Velocity Constraints Research Articles

Buffer Compliance Control of Space Robots Capturing a Non-Cooperative Spacecraft Based on Reinforcement Learning

Aiming at addressing the problem that the joints are easily destroyed by the impact torque during the process of space robot on-orbit capturing a non-cooperative spacecraft, a reinforcement learning control algorithm combined with a compliant mechanism is proposed to achieve buffer compliance control. The compliant mechanism can not only absorb the impact energy through the deformation of its internal spring, but also limit the impact torque to a safe range by combining with the compliance control strategy. First of all, the dynamic models of the space robot and the target spacecraft before capture are obtained by using the Lagrange approach and Newton-Euler method. After that, based on the law of conservation of momentum, the constraints of kinematics and velocity, the integrated dynamic model of the post-capture hybrid system is derived. Considering the unstable hybrid system, a buffer compliance control based on reinforcement learning is proposed for the stable control. The associative search network is employed to approximate unknown nonlinear functions, an adaptive critic network is utilized to construct reinforcement signal to tune the associative search network. The numerical simulation shows that the proposed control scheme can reduce the impact torque acting on joints by 76.6% at the maximum and 58.7% at the minimum in the capturing operation phase. And in the stable control phase, the impact torque acting on the joints were limited within the safety threshold, which can avoid overload and damage of the joint actuators.

The kinematics of curved profiles mating with a caged idle roller - higher-path curvature analysis

This investigation focuses on the relative motion of a force-closure higher pair mechanism, herein termed caged-roller joint and composed of a cylindrical roller meshing with two slot profiles, carved on different bodies. A distinctive feature of such a mechanism is the pure rolling velocity constraint imposed between its components to limit friction losses. This makes the caged-roller joint an ideal candidate to control the kinematics of high-speed operating devices, such as centrifugal pendulum vibration absorbers.In this paper, a theoretical framework for the motion of caged-roller joint is proposed, employing intrinsic geometry, higher-path curvature and envelope theory. For design-analysis purposes, the correlations between instantaneous invariants, slots profiles curvature properties and pure rolling conditions within the higher pairs have been established. Eventually, the obtained results have been verified for three particular curves profiles, to test their consistency and offer an immediate application.

Calibration of a frontal ablation parameterisation applied to Greenland's peripheral calving glaciers

AbstractWe calibrate the calving parameterisation implemented in the Open Global Glacier Model via two methods (velocity constraint and surface mass balance (SMB) constraint) and assess the impact of accounting for frontal ablation on the ice volume estimate of Greenland tidewater peripheral glaciers (PGs). We estimate an average regional frontal ablation flux of 7.38±3.45 Gta−1 after calibrating the model with two different satellite velocity products, and of 0.69±0.49 Gta−1 if the model is constrained using frontal ablation fluxes derived from independent modelled SMB averaged over an equilibrium reference period (1961–90). This second method makes the assumption that most PGs during that time have an equilibrium between mass gain via SMB and mass loss via frontal ablation. This assumption serves as a basis to assess the order of magnitude of dynamic mass loss of glaciers when compared to the SMB imbalance. The differences between results from both methods indicate how strong the dynamic imbalance might have been for PGs during that reference period. Including frontal ablation increases the estimated regional ice volume of PGs, from 14.47 to 14.64±0.12 mm sea level equivalent when using the SMB method and to 15.84±0.32 mm sea level equivalent when using the velocity method.

An Improved Particle Number-Based Oil Spill Model Using Implicit Viscosity in Marine Simulator

Improving the physical realism of oil spill scenes in marine simulators can further enhance the emergency response capabilities of officials in charge and crew members and help reduce losses caused by oil spill disasters. In order to uniformly simulate the spreading, drift, breakup, and merging of oil spills at sea, we propose an improved divergence-free position-based fluid (DFPBF) framework based on the particle number density model. In our DFPBF framework, the governing equations for oil spills and ocean are discretized by Lagrangian particles, and the incompressibility of oil spills and ocean is ensured by solving the divergence-free velocity constraint solver and constant density constraint solver. In order to stably simulate the fate and transport of oil spills with higher viscosity, we introduce an implicit viscosity solution scheme for our DFPBF framework. The implicit solver uses a splitting concept to decouple viscosity solve and adopts an implicit scheme to discretize the integration of viscous force. Moreover, our DFPBF framework can ensure a divergence-free velocity field before applying the implicit viscosity scheme, which avoids the undesired bulk viscosity effects. The simulation results show that our DFPBF framework can stably simulate oil spills of various viscosities, especially high-viscosity crude oils.

Containment control of fractional discrete-time multi-agent systems with nonconvex constraints

This paper is devoted to the containment control problem of fractional discrete-time multi-agent systems (FDTMASs) with nonconvex velocity and control input constraints. First, distributed containment controllers with nonlinear projection algorithms are proposed for all followers. Then, some sufficient conditions are deduced during the convergence analysis of the closed-loop systems. By using Lyapunov stability theory and properties of fractional calculus, it proved that the containment control of the systems could be achieved with the distributed containment controller. Finally, some numerical examples are given to show the correctness of the proposed theoretical results.

Analysis of parasitic motion with the constraint embedded Jacobian for a 3-PRS parallel manipulator

This study derives the equation of parasitic motion of 3-DoFs parallel manipulator from the velocity-level analytic-constraint equation and compares it with a well-known position-level geometric method. The velocity-level constraint is formulated based on the extended Jacobian, derived from the instantaneous motion space (IMS) and the instantaneous restriction space (IRS) for free motion and constraint. In contrast, the position-level constraint, adopted in previous studies, is geometrically obtained by analyzing the moving platform and limb motions. The velocity-level analytic-constraint matrix is used to further analyze the task-space motion. In this paper, the procedure of detecting and identifying the parasitic terms from the independent terms is introduced utilizing the property that comes from the virtue of analytic constraint and inverse rate kinematics algorithm. Then, an equation for the constraint-compatible task motion and a coupling relation between the parasitic and independent motions are derived during further analysis. The paper derived the parasitic motion from position constraint, and an algebraic equivalency with the velocity constraint is shown by taking the time derivative of a point-plane position level constraint for comparison. Finally, numerical simulations are provided to validate the proposed approach and demonstrate the effect of the constraints on the given input velocity within the entire rotational workspace.

Constrained Feedback Control for Spacecraft Reorientation With an Optimal Gain

This article addresses the problem of spacecraft reorientation subject to attitude pointing, angular velocity, and actuator constraints. In order to tackle the attitude pointing constraints, a potential function is proposed, which is parameterized to allow for a wider range of optimal repointing solutions with attitude pointing constraints. Based on the potential function, a feedback control law is then designed for ensuring the system stability. The controller gains are optimized using a gradient-based optimal parameter tuning method. Furthermore, by imposing the angular velocity constraints and the actuator constraints into the formulation, the optimal parameter tuning method also ensures the satisfaction of these constraints. Therefore, stability, optimality, and feasibility are achieved simultaneously. Numerical simulations demonstrate accurate repointing maneuvering under different types of constraints.

Quasi-velocities definition in Lagrangian multibody dynamics

Based on Lagrangian mechanics, use of velocity constraints as a special set of quasi-velocities helps derive explicit equations of motion. The equations are applicable to holonomic and nonholonomic constrained multibody systems. It is proved that in proposed quasi-spaces, the Lagrange multipliers are eliminated from equations of motion; however, it is possible to compute these multipliers once the equations of motion have been solved. The novelty of this research is employing block matrix inversion to find the analytical relations between the parameters of quasi-velocities and equations of motion. In other words, this research identifies arbitrary submatrices and their effects on equations of motion. Also, the present study aimed to provide appropriate criteria to select arbitrary parameters to avoid singularity, reduce constraints violations, and improve computational efficiency. In order to illustrate the advantage of this approach, the simulation results of a 3-link snake-like robot with nonholonomic constraints and a four-bar mechanism with holonomic constraints are presented. The effectiveness of the proposed approach is demonstrated by comparing the constraints violation at the position and velocity levels, conservation of the total energy, and computational efficiency with those obtained via the traditional methods.

Design framework for optimizing waypoints of vehicle trajectory considering terminal velocity and impact angle constraints

Ballistic missiles often require the terminal velocity and impact angle to be confined to a certain region around a desired value considering a wide variety of uncertain initial conditions and operational ranges. This study presents a design framework to determine optimum waypoints that satisfy constraints for given launch conditions and mission profiles. As a systematic approach to this kinodynamic motion planning problem, the proposed framework deterministically samples the waypoints. The trajectory generated by the determined waypoints in consideration of various conditions satisfies the terminal constraint. Numerical simulations are performed to demonstrate the effectiveness of the proposed method.

Sliding Mode Control with Minimization of the Regulation Time in the Presence of Control Signal and Velocity Constraints

In this paper, the design of the terminal continuous-time sliding mode controller is presented. The influence of the external disturbances is considered. The robustness for the whole regulation process is obtained by adapting the time-varying sliding line. The representative point converges to the demand state in finite time due to the selected shape of the nonlinear switching curve. Absolute values of control signal, system velocity and both of these quantities are bounded from above and considered as system constraints. In order to evaluate the dynamical performance of the system, the settling time is selected as a quality index and it is minimized. The approach presented in this paper is particularly suited for systems in which one state (or a set of states) is the derivative of the other state (or a set of states). This makes it applicable to a wide range of electromechanical systems, in which the states are the position and velocity of the mechanical parts.

Temporal Reasoning with Kinodynamic Networks

Temporal reasoning is central to Artificial Intelligence (AI) and many of its applications. However, the existing algorithmic frameworks for temporal reasoning are not expressive enough to be applicable to robots with complex kinodynamic constraints typically described using differential equations. For example, while minimum and maximum velocity constraints can be encoded in Simple Temporal Networks (STNs), higher-order kinodynamic constraints cannot be represented in existing frameworks. In this paper, we present a novel framework for temporal reasoning called Kinodynamic Networks (KDNs). KDNs combine elements of existing temporal reasoning frameworks with the idea of Bernstein polynomials. The velocity profiles of robots are represented using Bernstein polynomials; and dynamic constraints on these velocity profiles can be converted to linear constraints on the to-be-determined coefficients of their Bernstein polynomials. We study KDNs for their attractive theoretical properties and apply them to the Multi-Agent Path Finding (MAPF) problem with higher-order kinodynamic constraints. We show that our approach is not only scalable but also yields smooth velocity profiles for all robots that can be executed by their controllers.

Observer-based saturated proportional derivative control of perturbed second-order systems: Prescribed input and velocity constraints

This study introduces a new methodology for controlling second-order nonlinear systems in point-to-point tasks with simultaneous input and velocity saturation constraints. The proposed approach utilizes a robust disturbance observer for compensating for the unknown dynamics and disturbances affecting the system. Then, the disturbance observer is combined with a saturated proportional derivative (PD) controller. The resulting control signal allows solving the regulation problem and generating input values and velocities with some prescribed bounds defined by the user. Based on the Lyapunov-theory, asymptotic stability of the origin of the closed-loop error dynamics is attained, which implies that the position regulation objective is achieved while keeping the input and velocity values within prescribed bounds defined by the user. The new control scheme is assessed through numerical simulations, which corroborate the new saturated controller’s feasibility.

Neural network-based robust finite-time attitude stabilization for rigid spacecraft under angular velocity constraint

In this paper, the problem of attitude stabilization control of spacecraft under angular velocity constraint is investigated. A state-constrained finite-time attitude control scheme is designed by making full use of the model feature of the quaternion. Based on the homogeneous domination approach, the finite-time stability of the closed-loop system is proved. It proves that the angular velocity can be constrained within the limited range at any time. For the attitude loop dynamics subsystem with external disturbances, based on a radial basis function neural network, an integral terminal sliding mode controller is proposed. Finally, the validity and advantages of the proposed control scheme are demonstrated in the simulation section compared with the other two control methods.

Formation Reconfiguration for Fixed-Wing UAVs

This study proposes a coordinated path following approach to solve the formation reconfiguration problem in a guided manner. A novel coordinated path following control law is proposed, which steers a fleet of UAVs towards their closest projection points on their respective paths by controlling the angular velocity of each UAV, and achieves coordinated formation reconfiguration by synchronizing the UAVs’ closest projection points via controlling the linear velocity. Each UAV only uses its neighbors’ destination arc distances for coordination, which as a result saves communication bandwidth. The UAVs’ velocity constraints are also satisfied, with the linear velocity converging to the cruise speed under the proposed control law, which is helpful to prolong the flight time. The hardware-in-the-loop simulation, as well as the field experiments with seven to ten fixed-wing UAVs, are performed to validate the effectiveness of the proposed method.

Numerical Research on Vibration-Enhanced Heat Transfer of Elastic Scroll Tube Bundle

Based on a new type of elastic scroll tube bundle (ESTB) heat exchanger, the influence of shell-side fluid inlet velocity and tube bundle constraint condition on the enhanced heat transfer performances are researched by a two-way fluid–solid coupling calculation method. Numerical results show that the average heat transfer coefficient (HTC) increases with the shell-side fluid inlet velocity increases when the single group of scroll copper tubes is unconstrained. Within the range of calculated parameters in this paper, the maximum increase of average HTC is 140% under vibration conditions, and the maximum increase of average HTC is 216% under nonvibration conditions. The average HTC decreases as the number of constraints increases under vibration conditions, and the maximum decrease is 42.69%. The average performance evaluation criteria values are greater than 1.00, so the overall heat transfer performance of the ESTB heat exchanger is better.

Hierarchical image-based visual serving of underwater vehicle manipulator systems based on model predictive control and active disturbance rejection control

The image-based visual servoing (IBVS) problem of a redundant underwater vehicle manipulator system (UVMS) with an eye-in-hand camera is investigated in this paper. With consideration of system constraints, dynamic uncertainties, and the absence of vehicle velocity sensors for a typical UVMS, we propose a hierarchical control architecture, which is composed of an unscented Kalman filtering (UKF)-based vehicle motion estimator, a kinematic model predictive IBVS controller, and two decoupled dynamic velocity controllers for the vehicle and the manipulator, respectively. In details, the underwater vehicle velocities are estimated by UKF with visual measurements based on the UVMS kinematic model. With these estimates, a nonlinear model predictive controller (MPC) is designed to solve the IBVS problem of UVMSs and generate velocity commands for the underwater vehicle and the manipulator, simultaneously. The visual kinematic model of UVMSs is used to predict the future trajectories, and the field-of-view, manipulator joint angle, and UVMS velocity constraints are handled when solving the optimization problem. To reduce the system complexity of UVMSs, the high-dimensional UVMS’s dynamic model is decoupled into two low-dimensional models of the vehicle and the manipulator, and a dynamic inversion-based active disturbance rejection control (DI-ADRC) method is developed for dynamic controller design. The physical interaction effects between the vehicle and manipulator are considered as external disturbances acting on each other, which are estimated by extended state observers (ESO) in ADRC. The simulation experiments with a typical UVMS are performed to demonstrate the effectiveness of the proposed hierarchical IBVS controller in dealing with system redundancy, constraints and uncertainties.

Non-singular terminal sliding-mode control for a manipulator robot using a barrier Lyapunov function

This study introduces a design of robust finite-time controllers that aims to solve the trajectory tracking of robot manipulators with full-state constraints. The control design is based on the construction of a distributed state constraint non-singular terminal sliding mode (CNTSM). The CNTSM design includes the gain self-adapting tuning method, which can ensure finite-time convergence to the sliding surface aside from the states to its corresponding reference trajectories. The implementation of the time-varying gain ensures the fulfillment of the accurate tracking for the references while the position and velocity constraints are satisfied permanently. A barrier Lyapunov function is proposed to develop the finite-time stability analysis of the designed controllers. The CNTSM realization uses the tracking error as well as its estimated derivative, which is calculated using a variant of adaptive super-twisting algorithm operating as robust differentiator. The proposed CNTSM is numerically evaluated on a two-link RM with uncertain inertia and Coriolis matrices. Simulation and experimental results evidence the efficiency of the CNTSM controller demonstrating a better tracking performance while the full-state constraints are satisfied in counterpart with the classical non-singular terminal sliding mode which is not able to keep such restrictions.

Temporal Coupling of Dynamical Movement Primitives for Constrained Velocities and Accelerations

The framework of Dynamical Movement Primitives (DMPs) has become a popular method for trajectory generation in robotics. Most robotic systems are subject to saturation and/or kinematic constraints on motion variables, but DMPs do not inherently encode constraints and this may lead to poor tracking performance. Temporal coupling (online temporal scaling) of DMPs represents a possible way for handling constrained systems. This letter presents a temporal coupling for DMPs to handle velocity and acceleration constraints for the generated trajectory. A novel filter is presented based on a potential function which proactively scales the trajectory before reaching the acceleration limits. In this way, the velocities and accelerations remain within the limits even for trajectories with aggressive accelerations and stricter bounds. The performance of the proposed method is demonstrated by means of simulations and experiments on a UR10 robot.

Stereo visual odometry with velocity constraint for ground vehicle applications

AbstractThis paper proposes a novel method of error mitigation for stereo visual odometry (VO) applied in land vehicles. A non-holonomic constraint (NHC), which imposes physical constraint to the rightward velocity of a land vehicle, is implemented as an observation in an extended Kalman filter (EKF) to reduce the drift of stereo VO. The EKF state vector includes position errors in an Earth-centred, Earth-fixed (ECEF) frame, velocity errors in the camera frame, angular rate errors and attitude errors. All the related equations are described and presented in detail. In this approach, no additional sensors are used but NHC, namely velocity constraint in the right direction , is applied as an external measurement to improve the accuracy. Tests are conducted with the Karlsruhe Institute of Technology and Toyota Technological Institute (KITTI) datasets. Results show that the relative horizontal positioning error improved from 0⋅63% to 0⋅22% on average with the application of the velocity constraints. The maximum and root mean square of the horizontal error with velocity constraints are both reduced to less than half of the error with stand-alone stereo VO.

Energy-Saving Trajectory Planning for Robotic High-Speed Milling of Sculptured Surfaces

In the field of sculptured surfaces machining, the robot trajectory planning, under high-order complex constraints, aiming at minimizing energy or time, is always a challenge. The complexity of curvature characteristics of sculptured surfaces and the nonlinearity of relevant constraints are the main reasons. This article proposes an efficient planning method of minimum-energy robot trajectory, for high-speed machining of sculptured surfaces. First, the energy characteristic model of the robot machining system (RMS) is established, to acquire the energy-optimal feedrate, under velocity constraints, to use in the subsequent trajectory planning. Next, a trajectory planning model, with complex constraints, is developed. The proposed method transforms the original trajectory planning into a minimal modification of the initial objective-optimal B-spline feedrate curve (BFC). Furthermore, two main coupling problems, which influence the minimal change of curves, in the direct evolution-based BFC modification, are addressed. Based on the derived solutions, a novel modification algorithm of BFC, with a callback mechanism (CBM), is proposed. Finally, the performance of the proposed method and the specific algorithm is validated by two case studies. Results show that the proposed method can significantly improve the efficiency of robot trajectory planning, aiming at minimum energy, while exhibiting excellent performance. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work was motivated by how to automatically and effectively acquire the energy-saving trajectory of a robotic system, executing sculptured surface machining. This article suggests a new approach that transforms the original trajectory optimization into a minimal modification of the initial energy-optimal BFC, obtained under velocity constraints. This approach calculates the complex energy formula only once. A CBM, for constraint-based BFC modification, is proposed, to revise the redundant reduction of the feedrate. The proposed modification algorithm significantly decreases the detrimental effect of two coupling problems, on the adjustment of the BFC. Results show that the computational efficiency of the proposed method is significantly superior to the one of the direct optimization method. The performance of the proposed modification algorithm is obviously advanced compared to the existing B-spline evolution algorithm. In blade machining, after optimizing the trajectory using the proposed method and algorithm, both energy and time decrease by more than 45% compared to the conservative feed. The proposed algorithm improves significantly the trajectory compared to the prior art algorithm. Technologists benefit from reduced planning time and improved machining performance. However, incorporation into a CAM or manufacturing system has not yet been realized and remains a significant work to be done in the future.