Motion Planning Research Articles

As part of the robotics technologies required for In-situ resource utilization (ISRU), the development of cargo rovers for transporting resources is needed. However, these cargo rovers have unique technical challenges that differ from conventional exploration rovers, including the need to traverse rough terrains with their varying mass due to transporting payloads. Moreover, research addressing these challenges has been limited, and the relevant technologies have not been fully established. To address these challenges, this paper proposes a parametric model for estimating wheel slippage. The model is formulated as a function of four input parameters: slope angle, rover heading angle, payload mass, and wheel angular velocity, and is applicable to resource-transporting rovers with varying mass. Additionally, the use of a parametric model reduces computational load, which offers advantages for onboard implementation. The proposed estimation model was quantitatively evaluated by comparing datasets obtained from multi-body dynamics analysis. This paper also introduces a new traversability assessment model which incorporates the proposed slip estimation model. We demonstrated the proposed model by integrating it into a sampling based motion planning. The simulation result of the motion planning show that the planner with our model can generate safer motions and enables the rover to reach the target regardless of the cargo payload.

Bzier curves have proven to be one of the most powerful tools in geometric design and engineering due to their simplicity, efficiency, and flexibility. This paper discusses the mathematical theory and algorithms behind the construction of Bzier curves, including the classical de Casteljau method and cubic spline extensions, and introduces an online Streamlit-based tool for visualizing their applications. By generalizing these algorithms, our framework provides enhanced shape adjustability in curve design and facilitates interactive exploration of their properties. The tool demonstrates Bzier curves wide-ranging applications in computer-aided design, generative digital art, airfoil design optimization, and motion planning for autonomous systems. These examples highlight how a single mathematical framework can unify diverse domains, reducing fragmentation between theory and practice. In addition to illustrating established algorithms, we show how Bzier-based parameterizations enable intuitive geometric manipulation and maintain stability under affine transformations. The educational utility of our platform also helps students and engineers bridge the gap between abstract mathematics and real-world engineering challenges. Future extensions of this work include expanding to three-dimensional curve and surface generation, incorporating optimization methods for design automation, and applying the framework to real-time simulations. Overall, our study highlights the enduring importance of Bzier curves as a versatile and practical tool that connects mathematics, engineering, and digital creativity.

A crash-injury-aware driving safety field for real-time risk assessment and its application in autonomous vehicle motion planning.

Continuum robots (CR) can achieve excellent dexterity and flexibility, making them suitable for navigating through cluttered environments and safely interacting with obstacles. Due to the underactuated nature of CRs, the contact mode between the robot and environment affects the static robot configuration. We show that the configuration space topology induced by environmental obstacles can be characterized by a quotient structure with a quotient space consisting of zero-actuation configurations. We propose to use the quotient space as a road map for motion planning to reduce computational load for exploration. Specifically, we propose an algorithm that identifies the quotient space as a graph of configuration modes by constructing a graph of convex sets in the free workspace, conducting tree search and convex optimizations to find candidate configurations, and then using elastic energy minimization to find the modes. We then use a motion planner which finds a path in the quotient space graph and constructs a continuous path in the configuration space. We demonstrate our method in several complex 3D environments and show that our method outperforms baselines in terms of computation time and success rate.

Interactive Risk (IR): An omnidirectional safety metric of CAVs based on multimodal trajectory prediction and driving risk field.

Guaranteed rejection-free sampling method using past behaviours for motion planning of autonomous systems

Exponential control barrier function and model predictive control for jerk-level reactive motion planning of quadrotors

SwarmGPT: Combining Large Language Models With Safe Motion Planning for Drone Swarm Choreography

Optimal motion planning and navigation for nonholonomic agricultural robots in multi-constraint and multi-task environments

DAPlanner: Dual-agent framework with multi-modal large language model for autonomous driving motion planning

A noniterative linear-variational-inequality based primal-dual neural network for repetitive motion planning of robots

Multi-robot consistent formation control based on novel leader-follower model and optimization motion planning approach

Motion planning in robotic systems, particularly in industrial contexts, must balance execution speed, precision, and safety. Excessive accelerations, especially centripetal ones in high, curvature regions, can cause vibrations, reduce tracking accuracy, and increase mechanical wear. This paper presents an off-line motion planning method that integrates curvature-based velocity modulation with jerk- and acceleration-limited S-curve profiles. The approach autonomously adjusts the speed along a predefined path according to local curvature by planning the motion at piecewise constant velocity and ensuring compliance with dynamic constraints on jerk, acceleration, and velocity. A non-linear filter tracks the velocity reference and smooths transitions while maintaining fluid motion, automatically adjusting velocity based on path curvature, ensuring smooth S-curve trajectories without requiring manual intervention. By jointly addressing geometric feasibility and dynamic smoothness, the proposed method reduces execution time while minimizing vibrations in applications involving abrupt curvature variations, as confirmed by its application to planar and spatial trajectories with varying curvature complexity. The method applies to smooth parametric trajectories and is not intended for paths with tangent discontinuities. The simulation results confirm full compliance with the imposed acceleration and jerk limits; nevertheless, future work will include experimental validation on realistic process trajectories and a quantitative performance assessment.

Abstract As a critical enabler of trackless mining operations, load-haul-dump (LHD) vehicles rely heavily on efficient and safe path planning to support the industrial deployment of autonomous driving systems. However, existing planning algorithms often suffer from heavy computational demands, limited adaptability to the constrained kinematics of articulated LHDs, and insufficient robustness in complex underground environments. To address these challenges, we propose a Hybrid A* path planning method guided by high-level reference states. The method first integrates the A* algorithm with generalized Voronoi diagrams to rapidly generate a reference state set along tunnel centerlines. This reference serves as a structural guide for downstream search. Then, a region-aware dynamic node expansion strategy and a multi-objective heuristic cost function are introduced to improve planning efficiency and path quality. Comparative evaluations across three representative underground tunnel scenarios demonstrate that the proposed approach outperforms baseline methods in terms of safety, efficiency, and robustness, providing a viable solution for motion planning of LHDs in confined underground spaces.

Abstract Underactuated Cable-Driven Parallel Robots ( UACDPRs ) typically rely on relative internal sensors to estimate the end-effector ( EE ) state. Therefore, at startup, the reference values of the quantities measured by these sensors are unknown, and so is the initial pose of the EE . The problem of determining the reference values of the internal sensors is called initial-pose self-calibration. The latter is often formulated as an overdetermined system of nonlinear equations and solved using nonlinear weighted least-squares methods, minimizing the error between modeled and measured variables, and its effectiveness is highly influenced by the choice of measurement configurations, as well as the motion planning and control strategy used to reach them. This work presents two practical data acquisition methods for initial-pose self-calibration of UACDPRs , aiming to reduce the overall time required by the procedure and enhance process automation. The first method is slower but richer in data, as it relies on equilibrium poses and, therefore, can leverage cable-tension data, whereas the second method is faster and is based on geometric constraints only. The performance of the methods is evaluated in terms of acquisition time, number of measurements, and calibration accuracy on a 4-cable UACDPR prototype. The results highlight the merits and shortcomings of both methods, namely, trade-offs between the velocity of data collection and the precision of pose estimation.

This study explores the use of construction robots with collaborative path planning and coordination in complex building construction tasks. Current construction processes involving robots are often fragmented due to their single-task focus, with limited research focused on employing multiple construction robots to collaboratively perform tasks. To address such a challenge, this research proposes an improved A* algorithm for global path planning and obstacle avoidance, combined with the development of a BIM-based grid map of the construction site. The leader–follower method is utilized to guide the robot group in maintaining an optimal formation, ensuring smooth collaboration during construction. The methodology includes formalizing building construction site environments into BIM-based grid maps, path planning, and obstacle avoidance, which allows robot groups to autonomously navigate and complete specific tasks such as concrete, masonry, and decoration construction. The results of this study show that the proposed approach achieves significant reductions in pathlength and operational time of approximately 9% and 10%, respectively, while maintaining safety and efficiency compared with traditional manual methods. This research demonstrates the potential of collaborative construction robot groups to enhance productivity, reduce labor costs, and provide a scalable solution for the intelligent transformation of the construction industry; extends the classical A* algorithm by incorporating obstacle density into the heuristic function; and proposes a new node simplification strategy, contributing to the literature on robot motion planning in semi-structured environments.

The discrete-serpentine heterogeneous multi-arm space robot (DSHMASR) has more advantages than single discrete space robots or single serpentine space robots in complex tasks of on-orbit servicing. However, the mechanical structure complexity of the DSHMASR poses challenges for modeling and motion planning. In this paper, a coupled kinematic model and a coordinated trajectory planning method for the DSHMASR were proposed to address these issues. Firstly, an uncontrolled satellite and the DSHMASR were modeled based on the momentum conservation law. The generalized Jacobian matrix Jg of the space robotic system was derived. Secondly, the manipulation capability of the DSHMASR was analyzed based on the null-space of Jg. Furthermore, the cooperative capturing-monitoring trajectory planning method for DSHMASR was presented through the manipulability optimization. The expected trajectory of each arm’s tip can be obtained by pose deviations and velocity deviations between the tip and the target point. Additionally, the optimized joint velocities of each arm were calculated by combining differential kinematics and manipulability optimization. Therefore, the manipulability of DSHMASR in the direction of the capture operation was enhanced simultaneously as it approached the target satellite. Finally, the proposed algorithm was demonstrated by establishing the Adams–Simulink co-simulation model. Comparisons with traditional approaches further confirm the outperformance of the proposed method in terms of manipulation capability.

This review article explores the theory of control sets for linear control systems defined on two-dimensional Lie groups, with a focus on the plane R2 and the affine group Aff+(2). We systematically summarize recent advances, emphasizing how the geometric and algebraic structures inherent in low-dimensional Lie groups influence the formation, shape, and properties of control sets—maximal regions where controllability is maintained. Control sets with non-empty interiors are of particular interest as they characterize regions where the system can be steered between states via bounded inputs. The review highlights key results concerning the existence, uniqueness, and boundedness of these sets, including criteria based on the Ad-rank condition and orbit analysis. We also underscore the central role of the symmetry properties of Lie groups, which facilitate the systematic classification and description of control sets, linking the abstract mathematical framework to concrete, physically motivated applications. To illustrate the practical relevance of the theory, we present examples from mechanics, motion planning, and neuroscience, demonstrating how control sets naturally emerge in diverse domains. Overall, this work aims to deepen the understanding of controllability regions in low-dimensional Lie group systems and to foster future research that bridges geometric control theory with applied problems.

HighlightsWhat are the main findings?A hybrid structure planning method based on a Probabilistic Sampling Network (PSNet) and an Enhanced Artificial Potential Field (EAPF) is proposed to address high-dimensional robot motion planning in semi-structured environments.Experiments demonstrate that the proposed method outperforms MPNet and RRT-Connect in both 2-D point-mass robot and 6-DOF manipulator tasks, achieving higher success rates and more stable collision avoidance.What is the implication of the main finding?The proposed approach enhances the adaptability and robustness of industrial robots in intelligent manufacturing, maintaining efficient path planning in dynamic and complex scenarios.This study provides a new perspective for integrating learning-based methods with classical planning techniques, laying the foundation for future applications in autonomous robotic operations and human–robot collaboration.The advancement of adaptable industrial robots in intelligent manufacturing is hindered by the inefficiency of traditional motion planning methods in high-dimensional spaces. Therefore, a Dempster–Shafer evidence theory-based hybrid motion planner is proposed, in which a probabilistic sampling network (PSNet) and an enhanced artificial potential field (EAPF) cooperate with each other to improve the planning performance. The PSNet architecture comprises two modules: a motion planning module (MPM) and a fusion sampling module (FSM). The MPM utilizes sensor data alongside the robot’s current and target configurations to recursively generate diverse multimodal distributions of the next configuration. Based on the distribution information, the FSM was used as a decision-maker to ultimately generate globally connectable paths. Moreover, the FSM is equipped to correct collision path points caused by network inaccuracies through Gaussian resampling. Simultaneously, an augmented artificial potential field with a dynamic rotational field is deployed to repair local paths when worst-case collision scenarios occur. This collaborative strategy harmoniously unites the complementary strengths of both components, thereby enhancing the overall resilience and adaptability of the motion planning system. Experiments were conducted in various environments. The results demonstrate that the proposed method can quickly find directly connectable paths in diverse environments while reliably avoiding sudden obstacles.

As robotic applications rapidly expand into increasingly complex and dynamic environments, greater emphasis is being placed on the intelligence and safety of human–robot collaboration at the task execution level. In shared human–robot workspaces, even the most precise motion planning cannot fully prevent collisions. To address this critical safety concern, we propose a variational Bayesian Kalman filtering-based external torque estimation algorithm that integrates the robot’s dynamic model while avoiding additional system complexity. We begin by reviewing the robot dynamics framework and the classical external torque estimation method based on generalized momentum. We then derive a Kalman filter-based approach for external torque estimation in robotic manipulators and analyze the adverse effects arising from mismatches in process noise covariance. Finally, we introduce a sliding window-based variational Bayesian Kalman filter, which dynamically estimates the current process noise covariance while simultaneously mitigating the accumulation of recursive errors.