Momentum-based optimizers are widely adopted for training neural networks. However, the optimal selection of momentum coefficients remains elusive. This uncertainty impedes a clear understanding of the role of momentum in stochastic gradient methods. In this paper, we present a frequency domain analysis framework that interprets the momentum method as a time-variant filter for gradients, where adjustments to momentum coefficients modify the filter characteristics. Our experiments support this perspective and provide a deeper understanding of the mechanism involved. Moreover, our analysis reveals the following significant findings: high-frequency gradient components are undesired in the late stages of training; preserving the original gradient in the early stages, and gradually amplifying low-frequency gradient components during training both enhance performance. Based on these insights, we propose Frequency Stochastic Gradient Descent with Momentum (FSGDM), a heuristic optimizer that dynamically adjusts the momentum filtering characteristic with an empirically effective dynamic magnitude response. Experimental results demonstrate the superiority of FSGDM over conventional momentum optimizers.

Magnetic continuum robots (MCRs) with active steering capability hold great promise for improving interventional surgery due to their flexibility and controllability. However, achieving real-time tracking and automatic navigation of MCRs in tissue-mimicking multi-bifurcated vessels remains a significant challenge. This work proposes an ultrasound-guided real-time automatic navigation framework for magnetic guidewire robots to improve interventional surgery, including modeling, simulation, tracking and control. An ultrasound-guided magnetically controlled guidewire robot system (UMCGRS) is designed and validated in 3D vascular phantom. An equilibrium guidewire model is established to describe the quasi-static behavior of MCRs in a permanent magnetic field and to derive the control Jacobian for guidewire tip control, which is validated by magnetic navigation simulation. A network-based real-time ultrasound tracking method is developed for accurate guidewire detection (average detection error of 0.81 mm across various vessels), and a model-based path tracking control strategy is proposed for guidewire navigation. Experiments in a femoral artery gelatin phantom with tissue-mimicking environments demonstrate the effectiveness of the tracking and control (average tracking error of 1.50 ± 0.30 mm). The proposed UMCGRS and automatic navigation framework are expected to enhance the autonomy of MCRs, and will provide a reliable solution for improving interventional surgery.

This paper proposes a specific and effective real-time sequence planning method using robot manipulators to complete complex assembly tasks. Many previous studies developed different traversal methods to obtain the optimal assembly sequence. Besides, a number of algorithms were proposed to enhance flexibility when the conditions or rules were changed in various sequence optimization problems. However, these state-of-the-art (STOA) methods necessarily require modifications when task details are changed. Consequently, to further improve the generalization ability and improve the performance of the sequence optimization, a neural combinatorial optimization algorithm combined with a self-learning strategy is proposed for assembly sequence planning. In addition, obstacle avoidance and the non-collision constraints between workpieces in the assembly process are considered. According to the experiment results, the new method is superior to the STOA methods in terms of optimization efficiency. More importantly, the proposed method has satisfactory generalization ability for different assembly tasks.Note to Practitioners—This paper studies assembly sequence planning problems for different real-world applications in industrial and home service fields. Many assembly sequence planning solutions have been widely utilized before. However, the generalization ability of the previous methods is not satisfactory since the re-adjust process is required when the workpiece number or collision condition changes in different tasks.Motivated by the above reasons, this paper develops a learning-based assembly sequence planning solution to resolve complex assembly problems without parameter re-adjustment processes. Users can directly apply the developed workpiece identification and localization method to obtain the sensing information. Then, the newly designed collision-free cost function should be programmed as the core of the assembly sequence optimization. Next, the proposed neural combinatorial optimization (NCO) with the sensing information and target configuration as inputs can provide the optimal assembly sequence by self-learning. The learned NCO-based method can be directly applied to diverse planning tasks, even with different workpiece numbers. Users can also refer to the experimental examples in this paper for the extension of the proposed method to their own applications.

The bundle adjustment (BA) algorithm is a widely used nonlinear optimization technique in simultaneous localization and mapping (SLAM) systems. By leveraging the co-view relationships of landmarks from multiple perspectives, the BA method constructs a joint estimation model for both poses and landmarks, enabling the system to generate refined maps and reduce front-end localization errors. However, exploring a robust LiDAR BA estimator and achieving accurate solutions is a challenge. In this work, firstly we propose a novel mean square group metric (MSGM) to build the optimization objective of the LiDAR BA algorithm. This metric applies a mean square transformation to uniformly process the measurements of plane landmarks during one sampling period. The transformed metric ensures scale interpretability and does not require a time-consuming point-by-point calculation. Secondly, by integrating a robust kernel function, the metrics involved in the BA algorithm are reweighted, thus enhancing the robustness of the solution process. Thirdly, based on the proposed robust LiDAR BA model, we derived an explicit second-order estimator (RSO-BA). This estimator employs analytical formulas for Hessian and gradient calculations, ensuring the precision of the BA solution. Finally, we verify the merits of the proposed RSO-BA estimator against existing implicit second-order and explicit approximate second-order estimators using publicly available datasets and physical experiments. The experimental results demonstrate that the RSO-BA estimator outperforms its counterparts in terms of registration accuracy and robustness, particularly in dynamic or complex unstructured environments. Note to Practitioners—The motivation of this paper is to develop a novel LiDAR bundle adjustment (BA) algorithm that ensures accurate and consistent 3D scene modeling. Currently, most LiDAR BA algorithms use “group” processing to construct cost metrics, aiming to reduce the computational complexity of point-by-point operations. However, the cost metrics of these approaches lack scale interpretability, which makes it difficult to incorporate robust kernel functions into the model design, ultimately weakening the system’s robustness and reducing estimation accuracy. To address these issues, we propose a mean square group metric (MSGM) that considers the number of measurement points, to construct the optimization objective for the LiDAR BA (RSO-BA) problem. In each optimization iteration, a robust kernel function reweights each metric to ensure robustness in the solution. Additionally, we derive the analytical Hessian matrix and gradient vector required for solving the RSO-BA, with the inclusion of second-order terms enhancing estimation accuracy. The proposed method can be directly applied to the mobile robot system for automatic driving, home service and unmanned security applications. Furthermore, the proposed algorithm can be extended to sensors such as depth cameras, which provide direct depth information, for broader practical applications.

Target localization technology is widely applied in various applications, such as rescue missions, robot navigation, and the Internet of Things. However, in some scenarios, the positions of sensors are unknown due to the load limitation of the sensor carriers and environmental interferences, resulting in the instability of the global navigation satellite system (GNSS). This paper focuses on optimal angle-of-arrival (AOA) sensor placement using multiple position-unknown sensors for target localization accuracy improvement. To guarantee the uniqueness of the target coordinate, at least two anchors are needed. The anchors are some static benchmark objects in the environment with priori known positions. Firstly, a new optimization problem for AOA target localization accuracy improvement incorporating position-unknown sensors and anchors is formulated. Secondly, the optimal theoretical localization accuracies of the unknown sensors and target are derived by minimizing the trace of the Cramér-Rao lower bounds (CRLBs). Thirdly, a mixture optimization method, including a geometrical initialization and the new proposed simultaneous perturbation stochastic approximation and adaptive momentum estimation (SPSA-Adam) algebraic algorithm, is developed. Then, the correctness of the new theoretical findings and the effectiveness of the proposed sensor placement optimization method are verified by simulation examples.

Most prior robot learning methods focus on image-based observations, limiting their capability in 3-D robotic manipulation. Voxel representation naturally delivers rich spatial features but remains underutilized. Specifically, current voxel-based methods struggle with fine-grained tasks, since precise actions are not fully achievable. However, humans can accomplish these tasks well using vision and proprioception. Inspired by this, this article proposed a novel Fusion-Perception-to-Action Transformer (FP2AT) with cross-layer feature aggregation to handle fine-grained manipulation in 3-D space. In particular, a multiscale 3-D visual fusion attention mechanism is devised to draw attention to local regions of interest and maintain awareness of global scenes, thereby boosting the capabilities of visual perception and action planning. Meanwhile, a 3-D visual mutual attention mechanism is designed and it can also enhance spatial perception. Besides, we further explore the potential of FP2AT by developing its coarse-to-fine version, which progressively refines the action space for more precise predictions. In addition, a proprioceptive encoder is developed to mimic the perception of body movements and contact, elevating the effectiveness of the FP2AT. Furthermore, a new metric, the average number of key actions (ANKA), is introduced to evaluate efficiency and planning capability. In various simulated and real-robot examples, our methods significantly outperform state-of-the-art 3-D-vision-based methods in success rate and ANKA metrics.

This paper focuses on the angle-of-arrival (AOA) target tracking problem using a mobile unmanned aerial vehicle (UAV) equipped with an angle-of-arrival (AOA) sensor to observe targets in an external-denied (no global positioning system, inertial navigation system aid) environment. The mathematical formulations are based on two known anchors. The extended Kalman filter (EKF) is modified to calculate the UAV’s and target’s absolute coordinates. To improve the tracking accuracy, a gradient-based UAV path optimization algorithm using simultaneous perturbation stochastic approximation (SPSA) is developed. The geometry of anchors and UAV impacts the estimation accuracy, especially when the selected anchors are close to the target. The simulations have demonstrated the effectiveness of the proposed scheme.

This paper focuses on addressing the visual tracking problem using learning-based methods for object tracking tasks. This problem contains a major difficulty, i.e., how to acquire a satisfactory generalization ability of the developed system? In this paper, firstly, the object state tracking system, including a camera-in-hand, a 3D camera and a Rethink Baxter robot, is introduced. The problem formulation is also presented. Secondly, we propose a Kalman-based estimation strategy to acquire the object’s state. In addition, a learning-based tracking controller is developed using the Gaussian mixture models (GMM) method to steer the robot end-effector to track the mobile object. Thirdly, to guarantee system stability (i.e., the position and velocity errors between the object and end-effector will always converge to zeros), the controller parameter constraints are derived, which is a theoretical contribution of this paper. The controller parameter adjustment is avoided by the proposed training process. Thus, the proposed method becomes easy to implement, which is a practical contribution. Finally, the effectiveness of the proposed method is demonstrated by simulation and experimental examples, and the proposed method has satisfactory generalization ability. Note to Practitioners—This paper studies object tracking problems for different practical applications, such as industrial cutting, grasping and dynamic monitoring. Different trajectory tracking methods have been widely applied in the industrial area. However, users always complain that when the object or trajectory is changed, the tracking controller more or less needs to be re-adjusted. This re-adjust process always requires professional knowledge and programming experience, and thus a factory must employ some professional engineers. In addition, since the objects may be diverse in shape, color and size, to acquire the accurate object position and velocity, an appropriate solution is necessary. Motivated by the above introductions, this paper aims to develop a learning-based controller to track different complex trajectories without frequent and specific parameter adjustment processes. Firstly, a visual measurement system is developed to quickly find and estimate the position and velocity of an object. Secondly, with the object’s information, the learning from demonstration method (GMM method) is applied for the control policy design. Thirdly, the detailed system stability analysis is presented, and the corresponding controller parameter constraints are derived and considered in the proposed control policy. Subsequently, with the demonstration data, the packaged learning algorithm will automatically compute the controller parameters, and users can change the controller performance only by providing the desired demonstrations. In summary, this paper proposes a systematic object tracking solution, and it may bring a new idea to develop a practical object tracking system, using both the learning-based methods to improve the ability of generalization for tracking different objects.

The widespread application of learning-based methods in robotics has allowed significant simplifications to controller design and parameter adjustment. In this article, robot motion is controlled with learning-based methods. A control policy using a broad learning system (BLS) for robot point-reaching motion is developed. A sample application based on a magnetic small-scale robotic system is designed without detailed mathematical modeling of the dynamic systems. The parameter constraints of the nodes in the BLS-based controller are derived based on Lyapunov theory. The design and control training processes for a small-scale magnetic fish motion are presented. Finally, the effectiveness of the proposed method is demonstrated by convergence of the artificial magnetic fish motion to the targeted area with the BLS trajectory, successfully avoiding obstacles.

As the controller parameter adjustment process is simplified significantly by using learning algorithms, the studies about learning-based control attract a lot of interest in recent years. This article focuses on the intelligent servo control problem using learning from desired demonstrations. Compared with the previous studies about the learning-based servo control, a control policy using the broad learning system (BLS) is developed and first applied to a microrobotic system, since the advantages of the BLS, such as simple structure and no-requirement for retraining when new demos' data is provided. Then, the Lyapunov theory is skillfully combined with the complex learning algorithm to derive the controller parameters' constraints. Thus, the final control policy not only can obtain the movement skills of the desired demonstrations but also have the strong ability of generalization and error convergence. Finally, simulation and experimental examples verify the effectiveness of the proposed strategy using MATLAB and a microswimmer trajectory tracking system.

In this article, we address the trajectory tracking problem using the learning from demonstration (LFD) method. By using the LFD method, the parameter adjusting problem in the tracking controller is avoided. Consequently, a strategy can be provided to users with limited parameter adjusting experience. The kinematic tracking problem is formulated as a second-order system and the objective is to simultaneously reduce the errors in position and velocity. The extreme learning machines (ELM) algorithm is applied in the controller design. The velocity and position are utilized as the inputs and the output is the robot corrected kinematic movement. The controller parameters are learned from the desired human or programming demonstrations taking into consideration the stability constraints. In this work, we analyze the system local and global asymptotic stability in detail. The effectiveness of the proposed strategy is demonstrated by simulation comparisons and a practical experiment using a KUKA robot manipulator.

This letter investigates how to place the received-signal-strength (RSS) sensors to improve the static target localization accuracy in the three-dimensional (3-D) space. By using the A-optimality criterion, i.e., minimizing the trace of the inverse Fisher information matrix (FIM), a new optimal RSS sensor placement strategy is developed when sensors can be placed freely in the 3-D space. The smallest reachable trace of Cramér-Rao lower bound, i.e., the inverse FIM, is derived with the corresponding optimal sensor-target geometries. Besides, a resistor network method and a special configuration strategy are proposed to quickly determine the optimal geometries. The findings are concluded in three remarks, which are used to evaluate and improve the estimation accuracy. Simulation examples verified these findings.

This paper investigates the problem of how to optimize the path of a single moving own-ship for angle-of-arrival (AOA) target tracking in three-dimensional (3D) space. First, a novel 3D pseudolinear Kalman filter (PLKF) is proposed to reduce computational complexity and to improve stability of an extended Kalman filter solution. This filter consists of an xy-PLKF and a z-PLKF, transforming the nonlinear azimuth and elevation angle measurements into pseudolinear models. We show that when the own-ship and target are at the same height, the z-PLKF will be unbiased. Next, a gradient-descent path optimization algorithm is developed for the xy-PLKF aiming at minimizing the trace of the covariance matrix. Then, a grid search path optimization method is designed for the z-PLKF. Simulation examples verify the effectiveness of the proposed path optimization algorithm.

This paper is concerned with unmanned aerial vehicle (UAV) path optimization for AOA target localization via distributed processing. A distributed UAV path optimization algorithm based on gradient descent method is developed using the diffusion extended Kalman filter (DEKF). With this algorithm, a group of UAVs can realize self-adaptive path optimization in order to improve estimation performance. The presented distributed path optimization strategy aims to minimize the estimation mean squared error (MSE) by minimizing the trace of the error covariance matrix. The UAV dynamic communication topology caused by communication range constraint is analyzed. Furthermore, the UAV 6-degree-of-freedom (DOF) dynamic modeling is taken into consideration to generate realistic UAV trajectories. The properties and effectiveness of the proposed algorithm are discussed and verified with simulation examples.

This paper investigates the problem of how to improve angle-of-arrival (AOA) target localization accuracy by finding an optimal AOA sensor deployment strategy in 3D space. Under the assumption of constant absolute elevation angles for the sensors, a novel and simple optimal sensor deployment criterion is proposed based on minimizing the trace of inverse Fisher information matrix. Our analysis shows that when sensor elevation angles equal ±42.2869° and twice of azimuth angles have equal angular distribution with uniform distance from the target and equal noise covariance, the lowest mean squared error is achieved. Besides, with more sensors placed closer to the target, a lower mean squared error is attained. Simulation examples are presented to verify the effectiveness of the developed optimality criterion.