Artificial Potential Function Research Articles

Reduced Attitude Control for Boresight Alignment With Dynamic Pointing Constraints

The problem of boresight alignment control is studied when multiple dynamic pointing constraints and angular velocity constraints exist during the maneuver. The tracking errors and dynamic pointing constraints are defined using the reduced attitude, which has only two degrees of freedom and avoids the singularity and redundancy description. An artificial potential function and a barrier Lyapunov function are employed to derive the feedback control law for attitude tracking scenario with no violation of the constraints and limitations. The stability analysis shows that the proposed control law guarantees the asymptotical convergence of the tracking errors. Numerical simulations are conducted to demonstrate the efficacy and performance of the presented control design under several different scenarios.

Brain Teleoperation Control of a Nonholonomic Mobile Robot Using Quadrupole Potential Function

This paper presents the development of a brain-machine interfacing teleoperation control framework of a mobile robot using quadrupole potential function (QPF). The online brain-computer interface is based on steady-state visually evoked potentials, which employs the multivariate synchronization index classification algorithm to decode the human electroencephalograph (EEG) signals. In this way, human intentions can be recognized and EEG control commands can be produced for the mobile robot. Besides, a novel artificial potential function named QPF is designed to produce the potential fields to parameterize the EEG control commands. The classification results of the EEG signal are related to the distribution of the potential fields, and the collision-free path to a target position is automatically planned by the potential field. Such semi-automatic design builds the direct mapping from human intentions to the mobile robot's behavior and reduces mental effort or exhaustion on subject's part. Besides, based on the QPF with the capability of handling nonholonomic constraints, the integrated system can not only achieve obstacle avoidance but is also able to automatically stabilize the robot to a target configuration. Extensive experiment studies were conducted on several subjects to demonstrate the effectiveness of the proposed approaches.

Layered Formation-containment Control of Multi-agent Systems in Constrained Space

This paper addresses the layered formation-containment (LFC) problem for multiagents in the constrained space with a directed communication topology. The formation-containment problem is first defined using a layered framework, and a layered distributed finite-time estimator is proposed to acquire the target states for agents in each layer. Based on the proposed framework, the formation configuration and the mechanism of the information flow can be explored and designed naturally. To avoid collisions with borders, obstacles, as well as the other agents in the constrained space, an artificial potential function is designed based on the Dirac delta function. Further, a disturbance observer and adaptive neural networks (NNs) are applied to respectively tackle the external disturbance and the model uncertainties. The desired formation of each layer can be achieved while no collision occurs in the constrained space. The semi-global uniform ultimate boundedness of closed-loop errors is guaranteed by Lyapunov stability theory. Simulation results are given to show the effectiveness of the proposed approaches.

Robust consensus braking algorithm for distributed EMUs with uncertainties

In this study, the velocity tracking control of electric multiple units (EMUs) with non-linearity and uncertainty during braking is investigated. A consensus braking algorithm with distributed sliding mode observers is proposed. Firstly, a multi-agent model with non-linear coupling and uncertain external disturbances is established. Secondly, distributed observers are designed, in which a real-time estimation equation for coupling force and disturbances is established based on the equivalent control principle of sliding mode variable structure. Finally, a robust consensus algorithm is proposed to achieve a consensus velocity tracking of each carriage on the target braking curve. The distances between the adjacent carriages are stabilised at stationary distances in a safe range by an artificial potential field function. Experiments show that the algorithm has high accuracy and anti-interference ability in the braking process.

Real-Time Autonomous Spacecraft Proximity Maneuvers and Docking Using an Adaptive Artificial Potential Field Approach

In an effort to pursue more advanced missions in space, improved on-board trajectory optimization and path (re)planning capabilities are necessary. Over the past decades, numerous missions have pushed the state of the art in autonomous rendezvous and proximity operations (RPOs). Regardless of the mission, any RPO guidance algorithm must be able to react to a dynamic environment while generating a fuel-efficient trajectory. An adaptive artificial potential function (AAPF) guidance exhibiting these properties has been experimentally evaluated on a spacecraft air-bearing test bed and its performance compared to traditional APF and other real-time guidance methods.

Lane‐keeping control based on an improved artificial potential method and coordination of steering/braking systems

Based on the impact of the vehicle velocity on the potential field function, considering the overall lane-keeping performance and vehicle stability, the yaw angular adjusting factor is introduced to regulate the potential field function. The proportions of vehicle velocity and yaw angle factors in potential field function are distributed by extension decision. The sliding mode controller is designed based on the two-degree-of-freedom vehicle dynamics model to obtain the front wheel steering angle. The fuzzy decision is made for the dynamic thresholds of distance deviation and angle deviation of lane-keeping system to avoid the control frequently start-up. Next, the combined control strategy of active steering and differential braking systems is designed based on vehicle driving safety boundary, and the yaw angle rate and mass-centroid sideslip angle are selected as the characteristic variables for dividing the vehicle driving safety regions. The different weights are determined for the steering and braking systems in different regions. Finally, the simulation by Carsim/Simulink and the hardware-in-loop test are carried out to demonstrate that it is effective and superior by adopting the sliding-mode controller based on the improved artificial potential function and the coordination strategy of steering and braking systems.

Application of Floquet theory to formation flying in elliptic orbits via a Hamiltonian structure-preserving control

In this study, an improved Hamiltonian structure-preserving controller is applied for formation flying in elliptic orbits. The Lyapunov-Floquet theory is applied to the Tschauner-Hempel (TH) equation in order to generate its transformed form with two zero eigenvalues and two pairs of imaginary eigenvalues. Then, an improved Hamiltonian structure-preserving (HSP) control is introduced to the transformed system to eliminate the instability of double zeros. All bounded trajectories can be generated by basic solutions, which effectively reveal the following performances of the controller, such as the relationship between the frequencies of basic motions and control gains are detected and the wide selection of gains for stability. Local and global optimizations on gains are discussed based on different performances of the controller. One focuses on the sensitivity of output with respect to input of controller and the other aims at a minimal fuel consumption for the maximum likelihood. The ergodic relationship between the fuel consumption and initial condition is established for the minimal consumption. To avoid in-orbit collision, a collision-free strategy based on the artificial potential function is proposed to enhance the proposed controller, which make sure a minimum safety distance for the formation.

Path-guided time-varying formation control with collision avoidance and connectivity preservation of under-actuated autonomous surface vehicles subject to unknown input gains

This paper investigates the distributed time-varying formation control for a swarm of under-actuated autonomous surface vehicles subject to unknown input gains, in addition to model uncertainties and ocean disturbances. The fleet is required to follow a parameterized path with a time-varying formation while avoiding collisions and maintaining connectivity at a complex sea environment. At the kinematic level, a distributed guidance control law is proposed based on a consensus approach, a path-following design, artificial potential functions, and an auxiliary variable approach. At the kinetic level, an adaptive kinetic control law is designed based on an indirect model reference adaptive control approach where a neural estimator is developed for identifying unknown input gains, model uncertainties and ocean disturbances. The stability of the closed-loop system is proven via cascade stability analysis. The advantage of the proposed method is three-folds. First, the developed time-varying formation controller is able to achieve various coordinated behaviors such as cooperative target tracking and target enclosing. Second, the proposed time-varying formation controller is robust against model uncertainties, ocean disturbances and unknown input gains. Third, the proposed distributed controller holds the capability of collision avoidance and connectivity preservation. Simulation results substantiate the effectiveness of the proposed path-guided time-varying formation controllers.

Abstraction based approach for segregation in heterogeneous robotic swarms

The focus of this study is to design individual control laws that segregate multiple groups of mobile heterogeneous robots. Our approach is based on the use of abstractions to represent each group of robots and an artificial potential function to segregate the groups. Different from other works in the literature, we prove that with our controller the system will always converge to a state where robots of the same group will be together while separated from robots of different groups. We also propose a collision avoidance scheme which does not interfere in the segregation controller. Furthermore, our controller has a local property, meaning that the controller might not require global information of the whole swarm to converge to the segregated state. The approach is validated with simulations varying the number of robots and groups and experiments with real robots.

Bounded flight and collision avoidance control for satellite clusters using intersatellite flight bounds

Abstract A novel satellite cluster control method by means of a set of artificial potential functions is proposed in this paper. To avoid the huge difficulty of designing target configuration for a large-scale satellite cluster, the proposed cluster control method relies on intersatellite flight bounds so that satellites can autonomously converge to a given boundary range, rather than a set of exact orbit configuration. The analytic relative motion bounds in terms of relative orbital elements are deduced and used as variables in artificial potential functions. The accumulated control effort is minute, that shows great potential in micro satellite cluster control. On the other hand, collision avoidance as a key requirement for satellite cluster, also gets attention in this paper. For a long-term perspective, the minimum intersatellite flight bound rather than the real-time relative distance between satellites is introduced into the repulsive artificial potential function. Satellite members can adjust their control effort in real time according to nearby satellites, which reflect the characteristic of swarm intelligence. Monte Carlo simulation reveals the superiority in fuel consumption of the proposed collision avoidance control.

Artificial Potential Function Safety and Obstacle Avoidance Guidance for Autonomous Rendezvous and Docking with Noncooperative Target

The problem of artificial potential function (APF) safety and obstacle avoidance guidance for autonomous rendezvous and docking of chaser spacecraft with noncooperative spacecraft is studied. The relative motion equation of the chaser and the target is established based on the line-of-sight coordinate system, the reference state is designed, and the corresponding state error is deduced. The attitude motion equation of the noncooperative target spacecraft in space is established. The safety and obstacle avoidance guidance problem of autonomous rendezvous and docking with noncooperative target is transformed into a path planning problem in a dynamic environment. The attractive potential function is designed according to the state error. In order to ensure that the chaser can safely approach the noncooperative target spacecraft, a safe corridor with ellipse cissoid is designed in the final approaching stage of autonomous rendezvous and docking. The obstacle is assumed to be a sphere with a certain radius to avoid its influence in the approach, and the obstacle potential function is designed based on the Gaussian function method. The total potential function of the system is designed according to the attractive potential function, the safe potential function, and the obstacle potential function. The total potential function of the system is modified to ensure that the reference state is the minimum of the total potential function of the system. The stability of the system is proven according to the Lyapunov stability principle, and the conditions for satisfying the monotonic decrease in the total potential function of the system are deduced. Finally, the effectiveness of the proposed method is verified by three sets of numerical simulations.

Adaptive Pose Tracking Control for Spacecraft Proximity Operations Under Motion Constraints

A novel adaptive control solution for pose tracking problems of spacecraft proximity operations subject to not only motion constraints but also parameter uncertainties is proposed in this paper. Specifically, the dual-quaternion formalism is employed to model the coupled translational and rotational dynamics of a leader–follower spacecraft formation. A class of artificial potential functions (APFs) is introduced to encode information regarding the underlying motion constraints that should be followed during proximity operations. Moreover, parameter uncertainties are normalized through the adoption of specially defined dual regressor matrices, and subsequently followed by the presentation of an APF-based non-certainty-equivalence adaptive control solution. The salient feature of the proposed adaptive structure is that, by employing dynamic scaling gains, the monotonic convergence of a certain term composed of parameter estimation errors and system states is ensured; this beneficial result along with the properties of the presented APF further avoid the stubborn local minimum problem associated with conventional APF-based controllers. Accordingly, the overall control scheme guarantees the arrival of the follower at the docking port of the leader with a prescribed relative pose while simultaneously accommodating for parameter uncertainties and complying with motion constraints.

Establishment and control of spacecraft formations using artificial potential functions

The automated control of spacecraft formations in specified relative orbits is a challenging problem that is computationally intensive using traditional methods of numerically integrating trajectories and applying optimal control theory. In this paper, relative orbital elements and artificial potential functions are combined into a methodology that allows full control of the relative orbits of spacecraft formations. This method enables the intuitive design of geometrically complex formations, and allows collision avoidance during the formation establishment. The effectiveness of the control algorithm is illustrated with the numerical simulation of the establishment of various formation geometries.

Spacecraft formation reconfiguration with multi-obstacle avoidance under navigation and control uncertainties using adaptive artificial potential function method

In this paper, an adaptive artificial potential function (AAPF) method is developed for spacecraft formation reconfiguration with multi-obstacle avoidance under navigation and control uncertainties. Furthermore, an improved Linear Quadratic Regular (ILQR) is proposed to track the reference trajectory and a Lyapunov-based method is employed to demonstrate the stability of the overall closed-loop system. Compared with the traditional APF method and the equal-collision-probability surface (ECPS) method, the AAPF method not only retains the advantages of APF method and ECPS method, such as low computational complexity, simple analytical control law and easy analytical validation progress, but also proposes a new APF to solve multi-obstacle avoidance problem considering the influence of the uncertainties. Moreover, the ILQR controller obtains high control accuracy to enhance the safe performance of the spacecraft formation reconfiguration. Finally, the effectiveness of the proposed AAPF method and the ILQR controller are verified by numerical simulations.

Practical time-varying output formation tracking for high-order multi-agent systems with collision avoidance, obstacle dodging and connectivity maintenance

Practical time-varying output formation tracking problems with collision avoidance, obstacle dodging and connectivity maintenance for high-order multi-agent systems are investigated, and the practical time-varying output formation tracking error is controlled within an arbitrarily small bound. The outputs of followers are designed to track the output of the leader with unknown control input while retaining the predefined time-varying formation. Uncertainties are considered in the dynamics of the followers and the leader. Firstly, distributed extended state observers are developed to estimate the uncertainties and the leader’s unknown control input. A strategy of obstacle dodging is given by designing an ideal secure position for the followers which are in the threatened area of the obstacles. By constructing collision avoidance, obstacle dodging and connectivity maintenance artificial potential functions, corresponding negative gradient terms are calculated to achieve the safety guarantee. Secondly, a practical time-varying output formation tracking protocol is proposed by using distributed extended state observers and the negative gradient terms. Additionally, an approach is presented to determine the gain parameters in the protocol. The stability of the closed-loop multi-agent system with the protocol is analyzed by using Lyapunov stability theory. Finally, a simulation experiment is provided to illustrate the effectiveness of the obtained methods.

Output-Feedback Cooperative Formation Maneuvering of Autonomous Surface Vehicles With Connectivity Preservation and Collision Avoidance.

In this paper, a cooperative time-varying formation maneuvering problem with connectivity preservation and collision avoidance is investigated for a fleet of autonomous surface vehicles (ASVs) with position-heading measurements. Each vehicle is subject to unknown kinetics induced by internal model uncertainty and external disturbances. At first, a nonlinear state observer is used to recover the unmeasured linear velocity and yaw rate as well as unknown uncertainty and disturbances. Then, observer-based cooperative time-varying formation maneuvering control laws are designed based on artificial potential functions, nonlinear tracking differentiators, and a backstepping technique. The stability of closed-loop distributed formation control system is analyzed based on input-to-state stability and cascade stability. The salient features of the proposed method are as follows. First, cooperative time-varying formation maneuvering with the capability of connectivity preservation and collision avoidance can be achieved in the absence of velocity measurements. Second, the complexity of the cooperative time-varying formation maneuvering control laws is reduced without resorting to dynamic surface control. Third, the uncertainty and disturbance are actively rejected in the presence of position-heading measurements. Simulation results are given to substantiate the proposed output feedback control method for cooperative time-varying formation maneuvering of ASVs with connectivity preservation and collision avoidance.

Target-enclosing affine formation control of two-layer networked spacecraft with collision avoidance

This paper addresses a target-enclosing problem for multiple spacecraft systems by proposing a two-layer affine formation control strategy. Compared with the existing methods, the adopted two-layer network structure in this paper is generally directed, which is suitable for practical space missions. Firstly, distributed finite-time sliding-mode estimators and formation controllers in both layers are designed separately to improve the flexibility of the formation control system. By introducing the properties of affine transformation into formation control protocol design, the controllers can be used to track different time-varying target formation patterns. Besides, multi-layer time-varying encirclements can be achieved with particular shapes to surround the moving target. In the sequel, by integrating adaptive neural networks and specialized artificial potential functions into backstepping controllers, the problems of uncertain Euler-Lagrange models, collision avoidance as well as formation reconfiguration are solved simultaneously. The stability of the proposed controllers is verified by the Lyapunov direct method. Finally, two simulation examples of triangle formation and more complex hexagon formation are presented to illustrate the feasibility of the theoretical results.

Path Planning to a Reachable State Using Minimum Control Effort Based Navigation Functions

The purpose of this paper is to present a new path-planning algorithm for planetary exploration rovers that will guide the vehicle safely to a reachable state. In particular, this work will make use of a special class of artificial potential functions called navigation functions which are guaranteed to be free of local minimum. The construction of the navigation functions in this work is motivated by the grid-based wavefront expansion method but differs in that the contour levels are defined in terms of the control effort of the system. Two new methods will be introduced in this paper for defining the navigation function. The first method will generate a minimum control effort path plan and the second method will be based on an inverse dynamics approach. Each of the control effort based methods will generate a path plan that will guide the rover’s approach towards an objective reachable state. Finally, a stable backstepping-like controller is implemented to track a trajectory defined along the path plan to the rover’s objective.

Distributed RISE control for spacecraft formation reconfiguration with collision avoidance

In this paper, we investigate the distributed formation reconfiguration problem of multiple spacecraft with collision avoidance in the presence of external disturbances. Artificial potential function (APF) based virtual velocity controllers for the spacecraft are firstly constructed, which overcome the local minima problem through introducing auxiliary inputs weighted by bump functions. Then, based on the robust integral of the sign of the error (RISE) control methodology, a distributed continuous asymptotic tracking control protocol is proposed, accomplishing both formation reconfiguration and the collision avoidance among spacecraft and with obstacles. Furthermore, using tools from graph theory, Lyapunov analysis and backstepping technique, we show the stability and collision avoidance performance of the closed-loop multiple spacecraft system. Numerical simulations for a spacecraft formation are finally provided to validate the effectiveness of the proposed algorithm.

Control of non-cooperative spacecraft in final phase proximity operations under input constraints

This paper addresses the approaching trajectory control problem for the final phase of non-cooperative spacecraft proximity operations in the presence of disturbances and even input saturation. As a stepping stone, a novel line-of-sight tracking model is developed to describe attitude maneuver towards the target in the proximity. Then, a two-stage artificial potential function is employed to enable the pursuer spacecraft to comply the safety trajectory during approaching the target. In each stage, gradients of potential function are analyzed and the local minimum problem associated with potential function can be addressed. Furthermore, a saturated control law is proposed to ensure a reliable real-time tracking measurement of the target, and the controller rigorously enforces safe path and actuator magnitude constraints. The associated stability proof is accomplished through Lyapunov method. Simulations are carried out to evaluate the effectiveness of the proposed method.