Collision Constraints Research Articles

Trajectory Planning of Spacecraft Swarm Reconfiguration Using Reachable Set-Based Collision Constraints

Trajectory Planning of Spacecraft Swarm Reconfiguration Using Reachable Set-Based Collision Constraints

Research on Trajectory Planning and Tracking Algorithm of Crawler Paver

The implementation of unmanned intelligent construction on the concrete surfaces of an airport effectively improves construction accuracy and reduces personnel investment. On the basis of three known common tracked vehicle dynamics models, reference trajectory planning and trajectory tracking controller algorithms need to be designed. In this paper, based on the driving characteristics of the tracked vehicle and the requirements of the stepping trajectory, a quartic polynomial trajectory planning algorithm was selected with the stability of the curve as a whole and the end point as the optimization goal, combining the tracked vehicle dynamics model, collision constraints, start–stop constraints and other boundary conditions. The objective function of trajectory planning was designed to effectively plan the reference trajectory of the tracked vehicle’s step-by-step travel. In order to realize accurate trajectory tracking control, a nonlinear model predictive controller with transverse-longitudinal integrated control was designed. To improve the real-time performance of the controller, a linear model predictive controller with horizontal and longitudinal decoupling was designed. MATLAB 2023A and CoppeliaSim V4.5.1 were used to co-simulate the two controller models. The experimental results show that the advantages and disadvantages of the tracked vehicle dynamics model and controller design are verified.

Trajectory Planning Design for Parallel Parking of Autonomous Ground Vehicles with Improved Safe Travel Corridor

In this paper, the concept of symmetry is utilized to design the trajectory planning for parallel parking of autonomous ground vehicles—that is, the construction and the solution of the optimization-based trajectory planning approach are symmetrical. Parking is the main factor that troubles most drivers for their daily driving travel, and it can even lead to traffic congestion in severe cases. With the rise of new intelligent and autonomous vehicles, automatic parking seems to have become a trend. Traditional geometric planning methods are less adaptable to parking scenarios, while the parking paths planned by graph search methods may only achieve local optimality. Additionally, significant computational time is often required by numerical optimization methods to find a parking path when a good initial solution is not available. This paper presents a hierarchical trajectory planning approach for high-quality parallel parking of autonomous ground vehicles. The approach begins with a graph search layer to roughly generate an initial solution, which is refined by a numerical optimization layer to produce a high-quality parallel parking trajectory. Considering the high dimensionality and difficulty of finding an optimal solution for the path planning optimization problem, this paper proposes an improved safe travel corridor (I-STC) with the construction of collision constraints isolated from surrounding environmental obstacles. By constructing collision constraints of the I-STC based on the initial solution, the proposed method avoids the complexities and non-differentiability of traditional obstacle avoidance constraints, and simplifies the problem modeling the subsequent numerical optimization process. The simulation results demonstrate that the I-STC is capable of generating parallel parking trajectories with both comfort and safety.

Online task allocation and scheduling in multi-manipulator system considering collision constraints and unknown tasks

Compared to a single robot, multi-robot systems (MRS) offer several advantages in complex multi-task scenarios. The overall efficiency of MRS relies heavily on an efficient task allocation and scheduling process. Multi-robot task allocation (MRTA) is often formulated as a multiple traveling salesman problem, which is NP-hard and typically addressed offline. This paper specifically addresses the online allocation problem in multi-manipulator systems within multi-task scenarios. The tasks are initially pre-allocated to alleviate the computational burden of online allocation. Subsequently, considering collision constraints, we search for the current feasible set of manipulators and employ greedy algorithms to achieve local optima as the online allocation result within this set. Our method can handle the online addition of new, unknown tasks to the task list. Moreover, we demonstrate the feasibility of our approach through simulations and on a realistic platform, where multiple manipulators are tasked with polishing the white body of automobile parts. The results demonstrate that our method is effective and efficient for online allocation and scheduling scenarios.

Distributed Formation Maneuvering Quantized Control of Under-Actuated Unmanned Surface Vehicles with Collision and Velocity Constraints

This paper focuses on a distributed cooperative time-varying formation maneuvering issue of under-actuated unmanned surface vehicles (USVs). A fleet of USVs is guided by a parameterized path with a time-varying formation while avoiding collisions and preserving the connectivity in the environment with multiple obstacles. In some surface missions, due to the obstacles in the external environment, the bandwidth limitations of the communication channel, and the hardware components/performance constraints of the USVs themselves, each vehicle is considered to be subject to model uncertainty, actuator quantization, sensor dead zone, and velocity constraints. During the control design process, the radial basis function (RBF) neural networks (NNs) are utilized to deal with nonlinear terms. Based on a nonlinear decomposition method, the relationship between the control signal and the quantization one is established, which overcomes the difficulty arising from actuator quantization. A Nussbaum function is introduced to handle the unknown output dead zone problem caused by reduced sensor sensitivity. Moreover, a universal-constrained function is employed to satisfy both the constrained and unconstrained requirements during formation keeping and obstacle avoidance. The Lyapunov stability theory confirmed that the error signals are uniformly ultimately bounded (UUB). The simulation results demonstrate the effectiveness of the proposed distributed formation control of multiple USVs.

Convex distributed robust model predictive control for collision and obstacle avoidance

AbstractThe article proposes a convex distributed robust model predictive control algorithm for collision avoidance in multi‐agent systems with additive disturbances, which utilizes the concept of tube model predictive control to address the disturbances. To tackle the coupled collision avoidance constraints, each agent integrates assumed nominal position and input trajectories from its neighbors, rather than relying on actual ones. Compatibility constraints are then designed using the normal vector of the constructed separating hyperplanes for collision avoidance and the residual collision avoidance margin of the optimal solutions at the last time step to restrict deviations between assumed and actual trajectories and ensure consistency among the agents. The nonconvex collision and obstacle avoidance constraints are convexified using the concept of safe sets, transforming them into time‐varying closed polyhedral constraints while accounting for the impact of disturbances. Particularly, the residual collision avoidance margin is incorporated into the construction of safe sets for the satisfaction of coupled collision avoidance constraints. Consequently, the original collision avoidance optimal control problems can be efficiently and simultaneously solved for all agents using standard quadratic programming techniques. Under the design of local terminal constraint sets for each agent, the proposed algorithm ensures a rigorous analysis of robust constraint satisfaction for collision avoidance constraints, as well as an assessment of recursive feasibility and closed‐loop stability. The effectiveness of the algorithm is demonstrated through an illustrative example, and simulation results validate its ability to successfully achieve collision and obstacle avoidance even in the presence of disturbances.

Packing optimization and design of the deployable parabolic rigid antenna based on origami

This paper introduces a novel approach for optimizing the packing and design of deployable parabolic rigid antenna structures based on origami, tailored to meet specific requirements related to the number of solid-surface blocks and the size of the folded antenna. The study begins by selecting a single-vertex four-crease configuration with one degree of freedom from the origami pattern, guided by mobility analysis, to optimize block arrangement. Subsequently, a planar model is employed to qualitatively examine the impact of geometric parameters on the stowage efficiency of the antenna. Building upon the insights gained from the planar model, an optimization framework for the parabolic rigid deployable antenna structure is established. The objective function of the optimization is the stowage volume, while simultaneously adhering to stiffness, collision, and mobility constraints. The design parameters of the antenna structure are thoroughly analyzed. To mitigate collision risks during folding, design considerations are applied to placement of support nodes, location of rotating axes, and block division, leveraging the optimized parameters. The practicality of the proposed method is successfully demonstrated through the folding of a simulated 3D model and of a physical 3D printed model. These tangible representations show the feasibility of the presented approach, affirming its potential applicability in the optimization and design of deployable parabolic rigid antenna structures.

Provably Feasible Semi-Infinite Program Under Collision Constraints via Subdivision

Provably Feasible Semi-Infinite Program Under Collision Constraints via Subdivision

Prescribed performance formation control for second-order multi-agent systems with connectivity and collision constraints

This paper studies the distributed formation control problem of second-order multi-agent systems (MASs) with limited communication ranges and collision avoidance constraints. A novel connectivity preservation and collision-free distributed control algorithm is proposed by combining prescribed performance control (PPC) and exponential zeroing control barrier Lyapunov functions (EZCBFs). In particular, we impose the time-varying performance constraints on the relative position and velocity errors between the neighboring agents, and then a PPC-based formation control algorithm is developed such that the connectivity of the communication graph can be preserved at all times, and the prescribed transient and steady performance on the relative position and velocity error can be achieved. Subsequently, by introducing the EZCBFs method, an inequality constraint condition on the control input is derived to guarantee the collision-free formation motion. By regarding the PPC-based formation controller as a nominal input, an actual formation control input is given by solving the quadratic programming (QP) problem such that each agent achieves collision-free formation motion while guaranteeing the connectivity and prescribed performance as much as possible. Finally, numerical simulation is carried out to validate the effectiveness of the proposed algorithm.

Learning‐based collision avoidance and robust H∞ optimal formation control for uncertain quadrotor UAV systems

AbstractThis paper investigates the robust optimal formation control for the position subsystem of quadrotor unmanned aerial vehicles (UAVs) subject to external disturbances and collision constraints. To prevent collision with both members of the formation and external obstacles, a collision avoidance potential function is constructed using relative position and velocity information. The basic bounded control input can ensure the stable flight and collision avoidance of a quadrotor UAV system. Based on the approximate dynamic programming (ADP) framework and two‐player zero‐sum differential game theory, the optimal controller is designed to further enhance the control performance of the system. The optimal value function is approximated by a single layer neural network, which avoids solving complex nonlinear Hamilton‐JacobiIsaac (HJI) equation. The stability of the closed loop system is proved. The effectiveness of the robust optimal formation controller based on learning is validated through MATLAB simulation in two distinct scenarios.

Trajectory Planning Framework Combining Replanning and Hierarchical Planning

To enable autonomous vehicles to respond quickly to changes in the surrounding environment and to generate safe and stable trajectory, we propose a safety-based hierarchical trajectory planning method that divides the planning module into two parts: the planner and the replanning monitor. In the planner, we first propose a fast linear trajectory planning method that uses the mass point model instead of the vehicle model and linearizes the collision avoidance constraint using the Big-M method for linear programming (Big-M) to obtain a linear programming model. The complete vehicle kinematic model is then built in the nonlinear programming stage, the collision constraints and cost functions are refined, and the rough solution of the linear programming is brought into it to obtain the exact solution. The replanning monitor is divided into safety and comfort monitors. The safety monitor will always pay attention to the changes in the surrounding environment and calculate whether the vehicle is in danger of collision in the future period, while the comfort monitor is more concerned with the comfort of driving the vehicle; when the monitor requirements are not met, replanning will be carried out. By simulating the driving environment, the proposed algorithm can form a safe and comfortable trajectory, which verifies the rationality of the proposed method.

DLSC: Distributed Multi-Agent Trajectory Planning in Maze-Like Dynamic Environments Using Linear Safe Corridor

This article presents an online distributed trajectory planning algorithm for a quadrotor swarm in a maze-like dynamic environment. We utilize a dynamic linear safe corridor to construct the feasible collision constraints that can ensure interagent collision avoidance and consider the uncertainty of moving obstacles. We introduce mode-based subgoal planning to resolve deadlock faster in a complex environment using only previously shared information. For dynamic obstacle avoidance, we adopt heuristic methods such as collision alert propagation and escape point planning to deal with the situation where dynamic obstacles approach the agents clustered in a narrow corridor. We prove that the proposed algorithm guarantees the feasibility of the optimization problem for every replanning step. In an obstacle-free space, the proposed method can compute the trajectories for 60 agents on average 7.66 ms per agent with an Intel i7 laptop and shows the perfect success rate. Also, our method shows 64.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> shorter flight time than buffered Voronoi cell and 34.6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> shorter than with our previous work. We conduct the simulation in a random forest and maze with four dynamic obstacles, and the proposed algorithm shows the highest success rate and shortest flight time compared to state-of-the-art baseline algorithms. In particular, the proposed algorithm shows over 97 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> success rate when the velocity of moving obstacles is below the agent's maximum speed. We validate the safety and robustness of the proposed algorithm through a hardware demonstration with ten quadrotors and two pedestrians in a maze-like environment.

Cooperative Dynamic Motion Planning for Dual Manipulator Arms Based on RRT*Smart-AD Algorithm.

Intelligent manufacturing requires robots to adapt to increasingly complex tasks, and dual-arm cooperative operation can provide a more flexible and effective solution. Motion planning serves as a crucial foundation for dual-arm cooperative operation. The rapidly exploring random tree (RRT) algorithm based on random sampling has been widely used in high-dimensional manipulator path planning due to its probability completeness, handling of high-dimensional problems, scalability, and faster exploration speed compared with other planning methods. As a variant of RRT, the RRT*Smart algorithm introduces asymptotic optimality, improved sampling techniques, and better path optimization. However, existing research does not adequately address the cooperative motion planning requirements for dual manipulator arms in terms of sampling methods, path optimization, and dynamic adaptability. It also cannot handle dual-manipulator collaborative motion planning in dynamic scenarios. Therefore, in this paper, a novel motion planner named RRT*Smart-AD is proposed to ensure that the dual-arm robot satisfies obstacle avoidance constraints and dynamic characteristics in dynamic environments. This planner is capable of generating smooth motion trajectories that comply with differential constraints and physical collision constraints for a dual-arm robot. The proposed method includes several key components. First, a dynamic A* cost function sampling method, combined with an intelligent beacon sampling method, is introduced for sampling. A path-pruning strategy is employed to improve the computational efficiency. Strategies for dynamic region path repair and regrowth are also proposed to enhance adaptability in dynamic scenarios. Additionally, practical constraints such as maximum velocity, maximum acceleration, and collision constraints in robotic arm applications are analyzed. Particle swarm optimization (PSO) is utilized to optimize the motion trajectories by optimizing the parameters of quintic non-uniform rational B-splines (NURBSs). Static and dynamic simulation experiments verified that the RRT*Smart-AD algorithm for cooperative dynamic path planning of dual robotic arms outperformed biased RRT* and RRT*Smart. This method not only holds significant practical engineering significance for obstacle avoidance in dual-arm manipulators in intelligent factories but also provides a theoretical reference value for the path planning of other types of robots.

RS-Aug: Improve 3D Object Detection on LiDAR With Realistic Simulator Based Data Augmentation

Light detection and ranging (LiDAR) is an essential sensor for three dimensional (3D) object detection via generating 3D point cloud of the surroundings, and it has been widely used in the various visual applications, especially autonomous driving. However, limited numbers of labeled LiDAR datasets brutally restrain the development of 3D object detector, and this situation breeds an urgent demand on data augmentation in this field. By far, most of the traditional methods reuse the labeled samples, while those unlabeled are hastily untaken. Motivated by this, we propose a Realistic Simulator based data augmentation (RS-Aug). It aims to construct augmented real scenes to enrich the diversity of training dataset. To train 3D object detector in a supervised learning way, the first step of RS-Aug is auto-annotation. Time-continuous LiDAR frames are used to construct the dense scene, which is beneficial to annotation and the subsequent rendering augmentation. However, 3D points with incorrect semantic labels are naturally gathered during multi-view reconstruction, causing the negative effect on auto-annotation. We propose an algorithm of cluster guided <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula> -nearest neighbor (c- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula> NN). It emphasizes on de-nosing semantic labels of clustered points using distance and intensity constraints. Then, the next step of RS-Aug is rendering augmentation on the real scene. To enhance the rendering quality using collision and distance constraints with the less computation complexity, we propose a scheme of heuristic search (HS) based object insertion. It estimates the proper position of the inserted object from 2D bird’s eye view (BEV). Experiments demonstrate the de-noising accuracy of c- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula> NN, rendering quality of HS based object insertion, and improvement of RS-Aug on object detection.

Application of the Improved Rapidly Exploring Random Tree Algorithm to an Insect-like Mobile Robot in a Narrow Environment.

When intelligent mobile robots perform global path planning in complex and narrow environments, several issues often arise, including low search efficiency, node redundancy, non-smooth paths, and high costs. This paper proposes an improved path planning algorithm based on the rapidly exploring random tree (RRT) approach. Firstly, the target bias sampling method is employed to screen and eliminate redundant sampling points. Secondly, the adaptive step size strategy is introduced to address the limitations of the traditional RRT algorithm. The mobile robot is then modeled and analyzed to ensure that the path adheres to angle and collision constraints during movement. Finally, the initial path is pruned, and the path is smoothed using a cubic B-spline curve, resulting in a smoother path with reduced costs. The evaluation metrics employed include search time, path length, and the number of sampling nodes. To evaluate the effectiveness of the proposed algorithm, simulations of the RRT algorithm, RRT-connect algorithm, RRT* algorithm, and the improved RRT algorithm are conducted in various environments. The results demonstrate that the improved RRT algorithm reduces the generated path length by 25.32% compared to the RRT algorithm, 26.42% compared to the RRT-connect algorithm, and 4.99% compared to the RRT* algorithm. Moreover, the improved RRT algorithm significantly improves the demand for reducing path costs. The planning time of the improved RRT algorithm is reduced by 64.96% compared to that of the RRT algorithm, 40.83% compared to that of the RRT-connect algorithm, and 27.34% compared to that of the RRT* algorithm, leading to improved speed. These findings indicate that the proposed method exhibits a notable improvement in the three crucial evaluation metrics: sampling time, number of nodes, and path length. Additionally, the algorithm performed well after undergoing physical verification with an insect-like mobile robot in a real environment featuring narrow elevator entrances.

Planning and control of drifting-based collision avoidance strategy under emergency driving conditions

Automated emergency collision avoidance (CA) technology has made tremendous progresses in recent years. However, the existing CA approaches, either braking or steering based, cannot handle well the extremely emergency CA scenarios with limited space and time. This is a research gap to be bridged before the zero-fatality vision of road traffic, namely Vision Zero, can be realized. To further extend the safety limits of vehicles, especially that of automated vehicles in future, we propose a drifting-based CA approach that adopts an aggressive, but controllable, over-steering maneuver. To this end, first the trajectory planning of drifting is formulated and solved as a constrained optimal control problem, which considers vehicle dynamics, actuator limits and collision constraints. Then the knowledge of the three CA approaches’ capability limits is obtained and used for CA decision. Given a planned trajectory, a feedback linearization based controller is further designed to complete the drifting maneuver. Finally, using a real vehicle with by-wire actuators, a series of simulations and road tests are carried out. Results show that our proposed drifting-based algorithm can successfully fulfill agile CA tasks in extreme conditions. With further improvements, this preliminary and conceptual work may contribute as a promising complement to current active safety technologies.

Two-level Approach for Heterogeneous Multi-Robot Optimal Navigation

This paper proposes a two-level optimization approach for a multi-robot navigation problem. Our aim is to achieve tasks with optimal strategies, optimal trajectory planning and to give better and feasible solutions. Optimal alternatives are selected by combining game theory strategic decision with an optimal trajectory planning method. This is solved at the top level by applying Sequential Quadratic Programming (SQP). At the bottom, Pure Nash equilibrium is solved using the Simulated Annealing (SA) algorithm. The trajectory planning for the multi-robot system is performed by decomposition where the b-spline technique is initially used to describe the robots path in an environment with obstacles. The cubic spline technique is then introduced to set up the motion along the desired path. The kinematic and dynamic constraints inherent to the robot behavior are taken into account and collision constraints are handled by penalization. The proposed approach is applied to heterogeneous Unicycle Wheeled Mobile Robots and simulated in endowed obstacles environment. Optimal collision-free trajectories of the robot team are obtained with smooth line paths and good-quality solutions. Simulation results are given to show the effectiveness and robustness of proposed algorithm.

Distributing Collaborative Multi-Robot Planning With Gaussian Belief Propagation

Precise coordinated planning over a forward time window enables safe and highly efficient motion when many robots must work together in tight spaces, but this would normally require centralised control of all devices which is difficult to scale. We demonstrate GBP Planning, a new purely distributed technique based on Gaussian Belief Propagation for multi-robot planning problems, formulated by a generic factor graph defining dynamics and collision constraints over a forward time window. In simulations, we show that our method allows high performance collaborative planning where robots are able to cross each other in busy, intricate scenarios. They maintain shorter, quicker and smoother trajectories than alternative distributed planning techniques even in cases of communication failure. We encourage the reader to view the accompanying video demonstration.

On the discontinuous dynamics of a class of 2-DOF frictional vibration systems with asymmetric elastic constraints

&lt;abstract&gt;&lt;p&gt;In this paper, the discontinuous dynamic behavior of a two-degree-of-freedom frictional collision system including intermediate elastic collision and unilateral elastic constraints subjected to periodic excitation is studied by using flow switching theory. In this system, given that the motion of each object might have a velocity that is either greater than or less than zero and each object experiences a periodic excitation force that has negative feedback, because the kinetic and static friction coefficients differ, the flow barrier manifests when the object's speed is zero. Based on the discontinuity or nonsmoothness of the oscillator's motion generated by elastic collision and friction, the motion states of the oscillator in the system are divided into 16 cases and the absolute and relative coordinates are used to define various boundaries and domains in the oscillator motion's phase space. On the basis of this, the G-function and system vector fields are used to propose the oscillator motion's switching rules at the displacement and velocity boundaries. Finally, some dynamic behaviors for the 2-DOF oscillator are demonstrated via numerical simulation of the oscillator's stick, grazing, sliding and periodic motions and the scene of sliding bifurcation. The mechanical system's optimization designs with friction and elastic collision will benefit from this investigation's findings.&lt;/p&gt;&lt;/abstract&gt;

Barrier-Certified Model Predictive Cooperative Path Following Control of Connected Autonomous Surface Vehicles

This paper investigates the safe cooperative path following of connected autonomous surface vehicles subject to static and dynamic obstacles, as well as physical constraints. A barrier-certified model predictive cooperative path following control method is proposed with the capability of collision avoidance and constraint satisfaction. Specifically, a robust-exact-differentiators-based extended state observer is employed to estimate the unknown kinetics including model uncertainties and external disturbances. Based on a path variable containment approach, a nominal receding-horizon control law is designed to achieve cooperative path following task within the physical constraints. A safe optimal control law is designed based on control barrier functions to generate optimal surge force and heading angle within the safety constraints. A receding-horizon heading control law is designed to track the desired heading signals. Constrained quadratic programming problems are formulated and solved via neurodynamic optimization. Simulation results are elaborated to validate the efficacy of the proposed barrier-certified model predictive control method for cooperative path following subject to static and dynamic obstacles.