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This paper proposes a pose control scheme of for proximity maneuvering for tracking and observing noncooperative targets with unknown acceleration, which is an important prerequisite for on-orbit operations in space. It mainly consists of a finite-time extended state observer and constraint processing procedures. Firstly, relative pose-coupled kinematics and dynamics models with unknown integrated disturbances are established based on dual quaternion representations. Then, a finite-time extended state observer is designed using the super-twisting algorithm to estimate the integrated disturbances. Both observation field of view and collision avoidance pose-constrained models are constructed to ensure that the service spacecraft continuously and safely observes the target during proximity maneuvering. And the constraint models are further incorporated into the design of artificial potential function with a unique minimum. After that, the proportional–derivative-like pose-constrained tracking control law is proposed based on the estimated disturbances and the gradient of the artificial potential function. Finally, the effectiveness of the control scheme is verified through numerical simulations. [ABSTRACT FROM AUTHOR]

• Introduce a novel low-thrust constellation reconfiguration control method using artificial potential function. • Assure the Lyapunov stability including phase control and in the presence of perturbations. • Combine collision avoidance with reconfiguration simultaneously, lowering the risk of collision significantly. • Carry out comprehensive numerical simulations under diverse scenarios, including mega-constellation case. The configuration control of constellations which consist of numerous satellites presents significant challenges. Such space systems demand the capability for autonomous reconfiguration to accomplish specific missions. Individual satellites within constellations are primarily equipped with low-thrust systems, rendering traditional impulse control methods for satellite formation and mission planning ineffective. To address this issue, this paper proposes a low-thrust constellations reconfiguration control method utilizing an artificial potential function. Relying exclusively on neighboring state information, satellites can dynamically modulate their control efforts in real-time. The stability of the proposed reconfiguration control method is established under modelable, bounded perturbation using Lyapunov theory. Furthermore, a repulsive potential function is formulated to ensure collision avoidance among satellites. Numerical results indicate that the proposed method is stable, computationally efficient, and guarantees the safe distance during maneuvers. Consequently, this method is ideally suited for reconfiguration tasks across a spectrum of large space systems, including mega-constellations. [ABSTRACT FROM AUTHOR]

A novel safety-guaranteed rendezvous control (SGRC) method is proposed for obstacles avoidance during the rendezvous with a noncooperative target in this paper. An artificial potential field with the addition of a velocity safety corridor is used to describe the motion of space and achieve the constraint on the global velocity of the service spacecraft during the rendezvous. Furthermore, the velocity error term of the system is constrained by combining the prescribed performance control (PPC) method, thereby improving the steady- and transient-state performance of the system while reducing fuel consumption. On this basis, a newly constructed virtual auxiliary state containing both artificial potential fields and self-bounded system state error is developed, and a safety-guaranteed control method capable of achieving rendezvous with the noncooperative target for obstacle avoidance is designed. Two sets of numerical simulation results verify the effectiveness as well as the adaptability of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed formation control of a group of leader-following spacecraft with bounded actuation and limited communication ranges. In particular, connectivity-preserving and collision-avoidance controllers are proposed for the leader with constant or time-varying velocity, respectively. The communication graph between the spacecraft is modeled via a distance-induced proximity graph. By designing a virtual proxy for each spacecraft, the spacecraft–proxy couplings address the actuator saturation constraints. The inter-proxy dynamics incorporated with a bounded artificial potential function fulfill the coordination of all proxies. In addition, the bounded potential function can simultaneously tackle connectivity preservation and collision avoidance problems. The distributed formation controllers are proposed for multiple spacecraft with constant or time-varying velocities relative to the leader. A sliding mode control approach and the proxies' dynamics are used in the design of a distributed cooperative controller for spacecraft to address the cooperative problem between the followers and the leader. Numerical simulations confirm the effectiveness of the anti-saturation distributed connectivity preservation controller. [ABSTRACT FROM AUTHOR]

This paper proposes a pose control scheme of for proximity maneuvering for tracking and observing noncooperative targets with unknown acceleration, which is an important prerequisite for on-orbit operations in space. It mainly consists of a finite-time extended state observer and constraint processing procedures. Firstly, relative pose-coupled kinematics and dynamics models with unknown integrated disturbances are established based on dual quaternion representations. Then, a finite-time extended state observer is designed using the super-twisting algorithm to estimate the integrated disturbances. Both observation field of view and collision avoidance pose-constrained models are constructed to ensure that the service spacecraft continuously and safely observes the target during proximity maneuvering. And the constraint models are further incorporated into the design of artificial potential function with a unique minimum. After that, the proportional–derivative-like pose-constrained tracking control law is proposed based on the estimated disturbances and the gradient of the artificial potential function. Finally, the effectiveness of the control scheme is verified through numerical simulations.

Summary: This article proposes a novel path planning method for source seeking by UAV swarm using extremum seeking control mechanism and combined artificial potential functions, without the knowledge of position information. In particular, the swarm source seeking problem is reformulated as a minimum seeking of a combined artificial potential function that considers the potentials of obstacles, source, and collision avoidance between UAVs. The explicit form of the combined artificial potential function is unknown and its value can be measured by the sensors mounted on UAVs. The fast extremum seeking mechanism based on the normalized extremum seeking method is exploited to find the gradient of the combined artificial potential function and the target is located without using its position information. Finally, extensive simulations of source seeking for single UAV and swarm are presented to illustrate the effectiveness of the proposed path planning method. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed formation control of a group of leader-following spacecraft with bounded actuation and limited communication ranges. In particular, connectivity-preserving and collision-avoidance controllers are proposed for the leader with constant or time-varying velocity, respectively. The communication graph between the spacecraft is modeled via a distance-induced proximity graph. By designing a virtual proxy for each spacecraft, the spacecraft–proxy couplings address the actuator saturation constraints. The inter-proxy dynamics incorporated with a bounded artificial potential function fulfill the coordination of all proxies. In addition, the bounded potential function can simultaneously tackle connectivity preservation and collision avoidance problems. The distributed formation controllers are proposed for multiple spacecraft with constant or time-varying velocities relative to the leader. A sliding mode control approach and the proxies’ dynamics are used in the design of a distributed cooperative controller for spacecraft to address the cooperative problem between the followers and the leader. Numerical simulations confirm the effectiveness of the anti-saturation distributed connectivity preservation controller.

As the number of satellites in orbit increases, the issue of flight safety in spacecraft formation orbit control has become increasingly prominent. With this in mind, this paper designs a second-order terminal sliding mode controller for spacecraft formation obstacle avoidance based on an artificial potential function (APF). To demonstrate the effectiveness of the controller, this paper first constructs a Lyapunov function to prove its stability and then verifies its theoretical validity through numerical simulation. Finally, a satellite simulator is used for semi-physical simulation to verify the practical effectiveness of the controller proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper considers a polygon formation control of multiple robots with nonholonomic constraints enclosing a goal target and double-level-control collision avoidance scheme. Double-level-control scheme consisted of upper-level and lower-level controls are proposed for trajectory generation and tracking control of multi-robot systems. Both upper-level and lower-level controls operate collision avoidance mechanisms based on potential functions. The proposed control scheme guarantees that the group of robots are kept in the polygon formation and driven to a goal, while avoiding collisions during the travel. Moreover, the designed interaction between the upper- and lower-level controls guarantees that the mobile robots are not trapped in local minima or deadlock case. Experiments of the formation of three-robots are conducted to show the performance of the mobile robots in accomplishing a polygon formation while achieving the goal without any collision and no local minima. [ABSTRACT FROM AUTHOR]

Most of the multi-agent formation and obstacle avoidance algorithms in the literature are computationally expensive and/or presents an ad hoc method for a specific type of systems. A general inexpensive, in term of computational complexity, multi-agent formation and obstacle avoidance algorithm is modeled and designed in this paper. The method builds on the leader-follower strategy for the simplicity and applicability for a wide range of the engineering systems. A novel artificial potential function (APF) is proposed. The proposed function has unique attributes which differentiate it superior to what is reported in the literature. The proposed algorithm can be applied for first order systems, second order systems, and non-holonomic systems. Also, the proposed method is free of local minima problem and oscillations. In addition, a novel multi-agent system formation control design is proposed in this work. The proposed design allows to embed any formation in the system paradigm and reduces complexity. Moreover, the stability of the proposed method is investigated in terms of Riccati equation and Lyapunov method. Furthermore, to show the effectiveness of the proposed method it applied and simulated for a second order leader and one follower system with specific formation. Then, a five second order agents with leader in a circular formation avoiding simple and complex obstacles are also introduced with different scenarios. Finally, twenty agents with square formation with two obstacles are simulated and investigated.

This paper addresses the finite‐time constrained attitude regulation problem for spacecraft formation with disturbances on SO(3)$$ SO(3) $$. An artificial potential function (APF) is constructed based on the rotation matrix to handle the attitude constraints. By combining the terminal sliding mode control technique with the APF, a robust control law is proposed to achieve the almost globally constrained attitude regulation for spacecraft formation with disturbances in finite time. Then a leader‐following robust control law is developed using a modified finite‐time distributed observer when some spacecraft cannot obtain the desired attitude directly. Based on the Lyapunov stability theory and Artstein's transformation, the sufficient conditions are strictly derived for spacecraft formation to guarantee the almost globally leader‐following finite‐time constrained attitude regulation with disturbances and communication delay. Numerical simulations are presented to demonstrate the effectiveness of the proposed control laws. [ABSTRACT FROM AUTHOR]

This work presents a novel self-organizing control method for mega constellations to meet the continuous Earth observation requirements. In order to decrease the TT&C pressure caused by numerous satellites, constellation satellites are not controlled according to the designed configurations but are controlled with respect to intersatellite constraints. By analyzing the street-of-coverage (SOC) of coplanar constellation satellites, the continuous coverage constraint of the mega constellation is transformed into constraints of the right ascension of ascending node (RAAN) and relative motion bound between every two adjacent coplanar satellites. The proposed continuous coverage constraint can be satisfied by most ongoing or planned mega constellations. Artificial potential functions (APFs) are used to realize self-organizing control. The scale-independent relative orbital elements (SIROEs) are innovatively presented as the self-organizing control variables. Using the Gaussian equations and Lyapunov's theory, the stability of the APF control in quadratic form is proven, from which it can be concluded that the APF control variables of the controlled satellite should have the same time derivative as the target satellite states under two-body Keplerian motion condition, and SIROEs are ideal choices. The proposed controllers and self-organizing rules are verified in the sub-constellation of the GW-2 mega constellation by simulation. The results demonstrate the goodness in control effect and ground coverage performance. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new path planning algorithm based on the probabilistic roadmaps method (PRM), in order to effectively solve the autonomous path planning of mobile robots in complex environments with multiple narrow channels. The improved PRM algorithm mainly improves the density and distribution of sampling points in the narrow channel, through a combination of the learning process of the PRM algorithm and the APF algorithm. We also shortened the required time and path length by optimizing the query process. The first key technology to improve the PRM algorithm involves optimizing the number and distribution of free points and collision-free lines in the free workspace. To ensure full visibility of the narrow channel, we extend the obstacles through the diagonal distance of the mobile robot while ignoring the safety distance. Considering the safety distance during movement, we re-classify the all sampling points obtained by the quasi-random sampling principle into three categories: free points, obstacle points, and adjacent points. Next, we transform obstacle points into the free points of the narrow channel by combining the APF algorithm and the characteristics of the narrow channel, increasing the density of sampling points in the narrow space. Then, we include potential energy judgment into the construction process of collision-free lines shortening the required time and reduce collisions with obstacles. Optimizing the query process of the PRM algorithm is the second key technology. To reduce the required time in the query process, we adapt the bidirectional A* algorithm to query these local paths and obtain an effective path to the target point. We also combine the path pruning technology with the potential energy function to obtain a short path without collisions. Finally, the experimental results demonstrate that the new PRM path planning technology can improve the density of free points in narrow spaces and achieve an optimized, collision-free path in complex environments with multiple narrow channels. [ABSTRACT FROM AUTHOR]

This paper investigates a formation tracking problem of underactuated surface vessels (USVs) with collision avoidance and input saturation. All nonlinearities induced by model uncertainties and disturbances are assumed to be unknown. A design of observer based on neural network is used to recover the velocity data and unknown uncertainties and disturbances. Distributed control laws are designed based on artificial potential functions (APFs), the observer, and a backstepping technique. The APFs combined with a practical category are used to avoid collision. Additional controllers are employed to deal with the input saturation and underactuated problems without affecting the capability of collision avoidance. The stability of formation control system is proved by using the Lyapunov's direct method. Simulation results are performed to illustrate the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed dynamic event-triggered control that addresses the flocking control problem with a virtual leader for multiple unmanned surface vehicle (USV) systems. Unlike existing flocking algorithms, which often result in the formation of quasi α-lattice structures, the proposed approach combines artificial potential functions (APF), directionally consistent potential functions (DCPF), and a navigation feedback term to form an α-lattice. A novel artificial potential function is developed to facilitate flocking and maintain a safe distance between USVs to avoid collisions. Additionally, a dynamic event-triggered mechanism, initially employed in flocking control, is introduced to reduce communication among USVs. Furthermore, it is demonstrated that Zeno behavior does not occur. The algorithm employs Radial Basis Function Neural Networks (RBFNNs) and adaptive algorithms to dynamically estimate and compensate for parameter uncertainties and external disturbances. Finally, the effectiveness and robustness of the proposed algorithm are verified through numerical simulation. • A distributed dynamic event-triggered control is proposed for the first time to study the flocking problem in multi-USV systems. • A smooth artificial potential function is designed to take into account the collision avoidance problem among non-pointed agents. • A smooth artificial potential function is designed to guarantee the function with a bound cut-off. [ABSTRACT FROM AUTHOR]

Heavy Commercial Road Vehicle (HCRV) platooning is a promising solution to meet increasing freight transportation demands. This paper applies the concept of Artificial Potential Functions (APF) to design a string stable controller, viz., Potential Function-based String Stable (PFSS) controller, for establishing stable HCRV platoons under various operating conditions. A methodical approach for the design and selection of potential functions that would maintain the desired intervehicular spacing in the presence of perturbations has been presented. The proposed methodology has been evaluated on a complete vehicle dynamics model-based platoon framework, which would emulate actual vehicle operation. It provides string stable operation under different lead vehicle perturbation maneuvers on various road friction and slope conditions with homogeneous and heterogeneous loading conditions. Compared to existing string stable control approaches, the proposed PFSS controller has attributes such as minimal data requirement from neighboring vehicles, actuator feasible control actions, and simpler control structures.

This study is mainly focusing on the problem of spacecraft close-range proximity with obstacle avoidance in the presence of complex shape. A novel Gaussian mixture model–based nonsingular terminal sliding mode control (GMM-NTSMC) is proposed. This is achieved by developing GMM-based potential function with a switching surface of NTSMC. It is theoretically proved that the closed-loop system is globally stable. The main contribution of this study is that the GMM-based avoiding strategies, which include the GMM-based terminal sliding mode control (GMM-TSMC) and GMM-NTSMC, can solve the collision avoidance problem considering complex shape while the artificial potential function–based terminal sliding model control (APF-TSMC) fails. Moreover, the GMM-NTSMC and the GMM-TSMC require less energy with respect to the APF-TSMC. Furthermore, the GMM-NTSMC retains the advantage of the NTSMC and can avoid singularity problem while GMM-TSMC cannot. Finally, numerical simulations are performed to verify the effectiveness and superiority of the proposed GMM-NTSMC. [ABSTRACT FROM AUTHOR]

This article seeks to address the robust output-feedback motion tracking control problem for spacecraft close-range proximity maneuvers under the influence of forbidden zone, external disturbances, and input saturation. First, two superquadric cuboids are constructed in the body-fixed frame of the target to represent the forbidden zone in final proximity. Then, an adaptive output-feedback control scheme is proposed under the framework of extended state observer technique and sliding mode control methodology. The presented scheme can achieve concurrent position and attitude tracking without prior information of the velocity-level states, and avoid any unwanted collisions between the two spacecraft. Finally, simulation scenarios are investigated to show the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Spacecraft on-orbital services and docking require their autonomous rendezvous control system to have obstacle avoidance capability. Motivated by this, a suboptimal velocity artificial potential function-based control scheme is presented. An ellipsoid model is applied to describe the outer envelopes of the service spacecraft and the obstacles via an eigenvalue algorithm. This has better description precision than the traditional methods. The potential sigmoid function is used to generate repulsive force to avoid obstacles collision. A velocity artificial potential function-based controller is finally developed to ensure that the relative speed of the service spacecraft is reduced to zero before reaching the outer envelops of obstacles. The shaping parameters of the attractive potential function are adaptively optimized. Numerical simulations are performed to demonstrate that the approach can achieve a safe and autonomous rendezvous with fuel cost saved. [ABSTRACT FROM AUTHOR]

Autonomous spacecraft proximity technology is vital for current and future on-orbit service missions, especially to solve the difficult problem of ultra-close-range safe proximity to complex-shaped spacecraft. This paper designs a novel Gaussian mixture model (GMM) based artificial potential function (APF) to describe the movement constraint, which is generated by the complex shape of the target spacecraft. Next, a novel GMM-FTC controller is designed by combining fixed-time control (FTC) with GMM-APF. The proposed GMM-FTC not only retains the advantages of FTC method, whose stabilization time is independent of the initial state, but also solves the collision avoidance in the presence of complex shape obstacle. Finally, numerical simulation verifies the effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

This article presents a model predictive control (MPC) coupled with an artificial potential field (APF) to resolve the trajectory tracking while considering the obstacle avoidance. In this article, the obstacle avoidance problem is solved by a local path planning based on the artificial potential field by constructing a virtual goal. A virtual goal is generated to produce an attractive force to guide the mobile robot to a collision-free space. The planned path is controlled by a proportional–integral–derivative (PID) controller to avoid collision. After arriving at the virtual goal, an off-line explicit MPC is calculated to obtain the optimal control inputs to track the reference trajectory. The simulation results show that the proposed method can be applied to control the mobile robot in the environment with one obstacle. [ABSTRACT FROM AUTHOR]

This paper describes the design and development of a cleaning robot, using adaptive manufacturing technology and its use with a control algorithm for which there is a stability proof. The authors' goal was to fill the gap between theory and practical implementation based on available low-cost components. Adaptive manufacturing was chosen to cut down the cost of manufacturing the robot. Practical verification of the effectiveness of the control algorithm was achieved with the experiments. The robot comprises mainly three assemblies, a four-wheel-drive platform, a four-degrees-of-freedom robotic arm, and a vacuum system. The inlet pipe of the vacuum system was attached to the end effector of the robotic arm, which makes the robot more flexible to clean uneven areas, such as skirting on floors. The robot was equipped with a LIDAR sensor and web camera, giving the opportunity to develop more complex methods. A low-level proportional–integral–derivative (PID) speed controller was implemented, and a high-level controller that uses artificial potential functions to generate repulsive components, which avoids collision with obstacles. Robot operating system (ROS) was installed in the robot's on-board system. With the help of the ROS node, the high-level controller generates control signals for the low-level controller. [ABSTRACT FROM AUTHOR]

This paper presents control method for multiple two-wheeled mobile robots moving in formation. Trajectory tracking algorithm from [7] is extended by collision avoidance, and is applied to the different type of formation task: each robot in the formation mimics motion of the virtual leader with a certain displacement. Each robot avoids collisions with other robots and circular shaped, static obstacles existing in the environment. Artificial potential functions are used to generate repulsive component of the control. Stability analysis of the closed-loop system is based on Lyapunov-like function. Effectiveness of the proposed algorithm is illustrated by simulation results.

Thispaper investigates the micro-satellite cluster long-distance gathering control problem including initialization, orbit maintenance and collision avoidance operations. This problem is formulated using absolute orbital elements and newly developed quadratic artificial potential function based on these elements. Incorporating with the artificial potential function, a distributed autonomous low-thrust control method is proposed to solve the cluster gathering problem. Comparing with the fuel-optimal control problem formulated by equations established in Cartesian coordinates, the proposed method demonstrates geometrical intuition and possesses a low-cost computation burden. These advantages make the proposed method more suitable for controlling micro-satellite clusters. The stability of the autonomous low-thrust control method is proved using the Lyapunov method. Additionally, a Monte Carlo analysis is applied to demonstrate both the effectiveness and the collision avoidance ability of the presented algorithm. [ABSTRACT FROM AUTHOR]

Wireless solar blind ultraviolet (UV) scattering communication is a new type of atmosphere optics communication technology with the important and potential advantages of all-weather, non-line-of-sight and secret communication, which is suitable for the needs of cluster security of Unmanned Aerial Vehicle (UAV) formation flight. UV communication technology can be applied to share UAVs status information, combined with efficient formation control method can achieve autonomous assembly, collision avoidance and formation keeping in UAV formation flight. In order to avoid the collision avoidance problem between the UAVs in the classic formation control algorithm. In this paper, the artificial potential function of the formation control algorithm is improved and the improved algorithm is applied to a single virtual leader UAV and multi-virtual leader UAVs. The simulation results show that the algorithm can ensure that the UAVs speed in the formation is consistent with the speed of the virtual leader UAV. In the course of the flight, the UAVs can avoid collision. Finally, the formation flight is completed with the desired formation. [ABSTRACT FROM AUTHOR]

In this paper, a six-degree-of-freedom (6-DOF) control scheme for asteroid landing subject to collision avoidance and line-of-sight (LOS) constraints is developed within the newly established twistor framework. The controller guarantees a spacecraft touches down at a specified landing site in a desired attitude, meanwhile satisfies the constraints with the coupling effect between the translational and rotational motions involved. First, 6-DOF dynamics of a spacecraft relative to an asteroid is described by the twistor representation to model the translational and rotational motions in a unified way. Then, the collision avoidance and LOS constraints are formulated and expressed as functions of the twistor. Following that, the constraints are encoded into an artificial potential function (APF) and a control scheme that enforces the constraints is proposed by virtue of the APF technique with the stability of the controlled closed-loop system proved via Lyapunov analysis. Finally, numerical simulations are conducted, and the results demonstrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

In this brief, we focus on the study of formation tracking problem for a class of multiagent systems with nonlinear dynamics and external disturbances in the presence of relative distance constraints. A novel distributed formation control strategy is proposed based on an integration of radial basis function neural network (NN) with artificial potential field method. The relative distance constraints between arbitrary adjacent agents can be ensured by the artificial potential function. Based on the NN approximation property, it has been proposed to neutralize the nonlinear dynamics in agents. To account for the negative influence of the approximation error and external disturbances, a robustness term is employed. Finally, based on algebraic graph theory, matrix theory, and Barbalat’s lemma, some sufficient conditions are established to accomplish the asymptotical stability of the systems for a given communication graph. The study is with application to tethered space net robot. The simulation results are performed to illustrate the performance of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive tracking control scheme for multi-spacecraft formation with inter-collision avoidance, obstacle dodging, and connectivity preservation. The proposed scheme is distributed, i.e., each spacecraft only needs to communicate with its neighbours. Both connectivity preservation and distributed networking are critical features for small spacecraft formation with limited computation and communication capacities. New artificial potential functions are defined to preserve the connectivity of neighbour spacecraft while avoiding their inter-collision as well as collision with obstacles. An adaptive sliding-mode controller is designed for reaching and maintaining the predetermined formation configuration while satisfying the safety assurance requirements, including inter-collision avoidance, obstacle dodging, and connectivity preservation. The stability of the controller is proven through the Lyapunov analysis, in the presence of gravitational, solar radiation pressure, and atmosphere drag perturbations and dynamic uncertainties. The performance of the control scheme is demonstrated through several comparative simulation studies. [ABSTRACT FROM AUTHOR]

In terms of the motion planning problem of spacecraft proximity operations with obstacle avoidance under low uncertainty, the improved equal-collision-probability-curve and improved linear quadratic regulator (IECPC-ILQR) strategy is proposed. Firstly, the novel function of the IECPC algorithm is developed to generate the avoidance control impulse. Subsequently, the ILQR is designed to track the reference trajectory. Furthermore, combining the improved ECPC algorithm with the ILQR controller, the composite controller of the IECPC-ILQR strategy is obtained and is implemented on the chaser spacecraft. Compared with the traditional ECPC algorithm, the IECPC-ILQR strategy can avoid collision in the presence of low uncertainty. Furthermore, the proposed avoidance strategy can obtain higher control precision while requiring the same fuel. Finally, numerical simulations verify the effectiveness of the proposed IECPC-ILQR strategy. [ABSTRACT FROM AUTHOR]

Summary: Position-tracking problems in the structures of rigid formations of nonholonomic mobile robots, such as fixed-wing unmanned aerial vehicle (UAVs), must reconcile tracking precision and flight stability, which usually exclude each other due to nonholonomic motion constraints. Therefore, a position-tracking control that is based on distance and position displacement, defined as inputs of control loops, requires the application of dead zones around target positions, which are the points of instability. For this reason, the control becomes sensitive to any external disturbance causing oscillations of control signals and so it becomes difficult to maintain a zero value of position displacement over a long time horizon. Thus, we propose an approach based on the adaptive mechanism of an asymmetrical local artificial potential field, which is defined by a local frame of reference whose origin is located in the tracked position of a UAV in the formation frame. It couples controls of both airspeed and heading angle into a nonlinear potential function of relative position and orientation with respect to the tracked position and adapts it according to heading rate of the leader. The function splits the area around the tracked position longitudinally into two zones of acceleration and deceleration; therefore, velocity vectors are longer (higher airspeed) only when a UAV is behind the tracked position and shorter (lower airspeed) when it is ahead. The area is laterally symmetrical, and orientations of velocity vectors align asymptotically to the longitudinal direction accordingly with the decrease in the lateral error. Finally, velocity vectors are rotated proportionally to the heading rate of the leader, which improves the tracking precision during turns. If we assumed that a UAV's tracked position is in motion, it could easily be proven that the position control based on the adaptive asymmetrical potential function becomes asymptotically stable in the tracked position. Numerical simulation verifies this thesis and presents more precise and stable position tracking due to the adaptation mechanism. [ABSTRACT FROM AUTHOR]

This paper presents control method for multiple two-wheeled mobile robots moving in formation. Trajectory tracking algorithm from [7] is extended by collision avoidance, and is applied to the different type of formation task: each robot in the formation mimics motion of the virtual leader with a certain displacement. Each robot avoids collisions with other robots and circular shaped, static obstacles existing in the environment. Artificial potential functions are used to generate repulsive component of the control. Stability analysis of the closed-loop system is based on Lyapunov-like function. Effectiveness of the proposed algorithm is illustrated by simulation results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of autonomous rendezvous and docking with a non-cooperative target spacecraft is studied. A coupled translational and rotational dynamics of the spacecraft is used, where the rotation matrix is used to represent the attitude of spacecraft to overcome the drawbacks related to the unwinding. An asymptotically stable autonomous rendezvous and docking collision-free controller is proposed based on a novel designed sliding surface. Then, a new nonsingular terminal sliding surface is given, based on which the developed autonomous rendezvous and docking collision-free controller can make the tracking errors converge into a small bounded area near the origin in a finite time. Using artificial potential function and virtual obstacles model established based on cissoid, both controllers ensure the chaser spacecraft strictly remains in the safety area to avoid the collision with the target spacecraft. The effectiveness of the proposed controllers is demonstrated by numerical simulation. [ABSTRACT FROM AUTHOR]

Abstract Self-organizing control for satellite clusters is a challenging and promising problem which has drawn considerable attention in the recent past. The artificial potential function method has been widely used for self-organizing control due to its elegant mathematical analysis and simplicity. This paper proposes a set of self-organizing control rules for satellite clusters described by artificial potential functions, so that the reconfiguration, uniform distribution and collision avoidance operations can be achieved spontaneously. It may work regardless of the failure of satellites, attendance of new members or existence of space debris, and the corresponding communication and control system are completely distributed. Particularly, the artificial potential functions are written in terms of relative orbital elements derived from T–H equations, so that the self-organizing control can reflect relative motion dynamics, and guide the satellite along a fuel-efficient trajectory. The proposed method is especially suitable for highly distributed micro-satellite clusters and large-scale clusters to track moving targets, with few fuel cost and relatively high control accuracy, and it is applicable to clusters in either deep space or near-earth space. The stability of the control was proved by Lyapunov second method, and verified by Monte Carlo simulation. Finally, the comparison between self-organizing control and fuel-optimal control was made to demonstrate the performance properties. [ABSTRACT FROM AUTHOR]

Highlights • A semi-cubical parabola based curve is introduced to describe the path constraint during the proximity process. • A nonlinear control strategy by combining the APF method and the sliding mode control technique is proposed. • The presented control strategy can provide a safe and feasible rendezvous trajectory for the chaser spacecraft. Abstract This paper deals with the safety control problem for spacecraft rendezvous and docking with coupled position and attitude dynamics under external disturbances and unknown model parameters. Given the path constraint, a semi-cubical parabola based curve is employed to restrict the motion area of the chaser spacecraft during the process of rendezvous and proximity operations. By combining the sliding mode technique with the artificial potential function, a robust adaptive control strategy is presented for driving the chaser spacecraft to rendezvous and dock with a space target without violating the path constraint. The stability of the closed-loop system is then proved within the Lyapunov framework. Numerical simulations are carried out to illustrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the relative position tracking and attitude synchronization problem of spacecraft rendezvous with the requirement of collision avoidance. To achieve the implementation of the rendezvous procedure, the docking port of the chaser is required to direct towards the counterpart of the target, while the relative distance between the two spacecraft should be larger than the radius of the danger zone during close proximity phase. In order to address the concerned problem, a novel sliding mode control strategy based on artificial potential function is developed, and more specifically, the sliding manifold of the close-loop system is chosen along the negative gradient of the artificial potential function. Within the Lyapunov framework, the proposed control laws are proved to guarantee the convergence of relative position and attitude errors while avoiding any accidental collision between the two spacecraft, even in the presence of external disturbance. Numerical simulations are carried out to demonstrate the effectiveness of the designed control laws. Highlights • Nonlinear relative pose control for spacecraft proximity operation with the requirement of collision avoidance is presented. • State feedback control laws are developed by employing artificial potential field and sliding mode technique. • A 6DOF simulation example is carried out to demonstrate the excellent performance of the proposed control laws. [ABSTRACT FROM AUTHOR]

This paper presents the formulation of a flocking control algorithm for a group of autonomous underwater vehicles (AUVs). A leader–follower control strategy is employed to flock a group of AUVs along a predefined desired path. In this approach, leader AUVs are assumed to have global knowledge of the desired trajectory and the follower AUVs are not provided with this information. For keeping all the AUVs connected in a group, a flocking center is estimated. This flocking center is a virtual point whose position at any instant of time can be predicted by using a consensus algorithm. The controllers for the leader and follower AUVs are developed by implementing mathematical and fuzzy artificial potential functions. A group of four AUVs is considered for analyzing the efficacy of the developed control algorithm. Simulations are carried out both in obstacle-free and obstacle-rich environments. From the obtained results, it is observed that the proposed fuzzy flocking control algorithm provides effective cooperative motion control of multiple AUVs along the desired paths and avoid obstacles successively. It is also observed that the flocking controller developed based on fuzzy artificial potential function outperforms the controller with mathematical potential functions despite uncertainties owing to external disturbances. [ABSTRACT FROM AUTHOR]

This paper is concerned with the trajectory tracking by multiple agents in formation. Each agent is modeled as a double-integrator system. The proposed algorithm works on a connected graph instead of a fully connected graph that requires lesser communication and computation. The three aspects of the control scheme—connectivity assurance, collision avoidance, and formation have been ensured by the design of the novel control law consisting of four terms. A novel bounded potential function has been introduced that ensures interagent collision avoidance through the innovative design of critical parameters associated with this potential function. Another novel bounded potential function has been designed to ensure the connectivity in the group. The concept of consensus has been used to acquire and maintain the desired formation pattern with velocity agreement among agents. The proposed control scheme is further extended to the problem of trajectory tracking while achieving other control objectives. Both the schemes have been shown to be convergent using Barbalat's Lemma. Detailed theoretical analysis of the algorithms has been carried out including boundedness of the control actions. The performance of proposed algorithms has been demonstrated through extensive simulations in 2-D and 3-D environments using 6 and 60 agents, respectively. [ABSTRACT FROM AUTHOR]

A novel guidance strategy is developed based on the artificial potential function for a chaser spacecraft to autonomously approach a freely tumbling target in the on-orbit servicing missions, which can generate the desired velocity instruction for the chaser spacecraft. Considering the collision avoidance constraints, the motion of the tumbling target is classified into three cases. The tumbling axis of the target is perpendicular to its docking port axis in Case 1, and the two axes are nonorthogonal in Case 2, and the two axes are in line in Case 3. Different safe boundaries are established for Case 1 and Case 2, and the desired velocity instruction is determined using the novel guidance strategy, respectively. The method for Case 3 is similar to Case 2. A sliding model controller is designed to control the chaser spacecraft to satisfy the desired velocity instruction. Numerical simulations are performed, and the results show that the developed guidance strategy is an effective method to solve the problem of autonomously approaching a tumbling target. [ABSTRACT FROM AUTHOR]

This paper explores a collision avoidance fault-tolerant control scheme for dynamic positioning vessels in the presence of velocity constraints and thruster faults. First, the collision avoidance problem for multiple static obstacles is described as security zone constraint and integrated into the controller design via an artificial potential function. Second, an indirect error vector including the gradient of potential function and vessel velocity information is constructed, and a time-varying asymmetric barrier Lyapunov function is adopted to concurrently guarantee the satisfaction of velocity constraints. With the help of robust adaptive techniques, the derived controller not only provides robustness against unknown parameters affections, ocean disturbances, and thruster faults, but also has a simple structure and inexpensive online computations for real-time implementation. Finally, the asymptotic convergence of the gradient of potential function and vessel velocity is demonstrated, while a positioning control task for a dynamic positioning vessel is presented to evaluate the effectiveness of the proposed method. • Formulate the collision avoidance problem affected by multiple static obstacles as safety zone constraints. • Designing an artificial potential function to guarantee that the position of a dynamic positioning vessel remains within the safety zone. • Constructing a time-varying asymmetric barrier Lyapunov function to indirectly achieve velocity constraints while avoiding obstacles. [ABSTRACT FROM AUTHOR]

Sub-Optimal Artificial Potential Function Sliding Mode Control (SOAPF-SMC) is proposed for the guidance and control of spacecraft rendezvous considering the obstacles avoidance, which is derived based on the theories of artificial potential function (APF), sliding mode control (SMC) and state dependent riccati equation (SDRE) technique. This new methodology designs a new improved APF to describe the potential field. It can guarantee the value of potential function converge to zero at the desired state. Moreover, the nonlinear terminal sliding mode is introduced to design the sliding mode surface with the potential gradient of APF, which offer a wide variety of controller design alternatives with fast and finite time convergence. Based on the above design, the optimal control theory (SDRE) is also employed to optimal the shape parameter of APF, in order to add some degree of optimality in reducing energy consumption. The new methodology is applied to spacecraft rendezvous with the obstacles avoidance problem, which is simulated to compare with the traditional artificial potential function sliding mode control (APF-SMC) and SDRE to evaluate the energy consumption and control precision. It is demonstrated that the presented method can avoiding dynamical obstacles whilst satisfying the requirements of autonomous rendezvous. In addition, it can save more energy than the traditional APF-SMC and also have better control accuracy than the SDRE. [ABSTRACT FROM AUTHOR]

In this study, the issue of the performance guaranteed fault-tolerant control for formation reconfiguration with collision avoidance in the multi-spacecraft system subjects to space perturbations and thruster faults is investigated. A new nonlinear iterative learning disturbance observer is constructed to accurately reconstruct the synthesized disturbance no matter it is time-varying or not. Then, an exponential artificial potential function with a simple structure and low computation requirement is designed to avoid collision between spacecrafts. A nonsingular terminal sliding mode fault-tolerant control method is explored to accomplish fault-tolerant formation reconfiguration with collision avoidance ability and prescribed robust performance. Finally, numerical simulations and comparisons are performed to validate the effectiveness and superiority of the proposed approaches. [ABSTRACT FROM AUTHOR]