In confined multi-obstacle environments, generating feasible paths for continuum robots is challenging due to the need to avoid obstacles while considering the kinematic limitations of the robot. This paper deals with the path-planning algorithm for continuum robots in confined multi-obstacle environments to prevent their over-deformation. By modifying the tree expansion process of the Rapidly-exploring Random Tree Star (RRT*) algorithm, a path-planning algorithm called the continuum-RRT* algorithm herein is proposed to achieve fewer iterations and faster convergence as well as generating desired paths that adhere to the kinematic limitations of the continuum robots. Then path planning and path tracking are implemented on a tendon-driven four-section continuum robot to validate the effectiveness of the path-planning algorithm. The path-planning results show that the path generated by the algorithm indeed has fewer transitions, and the path generated by the algorithm is closer to the optimal path that satisfies the kinematic limitations of the continuum robot. Furthermore, path-tracking experiments validate the successful navigation of the continuum robot along the algorithm-generated path, exhibiting an error range of 2.51%–3.91%. This attests to the effectiveness of the proposed algorithm in meeting the navigation requirements of continuum robots.

Hyper-redundant cable-driven manipulators (CDMs) are widely used for operations in confined spaces due to their slender bodies and multiple degrees of freedom. Most research focuses on their path following but not path planning. This work investigates a deep deterministic policy gradient (DDPG)-based path-planning algorithm for CDMs in multi-obstacle environments. To plan passable paths under many constraints, a DDPG algorithm is modified according to features of CDMs. To improve adaptability of planned paths, a specialized reward function is newly designed. In this function, such factors as smoothness, arrival time and distance are taken into account. Results of simulations and physical experiments are presented to demonstrate the performances of the proposed methods for planning paths of CDMs.

Path planning for the unmanned aerial vehicle (UAV) is to assist in finding the proper path, serving as a critical role in the intelligence of a UAV. In this paper, a path planning for UAV in three-dimensional environment (3D) based on enhanced gravitational search algorithm (EGSA) is put forward, taking the path length, yaw angle, pitch angle, and flight altitude as considerations of the path. Considering EGSA is easy to fall into local optimum and convergence insufficiency, two factors that are the memory of current optimal and random disturbance with chaotic levy flight are adopted during the update of particle velocity, improving the balance between exploration and exploitation for EGSA through different time-varying characteristics. With the identical cost function, EGSA is compared with seven peer algorithms, such as moth flame optimization algorithm, gravitational search algorithm, and five variants of gravitational search algorithm. The experimental results demonstrate that EGSA is superior to the seven comparison algorithms on CEC 2020 benchmark functions and the path planning method based on EGSA is more valuable than the other seven methods in diverse environments.

In this paper, a method of planning the expanded S-curve trajectory of robotic manipulators is proposed to minimize the execution time as well as to achieve the smoother trajectory generation in the deceleration stage for point-to-point motions. An asymmetric parameter is added to the piecewise sigmoid function for an improved jerk profile. This asymmetric profile is continuous and infinitely differentiable. Based on this profile, two analytical algorithms are presented. One is applied to determine the suitable time intervals of trajectory satisfying the time optimality under the kinematic constraints, and the other is to determine the asymmetric parameter generating the minimum execution time. Also, the calculation procedure for the time-scaled synchronization for all joints is given to decrease unnecessary loads onto the actuators. The velocity, acceleration, jerk and snap (the derivative of jerk) of the joints and the end-effector are equal to zero at two end points of motion. The simulation results through 3 DOF and 6 DOF robotic manipulators show that our approach reduces the jerk and snap of the deceleration stage effectively while decreasing the total execution time. Also, the analysis for a single DOF mass-spring-damper system indicates that the residual vibration could be reduced to 10% more than the benchmark techniques in case velocity, acceleration and jerk are limited to 1.24 m/s, 6 m/s2 and 80 m/s3, respectively and displacement is set to 0.8m. These results manifest that the performance of reducing residual vibrations is good and demonstrate an important characteristic of the proposed profile suitable for point-to-point motion.

Real-time and efficient path planning is critical for all robotic systems. In particular, it is of greater importance for industrial robots since the overall planning and execution time directly impact the cycle time and automation economics in production lines. While the problem may not be complex in static environments, classical approaches are inefficient in high-dimensional environments in terms of planning time and optimality. Collision checking poses another challenge in obtaining a real-time solution for path planning in complex environments. To address these issues, we propose an end-to-end learning-based framework viz., Path Planning and Collision checking Network (PPCNet). The PPCNet generates the path by computing waypoints sequentially using two networks: the first network generates a waypoint, and the second one determines whether the waypoint is on a collision-free segment of the path. The end-to-end training process is based on imitation learning that uses data aggregation from the experience of an expert planner to train the two networks, simultaneously. We utilize two approaches for training a network that efficiently approximates the exact geometrical collision checking function. Finally, the PPCNet is evaluated in two different simulation environments and a practical implementation on a robotic arm for a bin-picking application. Compared to the state-of-the-art path-planning methods, our results show significant improvement in performance by greatly reducing the planning time with comparable success rates and path lengths.

Snake robots can move flexibly due to their special bodies and gaits. However, it is difficult to plan their motion in multi-obstacle environments due to their complex models. To solve this problem, this work investigates a reinforcement learning-based motion planning method. To plan feasible paths, together with a modified deep Q-learning algorithm, a Floyd-moving average algorithm is proposed to ensure smoothness and adaptability of paths for snake robots’ passing. An improved path integral algorithm is used to work out gait parameters to control snake robots to move along the planned paths. To speed up the training of parameters, a strategy combining serial training, parallel training, and experience replaying modules is designed. Moreover, we have designed a motion planning framework consists of path planning, path smoothing, and motion planning. Various simulations are conducted to validate the effectiveness of the proposed algorithms.

A collision-free path planning method is proposed based on learning from demonstration (LfD) to address the challenges of cumbersome manual teaching operations caused by complex action of yarn storage, variable mechanism positions, and limited workspace in preform weaving. First, by utilizing extreme learning machines (ELM) to autonomously learn the teaching data of yarn storage, the mapping relationship between the starting and ending points and the teaching path points is constructed to obtain the imitation path with similar storage actions under the starting and ending points of the new task. Second, an improved rapidly expanding random trees (IRRT) method with adaptive direction and step size is proposed to expand path points with high quality. Finally, taking the spatical guidance point of imitation path as the target direction of IRRT, the expansion direction is biased toward the imitation path to obtain a collision-free path that meets the action yarn storage. The results of different yarn storage examples show that the ELM-IRRT method can plan the yarn storage path within 2s–5s when the position of the mechanism changes in narrow spaces, avoiding tedious manual operations that program the robot movements, which is feasible and effective.

Motion planning for high-DOF multi-arm systems operating in complex environments remains a challenging problem, with many motion planning algorithms requiring evaluation of the minimum collision distance and its derivative. Because of the computational complexity of calculating the collision distance, recent methods have attempted to leverage data-driven machine learning methods to learn the collision distance. Because of the significant training dataset requirements for high-DOF robots, existing kernel-based methods, which require $O(N^2)$ memory and computation resources, where $N$ denotes the number of dataset points, often perform poorly. This paper proposes a new active learning method for learning the collision distance function that overcomes the limitations of existing methods: (i) the size of the training dataset remains fixed, with the dataset containing more points near the collision boundary as learning proceeds, and (ii) calculating collision distances in the higher-dimensional link $SE(3)^n$ configuration space – here $n$ denotes the number of links – leads to more accurate and robust collision distance function learning. Performance evaluations with high-DOF multi-arm robot systems demonstrate the advantages of the proposed active learning-based strategy vis-$\grave{\text{a}}$-vis existing learning-based methods.

This paper is concerned with the problem of collision-free path planning for manipulators in multi-obstacle scenarios. Aiming at overcoming the deficiencies of existing algorithms in excessive time consumption and poor expansion quality, a path planning algorithm named Fast Bi-directional Rapidly-exploring Random Tree (FBi-RRT) with novel heuristic node expansion is proposed, which includes a selective-expansion strategy and a vertical-exploration strategy. The selective-expansion strategy is designed to guide the selection of the nearest-neighbor node to avoid the repeated expansion failure, thereby shortening the overall planning time. Also, the vertical-exploration strategy is developed to regulate the expansion direction of the collision nodes to escape from the obstacle space with less blindness, thus improving the expansion quality and further reducing time cost. Compared with previous planning algorithms, FBi-RRT can generate a feasible path for manipulators in a drastically shorter time. To validate the effectiveness of the proposed heuristic node expansion, FBi-RRT is conducted on a 6-DOF manipulator and tested in five scenarios. The experimental results demonstrate that FBi-RRT outperforms the existing methods in time consumption and expansion quality.

With the popularization of electric vehicles, early built parking lots cannot solve the charging problem of a large number of electric vehicles. Mobile charging robots have autonomous navigation and complete charging functions, which make up for this deficiency. However, there are static obstacles in the parking lot that are random and constantly changing their position, which requires a stable and fast iterative path planning method. The gray wolf optimization (GWO) algorithm is one of the optimization algorithms, which has the advantages of fast iteration speed and stability, but it has the drawback of easily falling into local optimization problems. This article first addresses this issue by improving the fitness function and position update of the GWO algorithm and then optimizing the convergence factor. Subsequently, the fitness function of the improved gray wolf optimization (IGWO) algorithm was further improved based on the minimum cost equation of the A* algorithm. The key coefficients AC1 and AC2 of two different fitness functions, Fitness1 and Fitness2, were discussed. The improved gray wolf optimization algorithm integrating A* algorithm (A*-IGWO) has improved the number of iterations and path length compared to the GWO algorithm in parking lots path planning problems.

As space missions are needed in the future, the assembly volume of the space truss will become larger and larger, and the advancing path of the on-orbit cellular robot to the mission target will become more and more complicated. If the shortest moving path cannot be found in the truss environment, the climbing time of the robot on the truss will be greatly increased. To improve the speed of the cellular robot moving to the target point on the large space truss, this paper designs a cellular robot structure and configuration suitable for climbing on the truss and uses the improved sparrow algorithm to solve the problem of robot motion path planning. By establishing a mathematical model of the space truss, the improved sparrow algorithm is used to find the shortest path between the starting point and the end point in the truss environment. Finally, the data of this algorithm are compared with the data of other algorithms. The data results show that the improved sparrow algorithm is very effective in solving the optimal path of the space truss. The improved sparrow algorithm keeps the same optimal path compared with the standard sparrow algorithm, and the overall reaction time is increased by 51.60%, and the number of effective iterations is increased by about 13.87%.

Even the shortest flight through unknown, cluttered environments requires reliable local path planning algorithms to avoid unforeseen obstacles. The algorithm must evaluate alternative flight paths and identify the best path if an obstacle blocks its way. Commonly, weighted sums are used here. This work shows that weighted Chebyshev distances and factorial achievement scalarising functions are suitable alternatives to weighted sums if combined with the 3DVFH* local path planning algorithm. Both methods considerably reduce the failure probability of simulated flights in various environments. The standard 3DVFH* uses a weighted sum and has a failure probability of 50% in the test environments. A factorial achievement scalarising function, which minimises the worst combination of two out of four objective functions, reaches a failure probability of 26%; A weighted Chebyshev distance, which optimises the worst objective, has a failure probability of 30%. These results show promise for further enhancements and to support broader applicability.

Navigation safety at sea is vital for each autonomous surface vehicle (ASV), which involves the problem of motion planning in dynamic environments and their robust tracking through feedback control. We present a practical path-planning method that generates smooth trajectories for a marine vehicle traveling in an unknown environment, where obstacles are detected in real time by millimetre wave (mmWave) radar. Our approach introduces a polynomial curve to describe the lateral and longitudinal trajectories in the Frenet frame, known as the ‘motion primitives’, whose combination ensures that the planning area is properly covered. In addition, we can select a feasible, optimal and collision-free trajectory from such a set of motion primitives that is generated by considering the vehicle dynamics and comfort. The capabilities of proposed algorithm are demonstrated in the experiment with static and dynamic obstacles.

Performance indexes are a powerful tool to evaluate the behavior of industrial manipulators throughout their workspace and improve their performance. When dealing with intrinsically redundant manipulators, the additional joint influences their performance; hence, it is fundamental to consider the influence of the redundant joint when evaluating the performance index. This work improves the formulation of the kinematic directional index (KDI) by considering redundant manipulators. The KDI represents an improvement over traditional indexes, as it takes into account the direction of motion when evaluating the performance of a manipulator. However, in its current formulation, it is not suitable for redundant manipulators. Therefore, we extend the index to redundant manipulators. This is achieved by adopting a geometric approach that allows identifying the appropriate redundancy to maximize the velocity of a serial manipulator along the direction of motion. This approach is applied to a 4-degree-of-freedom (DOF) planar redundant manipulator and a 7-DOF spatial articulated one. Experimental validation for the articulated robot is presented, demonstrating the effectiveness of the proposed method and its advantages.

Driven by the remarkable developments we have observed in recent years, path planning for mobile robots is a difficult part of robot navigation. Artificial intelligence applied to mobile robotics is also a distinct challenge; reinforcement learning (RL) is one of the most used algorithms in robotics. The exploration-exploitation dilemma is a motivating challenge for the performance of RL algorithms. The problem is balancing exploitation and exploration, as too much exploration leads to a decrease in cumulative reward, while too much exploitation locks the agent in a local optimum. This paper proposes a new path planning method for mobile robot based on Q-learning with an improved exploration strategy. In addition, a comparative study of Boltzmann distribution and $\epsilon$-greedy politics is presented. Through simulations, the better performance of the proposed method in terms of execution time, path length, and cost function is confirmed.

There has been a continuous interest in multi-robot formation systems in the last few years due to several significant advantages such as robustness, scalability, and efficiency. However, multi-robot formation systems suffer from well-known problems such as energy consumption, processing speed, and security. Therefore, developers are continuously researching for optimal solutions that can gather the benefits of multi-robot formation systems while overcoming the possible challenges. A backbone process required by any multi-robot system is path planning. Thus, path planning for multi-robot systems is a recent top research topic. However, the literature lacks a recent comprehensive review of path planning works designed for multi-robot systems. The aim of this review paper is to provide a comprehensive assessment and an insightful look into various path planning techniques developed in multi-robot formation systems, in addition to highlighting the basic problems involved in this field. This will allow the reader to discover the research gaps that must be solved for a better path planning experience for multi-robot formation systems. Finally, an illustrative comparative example is presented at the end of the paper to show the advantages and disadvantages of some popular path planning techniques.

The grey wolf optimizer (GWO) as a new intelligent optimization algorithm has been successfully applied in many fields because of its simple structure, few adjustment parameters and easy implementation. This paper mainly aims at the defects of GWO in path planning application, such as easily falling into local optimization, poor convergence and poor accuracy, and turn point grey wolf optimization (TPGWO) algorithm is proposed. First, the idea of cross-mutation and roulette is used to increase the initial population of GWO and improve the search range. At the same time, the convergence factor function is improved to become a nonlinear update. In the early stage, the search range is expanded, and in the later stage, the convergence speed is increased, while the parameters in the convergence factor function can be adjusted according to the number of obstacles and the map area to change the turning point of the function to improve the convergence speed and accuracy of the algorithm. The turning times and turning angles of the obtained path are added to the fitness function as penalty values to improve the path accuracy. The optimization test is carried out through 16 test functions, and the test results prove the convergence and robustness of TPGWO algorithm. Finally, the TPGWO algorithm is applied to the path planning of patrol robot for simulation experiments. Compared with the GWO algorithm and Particle Swarm Optimization, the simulation results show that the TPGWO algorithm has better convergence, stability and accuracy in the path planning of patrol robot.

Currently, most of the robot path planning methods for spray painting are based on slicing the Computer-Aided Design model of the target surface to generate a series of path points. They usually neglect the geometric boundary of the model and the smoothness of the generated path, leading to a non-uniform coating thickness. To ameliorate it, an improved “boundary fitting approach” is proposed. In this method, the upper and lower boundaries of the target surface are firstly detected based on the topology of the stereolithography model. For each pass, several sample points are extracted with a uniform length interval from the intersection points generated by the basic slicing method. The path pass is then described by a fourth-order polynomial curve. It fits the boundary points and sample points for the $z$ - $t$ and $y$ - $t$ relationships, respectively. Based on the spray gun’s motion direction and spray direction, the orientation of each path point is also defined. The parameters of the path pass are optimized by particle swarm optimization to get the optimal uniformity of the resulting coating thickness. Both of the global uniformity and the local uniformity between two adjacent passes are considered. The strength of the proposed approach is validated by comparing the simulation with the basic and other typical algorithms. The results denote that boundary fitting approach could improve the uniformity of coating thickness. It brings about a better performance for the painted workpiece.

This paper presents a mobile robot platform, which performs both indoor and outdoor localization based on an intelligent low-cost depth–inertial fusion approach. The proposed sensor fusion approach uses depth-based localization data to enhance the accuracy obtained by the inertial measurement unit (IMU) pose data through a depth–inertial fusion. The fusion approach is based on feedforward cascade correlation networks (CCNs). The aim of this fusion approach is to correct the drift accompanied by the use of the IMU sensor, using a depth camera. This approach also has the advantage of maintaining the high frequency of the IMU sensor and the accuracy of the depth camera. The estimated mobile robot dynamic states through the proposed approach are deployed and examined through real-time autonomous navigation. It is shown that using both the planned path and the continuous localization approach, the robot successfully controls its movement toward the destination. Several tests were conducted with different numbers of layers and percentages of the training set. It is shown that the best performance is obtained with 12 layers and 80% of the pose data used as a training set for CCN. The proposed framework is then compared to the solution based on fusing the information given by the XSens IMU–GPS sensor and the Kobuki robot built-in odometry solution. As demonstrated in the results, an enhanced performance was achieved with an average Euclidean error of 0.091 m by the CCN, which is lower than the error achieved by the artificial neural network by 56%.

This paper, based on the idea of redundancy angle discretisation, proposes an obstacle avoidance method for the fixed tip pose trajectory of a seven degrees-of-freedom (7-DOF) modular manipulator. First, for the case in which a specific redundancy angle is given, the analytical solutions of the redundant manipulator left 6-DOF subchain are found. Then, through the discretisation of the redundancy angle, the concept of the self-motion space of the tip pose is proposed and is extended to the concept of the self-motion space of the trajectory. Based on this discrete space, a path-planning algorithm is proposed to help select the appropriate redundancy angles to obtain the collision-free solution set of the fixed Cartesian trajectory. However, due to the large fluctuation of the obtained path, a path optimisation method based on the path cost is proposed to smooth the path, and the continuous and collision-free solution set of the manipulator tip’s trajectory is obtained. The method proposed in this paper provides a new thought for the problem of collision-free solution set planning for the Cartesian trajectory of a 7-DOF manipulator and it has great application potential in working environments with high accuracy requirements for the trajectory.