To overcome the bottleneck of classical path planning schemes in solving NP problems and address the predicament faced by current mainstream quantum path planning frameworks in the Noisy Intermediate-Scale Quantum (NISQ) era, this study attempts to construct a quantum path planning solution based on parallel Quantum Approximate Optimization Algorithm (QAOA) architecture. Specifically, the grid path planning problem is mapped to the problem of finding the minimum quantum energy state. Two parallel QAOA circuits are built to simultaneously execute two solution processes, namely connectivity energy calculation and path energy calculation. A classical algorithm is employed to filter out unreasonable solutions of connectivity energy, and finally, the approximate optimal solution to the path planning problem is obtained by merging the calculation results of the two parallel circuits. The research findings indicate that by setting appropriate filter parameters, quantum states corresponding to position points with extremely low occurrence probabilities can be effectively filtered out, thereby increasing the probability of obtaining the target quantum state. Even when the circuit layer number p is only 1, the theoretical solution of the optimal path coding combination can still be found by leveraging the critical role of the filter. Compared with serial circuits, parallel circuits exhibit a significant advantage, as they can find the optimal feasible path coding combination with the highest probability.

Modular self-reconfigurable satellites refer to satellite clusters composed of individual modular units capable of altering their configurations. The configuration changes enable the execution of diverse tasks and mission objectives. Existing path planning algorithms for reconfiguration often suffer from high computational complexity, poor generalization capability, and limited support for diverse target configurations . To address these challenges, this paper proposes a goal-oriented reinforcement learning-based path planning algorithm. This algorithm is the first to address the challenge that previous reinforcement learning methods failed to overcome, namely handling multiple target configurations. Moreover, techniques such as Hindsight Experience Replay and Invalid Action Masking are incorporated to overcome the significant obstacles posed by sparse rewards and invalid actions. Based on these designs, our model achieves a 95% and 73% success rate in reaching arbitrary target configurations in a modular satellite cluster composed of four and six units, respectively.

This paper presents a Riemannian metric-based model to solve the optimal path planning problem on two-dimensional smooth submanifolds in high-dimensional space. Our model is based on constructing a new Riemannian metric on a two-dimensional projection plane, which is induced by the high-dimensional Euclidean metric on two-dimensional smooth submanifold and reflects the environmental information of the robot. The optimal path planning problem in high-dimensional space is therefore transformed into a geometric problem on the two-dimensional plane with new Riemannian metric. Based on the new Riemannian metric, we proposed an incremental algorithm RRT*-R on the projection plane. The experimental results show that the proposed algorithm is suitable for scenarios with uneven fields in multiple dimensions. The proposed algorithm can help the robot to effectively avoid areas with drastic changes in height, ground resistance and other environmental factors. More importantly, the RRT*-R algorithm shows better smoothness and optimization properties compared with the original RRT* algorithm using Euclidean distance in high-dimensional workspace. The length of the entire path by RRT*-R is a good approximation of the theoretical minimum geodesic distance on projection plane.

The Dijkstra algorithm is a classic path planning method, which operates in a discrete graph space to determine the shortest path from a specified source point to a target node or all other nodes based on non-negative edge weights. Numerous studies have focused on the Dijkstra algorithm due to its potential application. However, its application in surface path planning for mobile robots remains largely unexplored. In this letter, a surface optimal path planning algorithm called RM-Dijkstra is proposed, which is based on Riemannian metric model. By constructing a new Riemannian metric on the 2D projection plane, the surface optimal path planning problem is therefore transformed into a geometric problem on the 2D plane with new Riemannian metric. Induced by the standard Euclidean metric on surface, the constructed new metric reflects environmental information of the robot and ensures that the projection map is an isometric immersion. By conducting a series of simulation tests, the experimental results demonstrate that the RM-Dijkstra algorithm not only effectively solves the optimal path planning problem on surfaces, but also outperforms traditional path planning algorithms in terms of path accuracy and smoothness, particularly in complex scenarios.

A cuspidal robot can move from one inverse kinematics (IK) solution to another without crossing a singularity. Multiple industrial robots are cuspidal. They tend to have a beautiful mechanical design, but they pose path planning challenges. A task-space path may have a valid IK solution for each point along the path, but a continuous joint-space path may depend on the choice of the IK solution or even be infeasible. This paper presents new analysis, path planning, and optimization methods to enhance the utility of cuspidal robots. We first demonstrate an efficient method to identify cuspidal robots and show, for the first time, that the ABB GoFa and certain robots with three parallel joint axes are cuspidal. We then propose a new path planning method for cuspidal robots by finding all IK solutions for each point along a task-space path and constructing a graph to connect each vertex corresponding to an IK solution. Graph edges are weighted based on the optimization metric, such as minimizing joint velocity. The optimal feasible path is the shortest path in the graph. This method can find non-singular paths as well as smooth paths which pass through singularities. Finally, this path planning method is incorporated into a path optimization algorithm. Given a fixed workspace toolpath, we optimize the offset of the toolpath in the robot base frame while ensuring continuous joint motion. Code examples are available in a publicly accessible repository.

This work addresses the path planning problem for a group of unmanned aerial vehicles (UAVs) to maintain a desired formation during operation. Our approach formulates the problem as an optimization task by defining a set of fitness functions that not only ensure the formation but also include constraints for optimal and safe UAV operation. To optimize the fitness function and obtain a suboptimal path, we employ the teaching-learning-based optimization algorithm and then further enhance it with mechanisms such as mutation, elite strategy, and multi-subject combination. A number of simulations and experiments have been conducted to evaluate the proposed method. The results demonstrate that the algorithm successfully generates valid paths for the UAVs to fly in a triangular formation for an inspection task.

This paper explores an eclectic range of path-planning methodologies engineered for rolling surfaces. Our focus is on the kinematic intricacies of rolling contact systems, which are investigated through a motion planning lens. Beyond summarizing the approaches to single-contact rotational surfaces, we explore the challenging domain of spin-rolling multi-contact systems. Our work proposes solutions for the higher-dimensional problem of multiple rotating objects in contact. Venturing beyond kinematics, these methodologies find application across a spectrum of domains, including rolling robots, reconfigurable swarm robotics, micro/nano manipulation, and nonprehensile manipulations. Through meticulously examining established planning strategies, we unveil their practical implementations in various real-world scenarios, from intricate dexterous manipulation tasks to the nimble manoeuvring of rolling robots and even shape planning of multi-contact swarms of particles. This study introduces the persistent challenges and unexplored frontiers of robotics, intricately linked to both path planning and mechanism design. As we illuminate existing solutions, we also set the stage for future breakthroughs in this dynamic and rapidly evolving field by highlighting the critical importance of addressing rolling contact problems.

This paper presents an advanced method for addressing the inverse kinematics and optimal path planning challenges in robot manipulators. The inverse kinematics problem involves determining the joint angles for a given position and orientation of the end-effector. Furthermore, the path planning problem seeks a trajectory between two points. Traditional approaches in computer algebra have utilized Gr\"obner basis computations to solve these problems, offering a global solution but at a high computational cost. To overcome the issue, the present authors have proposed a novel approach that employs the Comprehensive Gr\"obner System (CGS) and CGS-based quantifier elimination (CGS-QE) methods to efficiently solve the inverse kinematics problem and certify the existence of solutions for trajectory planning. This paper extends these methods by incorporating smooth curves via cubic spline interpolation for path planning and optimizing joint configurations using shortest path algorithms to minimize the sum of joint configurations along a trajectory. This approach significantly enhances the manipulator's ability to navigate complex paths and optimize movement sequences.

Path planning is a complex problem for many practical applications, particularly in robotics. Existing algorithms, however, are exhaustive in nature and become increasingly complex when additional side constraints are incorporated alongside distance minimization. In this paper, a novel approach using vision language models (VLMs) is proposed for enabling path planning in complex wireless-aware environments. To this end, insights from a digital twin (DT) with real-world wireless ray tracing data are explored in order to guarantee an average path gain threshold while minimizing the trajectory length. First, traditional approaches such as A* are compared to several wireless-aware extensions, and an optimal iterative dynamic programming approach (DP-WA*) is derived, which fully takes into account all path gains and distance metrics within the DT. On the basis of these baselines, the role of VLMs as an alternative assistant for path planning is investigated, and a strategic chain-of-thought tasking (SCoTT) approach is proposed. SCoTT divides the complex planning task into several subproblems and solves each with advanced CoT prompting. Results show that SCoTT achieves very close average path gains compared to DP-WA* while at the same time yielding consistently shorter path lengths. The results also show that VLMs can be used to accelerate DP-WA* by efficiently reducing the algorithm's search space and thus saving up to 62\% in execution time. This work underscores the potential of VLMs in future digital systems as capable assistants for solving complex tasks, while enhancing user interaction and accelerating rapid prototyping under diverse wireless constraints.

Rapidly-exploring Random Tree (RRT) algorithms have been applied successfully to challenging robot motion planning and under-actuated nonlinear control problems. However a fundamental limitation of the RRT approach is the slow convergence in configuration spaces with narrow channels because of the small probability of generating test points inside narrow channels. This paper presents an improved RRT algorithm that takes advantage of narrow channels between the initial and goal states to find shorter paths by improving the exploration of narrow regions in the configuration space. The proposed algorithm detects the presence of narrow channel by checking for collision of neighborhood points with the infeasible set and attempts to add points within narrow channels with a predetermined bias. This approach is compared with the classical RRT and its variants on a variety of benchmark planning problems. Simulation results indicate that the algorithm presented in this paper computes a significantly shorter path in spaces with narrow channels.