Collision-free robot motion planning is crucial in robotic applications. Traditional sampling-based methods struggle with kinematic/dynamic constraints and intermediate process constraints, limiting their use to point-to-point motion generation. Optimization-based methods, such as sequential convex programming, often face issues of artificial feasibility and soft failure. To enhance both the success rate and quality of robot motion generation, this article presents a novel iterative motion planning framework grounded in a dual collision constraint formulation. A smooth and differentiable continuous collision detection method is developed based on the strong duality of convex body collision constraints. Building on this, trajectory optimization problem is simplified and an iterative algorithm is designed for collision information updating and batch gradient descent. Simulation and physical experimental results demonstrate that the proposed method performs excellently in both free-space point-to-point motion tasks and continuous task-space tracking trajectory generation with comparison to multiple classical methods, suggesting its promising applications in various robotic automation scenarios.

Reinforcement learning (RL) agents are vulnerable to adversarial disturbances, which can deteriorate task performance or break down safety specifications. Existing methods either address safety requirements under the assumption of no adversary (e.g., safe RL) or only focus on robustness against performance adversaries (e.g., robust RL). Learning one policy that is both safe and robust under any adversaries remains a challenging open problem. The difficulty is how to tackle two intertwined aspects in the worst cases: feasibility and optimality. The optimality is only valid inside a feasible region (i.e., robust invariant set), while the identification of maximal feasible region must rely on how to learn the optimal policy. To address this issue, we propose a systematic framework to unify safe RL and robust RL, including the problem formulation, iteration scheme, convergence analysis and practical algorithm design. The unification is built upon constrained two-player zero-sum Markov games, in which the objective for protagonist is twofold. For states inside the maximal robust invariant set, the goal is to pursue rewards under the condition of guaranteed safety; for states outside the maximal robust invariant set, the goal is to reduce the extent of constraint violation. A dual policy iteration scheme is proposed, which simultaneously optimizes a task policy and a safety policy. We prove that the iteration scheme converges to the optimal task policy which maximizes the twofold objective in the worst cases, and the optimal safety policy which stays as far away from the safety boundary. The convergence of safety policy is established by exploiting the monotone contraction property of safety self-consistency operators, and that of task policy depends on the transformation of safety constraints into state-dependent action spaces. By adding two adversarial networks (one is for safety guarantee and the other is for task performance), we propose a practical deep RL algorithm for constrained zero-sum Markov games, called dually robust actor-critic (DRAC). The evaluations with safety-critical benchmarks demonstrate that DRAC achieves high performance and persistent safety under all scenarios (no adversary, safety adversary, performance adversary), outperforming all baselines by a large margin.

Iterative learning control (ILC) achieves high control precision across various motion systems during repetitive tracking tasks by successively updating the compensation. In identical control circumstances, tracking errors primarily comprise repetitive components to be eliminated, induced by the input signals and regular system disturbances. In order to mitigate repetitive errors efficiently, conventional ILC methods treat the high-frequency components of tracking errors as nonrepetitive noise and disturbances, employing the low-pass filter to exclude these components. However, this specific frequency criterion is not entirely accurate, as there can be interference in the low-frequency range and effective components in the high-frequency range. Therefore, an energy-selected ILC is proposed in this article to identify these components, thereby enhancing the filtering validity. The proposed method proposes a novel energy criterion to construct the robust filter, improving the capability to distinguish repetitive components. Based on this advanced robust filter, the trajectory modification is designed as the learning filter to accelerate the convergence rate. The stability and convergence of this method are thoroughly proven and analyzed. Various comparative experiments have been conducted to illustrate the effectiveness of this novel energy-selected ILC approach. Generally, the proposed method has the following superiorities: it achieves high control precision across various motion scenarios; it broadens wide bandwidth applicable in high-frequency and nonsmooth circumstances; and it has an accurate error analysis suitable for practical applications. Meanwhile, it improves the control performance of classic ILC while maintaining its ease of implementation.

In the realm of ultraprecision motion control, achieving high tracking accuracy, great trajectory generalization, and robust disturbance rejection simultaneously remains a challenge. This article proposes an intelligent gated recurrent unit real-time iterative compensation (GRU-RIC) position-loop feedforward compensation control method to tackle this issue. Specifically, a gated recurrent unit (GRU) neural network is first trained to accurately predict tracking errors for given reference trajectories in advance. The predicted error serves as an offline feedforward compensation signal to enhance tracking accuracy. To mitigate residual tracking errors arising from incomplete offline compensation and unexpected disturbances, a real-time iterative compensation (RIC) scheme that generates optimal online feedforward signals through real-time system prediction is proposed. Both offline and online compensation signals are synergistically applied to modify the reference trajectory in a position-loop feedforward manner. Experimental results on a nano-precision air-bearing motion stage confirm that the GRU-RIC method achieves 10-nm tracking accuracy, which is the same as iterative learning control (ILC), while outperforming ILC in trajectory generalization and disturbance rejection.

This article presents a novel real-time iterative compensation (RIC) method using plant-injection feedforward architecture for motion control of ultraprecision wafer stages, addressing the severe challenge of achieving extreme tracking accuracy along with strong task flexibility and disturbance rejection ability. The RIC method establishes an online prediction model to accurately predict upcoming tracking errors during real-time motion. The prediction result enables the online generation of optimal plant-injection feedforward signal at each sampling control instant via iterative calculation, which enhances tracking accuracy and dynamical regulation capability. Various trajectory tracking tasks have been implemented on an ultraprecision wafer stage. Experimental results demonstrate that RIC matches the high tracking accuracy of well-acknowledged iterative learning control while offering superior task flexibility and disturbance rejection ability.

Time-optimal trajectory planning aims to minimize the traversal time of arbitrary geometric paths. The demand for real-time planning widely exists in robotics, numerical control manufacturing, and autonomous vehicle applications. Existing trajectory planning methods either compromise on time optimality to improve computational efficiency or suffer from at least linear time complexity, preventing the planning of long trajectories in real time. Motivated by these challenges, this article proposes a novel set invariant trajectory planning (SITP) method to address the problem of real-time time-optimal planning for continuous multiaxis trajectories under complete second-order kinodynamic constraints. First, a backup control strategy is synthesized to construct an implicit control invariant set (CIS). This set is designed so that a feasible control input always exists to keep the system within the defined kinodynamic bounds. Then, utilizing the principles of bang–bang control theory, the optimal control is sought within the CIS. A local greedy linear programming method is proposed to calculate the time-optimal trajectory at each control cycle. The proposed method is computationally efficient for even 1-kHz real-time applications and the planned results maintain strict global time optimality, which makes it promising in real-time planning scenarios of various automatic applications.

Hybrid additive-subtractive manufacturing (HASM) has achieved universal application in aerospace, medicine, military industry, and other fields. The additive manufacturing (AM) process has a significant influence on manufacturing quality and efficiency in HASM. However, few process planning methods exist utilizing the interplay between different processes in HASM. For the first time to the best of our knowledge, this paper proposes a slice extension (SE) method for HASM, the key idea of which is to print an extended slice in the AM process and guarantee the final geometric accuracy in the subtractive manufacturing (SM) process. Firstly, an optimization problem minimizing the isoperimetric quotient, the area, and the perimeter of the extended slice, is designed and convexified. Then, a unilateral rolling circle (URC) method is proposed to guarantee that the extended slice covers the original slice. Finally, an approach to dealing with multiply connected slices is proposed to eliminate underfill near holes. Simulation experiments indicate that the proposed SE method achieved an 81.5% lower underfill rate than the conventional method, i.e., the widely-used contour-parallel (CP) method in the industry, with limited extra materials on average. The toolpath smoothness is also improved. The performance of the proposed SE method verifies its significant application potential in HASM, computer numerical control milling, and other fields.

In this article, an intelligent feedforward prediction and compensation scheme to combine with a dual-loop high-bandwidth controller is proposed for high-speed and high-precision tracking controls of a nanopositioning stage. First, the dual-loop controller consisting of an inner loop damping and an outer loop tracking controller is developed with all the parameters optimized simultaneously, which could provide a control bandwidth over the first resonant frequency of the stage. Next, the Gaussian process machine learning model is employed to capture the dynamic characteristics of the tracking error of the dual-loop controlled plant. Then, a feedforward compensator is constructed to add a compensation term to the initial reference trajectory. Experimental investigations on a self-made piezoelectric-actuated stage validate the effectiveness of the intelligent tracking error prediction method and the excellent performance of the control strategy for high-precision tracking of high-frequency reference trajectories.

When the trajectory with high speed and high acceleration contains frequency contents matching with the structure mode, the inertial vibration of the structure is easily excited, reducing machining accuracy and surface finish. Input shaping can avoid vibration, but it introduces time-delay that causes multiaxis trajectory distortion and affects the accuracy of contour error estimation. This article presents time parameter mapping and contour error precompensation for multiaxis input shaping to suppress vibration. The mapping of time parameter domain of trajectories is established by deducing the relation between the local curvature extremums of the trajectories before and after shaping, which provides reference points for contour error estimation. The actual trajectory is predicted by the closed-loop servo dynamics model and reference trajectory, and then the Newton iterative algorithm based on time parameter mapping is used to seek the contour error point. Finally, the calculated contour error is low-pass filtered and projected to each axis, and then the shaped trajectory is precompensated to simultaneously reduce the contour error and avoid structural vibration. Comparative experiments are conducted to validate the effectiveness of the proposed method. Experimental results illustrate that the proposed method not only suppresses structural vibration, but also significantly improves the estimation accuracy and contouring performance by time parameter mapping.

Back electromotive force (EMF)-based sensorless control strategies for permanent-magnet linear synchronous motor (PMLSM) have the potential to simplify the mechatronic system, reduce the cost and prolong the service life. However, the poor performance in the low-to-zero speed region limits their application range. In this article, a novel back EMF-based mover position estimator is proposed to achieve consistent good accuracy in the whole speed range including high speed, medium speed, low speeds, temporary standstill, and speed reversals. The three-phase flux linkages are obtained by directly calculating the integration of back EMF. To overcome the curve drift caused by the integrator, this article proposes a jumping correction algorithm and a uniform correction algorithm. The mover position is calculated from the corrected flux linkages. This article also realizes a closed-loop sensorless trajectory tracking control system using the proposed position estimator. Experimental results on a PMLSM demonstrate that the proposed position estimator can guarantee the stability and accuracy in the whole speed range. Compared with the existing back EMF-based methods working only well in high-speed region and usually with$mm$-level accuracy, the proposed method achieves an accuracy of sub-200$\mu$m regardless of the reference trajectory, and has exciting prospect in industrial applications.

For precision motion systems widely applied in industrial manufacturing equipments, it is critical to achieve both high trajectory tracking accuracy and superior disturbance rejection ability. In this article, a novel nonlinearity compensation and high-frequency flexibility suppression based real-time iterative compensation (RIC) method is proposed to achieve excellent tracking performance in practice. The unexpected nonlinearity and high-frequency flexible mode of the plant, which limits the achievable control performance, is first compensated and suppressed. Subsequently, a RIC method based on accurate linear prediction model is proposed to further reduce the tracking error by adding a compensation term to the initial reference trajectory. The trajectory compensation idea of RIC is comparative to remarkable iterative learning control (ILC), but the proposed RIC can online generate and adjust the compensation term during real-time motion without abundant offline iteration trials in ILC. This mechanism significantly enhances the robustness to trajectory variations and external disturbances. Comparative experiments carried out on a ball-screw-driven precision motion stage with full-closed loop position feedback validate the effectiveness and superiority of the proposed method for various trajectory tracking tasks. The proposed method outperforms ILC on tracking performance, and possesses the robustness to various disturbances and reference variations, which leads to industrial application significance.

In this article, to guarantee the good tracking performance of the precision motion system for various tracking tasks, an online iterative learning compensation method is proposed for closed-loop motion control systems. The prediction model is based on the closed-loop model of the linear second-order system with a proportional-integral-derivative controller, and an estimation term is added to deal with the influence of slow-varying uncertain disturbances. On the basis of the accurate state prediction, the dynamical feedforward compensation can be obtained, which suppresses the tracking error caused by the dynamical lag. Furthermore, in order to simultaneously compensate the errors caused by nonlinear factors such as uncertain disturbances and to guarantee the smoothness of the compensated trajectory, the optimal compensation gain is determined through online iterative calculation. The online iterative approach is similar to iterative learning control, but does not require several offline iterations of a repeating trajectory. Comparative experiments are carried out on an industrial motion stage. Various experimental results consistently demonstrate that the proposed compensation scheme can achieve the tracking accuracy comparable to iterative learning, while maintaining the robustness to trajectory changes and uncertain disturbances without reoffline iteration.

Contouring motion control plays an important role in modern precision multiaxis motion systems. In order to enhance the coordination between each axis and promote contouring performance, many research works have been conducted that mainly focus on contouring error online estimation and control. Essentially, most of existing control strategies based on emerged contouring error belong to feedback control, which cannot achieve perfect performance due to inevitable delay or lag. To fundamentally tackle the above problem, a novel position-loop feedforward contouring control method is proposed in this paper. Specifically, according to the linear model of each axis and the kinematics characteristics of reference contour, a dynamical model of contouring error in multiaxis systems is firstly developed, which can explain the essential causes of contouring error quantificationally. Then, based on the proposed contouring error model, a position loop feedforward control strategy can be designed for contouring following tasks. The effectiveness of the proposed method is tested on a three-axis computerized numerical control systems. Various experimental results consistently demonstrate that the contouring error model can accurately predict actual contouring error to some degree. Compared with the conventional model-based feedforward approach, the proposed strategy can not only point out the essential causes of contouring error directly, but also achieve better contouring performance.

In this paper, a neural network learning adaptive robust controller (NNLARC) is synthesized for an industrial linear motor stage to achieve good tracking performance and excellent disturbance rejection ability. The NNLARC scheme contains parametric adaption part, robust feedback part, and radial basis function (RBF) neural network (NN) part in a parallel structure. The adaptive part and the robust part are designed based on the system dynamics to meet the challenge of parametric variations and uncertain random disturbances. It must be noted that in actual industrial machining situations, precision motion equipment is always disturbed by unknown factors, which usually cannot be described by mathematical models but affect the tracking accuracy significantly. Therefore, the RBF NN part is employed to further approximate and compensate the complicated disturbances with high reconstructing accuracy and fast training rate. The stability of the proposed NNLARC strategy is analyzed and proved through the Lyapunov theorem. Comparative experiments under various external disturbances such as completely unknown disturbance added by polyfoam are conducted on an industrial linear motor stage. The experimental results consistently validate that the proposed NNLARC control strategy can excellently meet the challenge of complicated disturbance in practical applications. The proposed scheme also provides a guidance for control strategy synthesis with both good tracking performance and disturbance rejection.

Wafer stage is an important mechatronic unit of industrial lithography tool for manufacturing integrated circuits. To overcome the inherent limitations of fix-gain feedback control and improve the servo performance, a performance-oriented variable-gain control strategy with accelerated iterative parameter tuning is proposed for an ultra-precision wafer stage. The variable-gain controller comprises a fix-gain proportional-integral-derivative (PID) controller and add-on variable-gain elements, which are the focus of this paper. Specifically, the add-on variable-gain elements are significantly designed based on the main tracking error sources and error frequency of different reference trajectory phases. A weighted two-norm regarding the performance indexes of wafer stages, i.e., moving average (MA) and moving standard deviation (MSD) of the tracking error, is synthesized as the objective function, and the data-driven Levenberg–Marquardt-based iterative parameter tuning scheme is employed to find the optimal parameter values of the proposed variable-gain controller. Furthermore, to improve the convergence rate, a multiparameter accelerated iterative method is developed based on Aitken’s method. Finally, the proposed variable-gain control strategy is implemented on an ultra-precision wafer stage developed in our laboratory. Comparative experimental results demonstrate that the strategy performs best and achieves excellent improvement on both MA and MSD. During the scanning phase, MA and MSD are less than 1.02 and 2.35 nm, respectively. The proposed variable-gain control strategy is also suitable for other industrial applications.