are converted to the virtual state-dependent input constraints in linear multivariable polynomial. A composite feedback control law based on tube-model predictive control is designed into a convex combination of unconstrained and constrained control. The real control law can be obtained by inversion. The sum of squares technique is used to transform the polynomial constraints into the convex matrix sum of squares condition via linear matrix inequality. Finally, simulation results verify the effectiveness of the proposed controller.

A novel tracking control method for the distributed-drive and active-steering articulated virtual rail train

To realize the running control of distributed-drive and active-steering articulated virtual rail trains travelling on urban roads under non-contact virtual rail constraints, target trajectory generation and active-steering control are crucial issues. In this article, a novel tracking control method is proposed, which includes a dynamic target trajectory generation and a new active-steering tracking control system. First, a distributed-drive and active-steering articulated virtual rail train kinematics model with n-sections is derived, and then a new target trajectory generation method is proposed using data filtering and compression, coordinate transformation and spline difference, and the simulation comparison shows that the proposed method has less data storage space and high computational efficiency. Second, a new active-steering tracking control system composed of a rear axle preview active-steering controller, a front axle coordinated steering controller, and a differential-distribution controller is designed to achieve tracking control and coordinated movement of distributed-drive and active-steering articulated virtual rail train. Finally, a distributed-drive and active-steering articulated virtual rail train simulation model was constructed in ADAMS, and then simulations are performed under three rail conditions and compared with the other two methods, which show that the proposed method has good tracking control accuracy, adaptability, and superiority under various rails and different speeds.

Analysis of Obstacle Avoidance Strategy for Dual-Arm Robot Based on Speed Field with Improved Artificial Potential Field Algorithm

In recent years, dual-arm robots have been favored in various industries due to their excellent coordinated operability. One of the focused areas of study on dual-arm robots is obstacle avoidance, namely path planning. Among the existing path planning methods, the artificial potential field (APF) algorithm is widely applied in obstacle avoidance for its simplicity, practicability, and good real-time performance over other planning methods. However, APF is firstly proposed to solve the obstacle avoidance problem of mobile robot in plane, and thus has some limitations such as being prone to fall into local minimum, not being applicable when dynamic obstacles are encountered. Therefore, an obstacle avoidance strategy for a dual-arm robot based on speed field with improved artificial potential field algorithm is proposed. In our method, the APF algorithm is used to establish the attraction and repulsion functions of the robotic manipulator, and then the concepts of attraction and repulsion speed are introduced. The attraction and repulsion functions are converted into the attraction and repulsion speed functions, which mapped to the joint space. By using the Jacobian matrix and its inverse to establish the differential velocity function of joint motion, as well as comparing it with the set collision distance threshold between two robotic manipulators of robot, the collision avoidance can be solved. Meanwhile, after introducing a new repulsion function and adding virtual constraint points to eliminate existing limitations, APF is also improved. The correctness and effectiveness of the proposed method in the self-collision avoidance problem of a dual-arm robot are validated in MATLAB and Adams simulation environment.

Genetic Algorithm for the Retailers’ Shelf Space Allocation Profit Maximization Problem

This paper discusses the problem of retailers’ profit maximization regarding displaying products on the planogram shelves, which may have different dimensions in each store but allocate the same product sets. We develop a mathematical model and a genetic algorithm for solving the shelf space allocation problem with the criteria of retailers’ profit maximization. The implemented program executes in a reasonable time. The quality of the genetic algorithm has been evaluated using the CPLEX solver. We determine four groups of constraints for the products that should be allocated on a shelf: shelf constraints, shelf type constraints, product constraints, and virtual segment constraints. The validity of the developed genetic algorithm has been checked on 25 retailing test cases. Computational results prove that the proposed approach allows for obtaining efficient results in short running time, and the developed complex shelf space allocation model, which considers multiple attributes of a shelf, segment, and product, as well as product capping and nesting allocation rule, is of high practical relevance. The proposed approach allows retailers to receive higher store profits with regard to the actual merchandising rules.

Experimental Application of Robust and Converse Dynamic Control for Rotary Flexible Joint Manipulator System

Performance evaluation of trajectory tracking for a rotary flexible joint system is demonstrated in this paper. The robust and converse dynamic (RCD) technique is proposed and implemented for this evaluation. This control methodology is of the left inversion type, i.e., the control inputs are obtained by means of plant output error feedback. RCD control encompasses the baseline inverse (BI) control and sliding mode control-based discontinuous control element. The baseline inverse controller enforces the prescribed servo (virtual) constraints that represent the control objectives. The control objectives of the baseline inverse controller are enclosed in the form of servo (virtual) constraints which are inverted using Moore–Penrose Generalized Inverse (MPGI) to solve for the baseline control law. To boost the robust attributes against parametric uncertainties and disturbances, a discontinuous control function is augmented with baseline controller such that semiglobal practical stability is guaranteed in the sense of Lyapunov. To exhibit the effectiveness of RCD control in terms of tracking performance, computer simulations are conducted in Simulink/Matlab environment. Furthermore, the practical implementation is also investigated through a real-time experiment on Quanser’s rotary flexible joint manipulator system. The experimental results obtained by RCD are compared to the conventional sliding mode and fractional-order control techniques.

Omnidirectional Walking Pattern Generator Combining Virtual Constraints and Preview Control for Humanoid Robots.

This paper presents a novel omnidirectional walking pattern generator for bipedal locomotion combining two structurally different approaches based on the virtual constraints and the preview control theories to generate a flexible gait that can be modified on-line. The proposed strategy synchronizes the displacement of the robot along the two planes of walking: the zero moment point based preview control is responsible for the lateral component of the gait, while the sagittal motion is generated by a more dynamical approach based on virtual constraints. The resulting algorithm is characterized by a low computational complexity and high flexibility, requisite for a successful deployment to humanoid robots operating in real world scenarios. This solution is motivated by observations in biomechanics showing how during a nominal gait the dynamic motion of the human walk is mainly generated along the sagittal plane. We describe the implementation of the algorithm and we detail the strategy chosen to enable omnidirectionality and on-line gait tuning. Finally, we validate our strategy through simulation experiments using the COMAN + platform, an adult size humanoid robot developed at Istituto Italiano di Tecnologia. Finally, the hybrid walking pattern generator is implemented on real hardware, demonstrating promising results: the WPG trajectories results in open-loop stable walking in the absence of external disturbances.

A new calibration method for hybrid machine tools using virtual tool center point position constraint

Kinematic calibration is an effective way to improve the accuracy of hybrid machine tools. Traditionally, the position and orientations of the moving platform need to be measured. This process, especially the measurement of orientation, is time-consuming and difficult. Meanwhile, measurement noise and the inhomogeneity of position and orientation affect the accuracy. In this study, the position and orientation errors of the moving platform are transformed into the position error of the tool center point (TCP) by introducing the tool length, and the identification matrix based on the TCP position is formulated. Then, the concept of the virtual TCP position constraint is introduced, and a new measurement method using virtual TCP position constraint is proposed. The proposed method considerably reduces the measurement cost and avoids the inhomogeneity. To minimize the influence of measurement error, a pose selection algorithm is presented. Finally, the proposed calibration method is confirmed through simulations and experiments.

Multimobile Robot Cluster System for Robot Machining of Large-Scale Workpieces

In this article, a novel work pattern for large-scale workpiece machining, that is, multimobile robot cluster machining, is proposed. The key idea is to use distributed coordination control to link multiple robots as a cluster system. The coordination control law acts as a virtual constraint, and multiple robots move synchronously under a common leader. Two topological structures are introduced to describe the communication networks of the cluster system, namely, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -chain and close-loop topologies. The convergence rate and resistance index of different topological structures are analyzed, and the applications of different topologies in varied machining scenarios are discussed. Two experiments are conducted on the multimobile robot system. The cluster system with a close-loop topology is used for the collaborative handling task, where the relative distance of two mobile robots can be limited within 6 cm. The cluster system with an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -chain topology is used for large-scale wind turbine blade machining. The cluster machining system requires little manual intervention and guarantees the synchronization performance of the machining system.