This paper proposes a force and position hybrid control method for robot manipulators, which makes some of the workspace variables controlled by PD and the other by Kinetic Potential Energy Shaping (KPES). The conventional energy shaping method allows one to design a stabilizing controller with a Lyapunov function candidate consisting of an artificial potential function that plays the role of a design parameter. The potential function depends only on position, and this framework is a natural generalization of the well-known PD control for linear systems. KPES generalizes the conventional method such that it allows one to select an artificial potential function depending on both position and velocity variables. One of the benefits of the conventional method is to preserve the passivity of the original plant system, which enhances the safety of the control system. However, KPES does not preserve passivity in general. This paper proposes a hybrid control method for robot manipulators, which makes some of the configuration variables controlled by PD and the other by KPES. The realized system enables position control of subsystems by KPES and preserves the passivity of the entire system when an external force acts on subsystems controlled by PD. This hybrid control system will be useful from a safety perspective for control problems in which the feedback system still has physical interaction with its environment. This paper presents a method to design a feedback system that guarantees asymptotic stability of the entire system, preserves passivity, and discusses application to a force and position hybrid control with respect to workspace variables of a robot manipulator. Furthermore, numerical examples are presented for a robot manipulator.

This paper presents a novel trajectory optimization method for nonlinear l1-optimal control problems in which the control horizon is treated as a free variable, allowing both the control duration and the l1-norm of the control input to be evaluated. Unlike traditional approaches that minimize the l1-norm of the input under a fixed control horizon, the proposed method treats both the control input and control horizon as design variables, enabling joint optimization of energy and temporal efficiency. The method extends a Newton-based algorithm to accommodate this objective, leveraging gradient information with respect to both variables. This formulation enables one to find high-fidelity optimal trajectories without pre-specifying the control horizon. The effectiveness and robustness of the method are demonstrated through numerical simulations, in which the proposed algorithm recovers the analytical solution to the spacecraft Hohmann transfer, and determines an optimal control horizon for an Earth-Moon transfer.

In this paper, we propose a new second-order sliding mode controller for mechanical port-Hamiltonian systems. This paper proposes a passivity-based sliding mode controller based on kinetic-potential energy shaping (KPES). So far this type of controller was only able to achieve first-order sliding mode control, since the KPES allows one to embed a subsystem whose dimension is the same as that of the input into the closed-loop system. This paper extends the KPES to incorporate a higher-order subsystem in the closed-loop system, which enables us to obtain the subsystem that can realize second-order sliding mode control. The proposed controller is integration of a passivity-based controller and a second-order sliding mode controller which does not cause undesirable chattering phenomena. It ensures finite-time convergence of the subsystem and asymptotic stability of the entire closed-loop system by utilizing two Lyapunov functions. Moreover, due to the design freedom in selecting a Lyapunov function candidate of the KPES, it can deal with several control objectives including trajectory tracking control. A numerical example demonstrates the effectiveness of the proposed method.

In this paper, we propose a new second-order sliding mode controller for mechanical port-Hamiltonian systems. This paper proposes a passivity-based sliding mode controller based on kinetic-potential energy shaping (KPES). So far this type of controller was only able to achieve first-order sliding mode control, since the KPES allows one to embed a subsystem whose dimension is the same as that of the input into the closed-loop system. This paper extends the KPES to incorporate a higher-order subsystem in the closed-loop system, which enables us to obtain the subsystem that can realize second-order sliding mode control. The proposed controller is integration of a passivity-based controller and a second-order sliding mode controller which does not cause undesirable chattering phenomena. It ensures finite-time convergence of the subsystem and asymptotic stability of the entire closed-loop system by utilizing two Lyapunov functions. Moreover, due to the design freedom in selecting a Lyapunov function candidate of the KPES, it can deal with several control objectives including trajectory tracking control. A numerical example demonstrates the effectiveness of the proposed method.

This paper presents a new approach to quadrotor state estimation and control using ultra-wideband (UWB)-based bidirectional ranging and angle of arrival (AoA) measurements. This method offers a significant advantage over traditional motion capture systems or time-of-arrival (ToA) based positioning by requiring only a single, compact UWB anchor, greatly simplifying setup and reducing infrastructure requirements. We address the challenge of significant noise in UWB measurements by integrating them with an inertial measurement unit (IMU) data through an extended Kalman filter (EKF). Our key contributions also include proposing a magnetometer-free yaw estimation method utilizing bidirectional AoA measurements. This method effectively addresses gyroscope drift in indoor environments where magnetometers are unreliable. We also provide theoretical validation of the system's observability, and experimentally demonstrate successful stabilization control of a micro quadrotor using the estimated states. The experimental results show significant reduction in estimation errors compared to raw sensor data. Additionally, we conduct control experiments in rainy environments and confirm that UWB-based control can be effective in a wide range of conditions, including rainy weather. Our approach offers a robust, cost-effective solution for quadrotor navigation and control in GPS-denied environments, particularly indoors, and in rainy conditions, while minimizing setup complexity and hardware requirements.

This paper investigates the effects of setting the sampling frequency significantly higher than conventional guidelines in system identification. Although continuous-time identification methods resolve the numerical difficulties encountered in discrete-time approaches when employing fast sampling (e.g., the problems caused by all poles approaching unity), the potential benefits of using sampling frequencies that far exceed traditional rules like the "ten times the bandwidth" guideline remained largely unexplored. We show that using a state variable filter (SVF)-like least squares approach, the variance of the estimation error scales as $O(h)$ with the sampling interval $h$. Importantly, this scaling holds even with colored noise or noise correlations between variables. Thus, increasing the sampling frequency and applying the SVF method offers a novel solution for challenging problems such as closed-loop system identification and measurements with offsets. Theoretical findings are supported by numerical examples, including the closed-loop identification of unstable multi-input multi-output (MIMO) systems.

Nonlinear Model Predictive Control (NMPC) offers a powerful approach for controlling complex nonlinear systems, yet faces two key challenges. First, accurately modeling nonlinear dynamics remains difficult. Second, variables directly related to control objectives often cannot be directly measured during operation. Although high-cost sensors can acquire these variables during model development, their use in practical deployment is typically infeasible. To overcome these limitations, we propose a Predictive Virtual Sensor Identification (PVSID) framework that leverages temporary high-cost sensors during the modeling phase to create virtual sensors for NMPC implementation. We validate PVSID on a Two-Degree-of-Freedom (2-DoF) direct-drive robotic arm with complex joint interactions, capturing tip position via motion capture during modeling and utilize an Inertial Measurement Unit (IMU) in NMPC. Experimental results show our NMPC with identified virtual sensors achieves precise tip trajectory tracking without requiring the motion capture system during operation. PVSID offers a practical solution for implementing optimal control in nonlinear systems where the measurement of key variables is constrained by cost or operational limitations.

This letter proposes an algorithm for solving finite-time nonlinear optimal control problems. The proposed method employs the Gauss pseudospectral method to transform the optimal control problem into a nonlinear programming problem, and sequential convex programming (SCP) to solve it. Furthermore, by applying the information of the solution obtained by SCP to the indirect shooting method, a more accurate optimal solution can be obtained. There was an attempt to solve a similar class of optimal control problems, but it was only applicable to a restrictive class of problems without state constraints. In contrast, the proposed method can solve a general class of optimal control problems, including those with state constraints, while ensuring the numerical stability of the algorithm. This objective is achieved without losing the numerical stability of the algorithm by introducing a slack variable and incorporating state constraints into the dynamics. Additionally, the proposed method guarantees quadratic convergence by appropriately limiting the update step size of the optimization variables. To demonstrate the effectiveness of the proposed method, we apply the proposed method to an L-1/L-2 -optimal control problem of a two-wheeled rover.

This paper proposes a novel nonsingular terminal sliding mode controller for mechanical systems based on passivity-based control. In the authors’ previous study, passivity-based sliding mode control is realized with kinetic potential energy shaping (KPES), which allows us to construct a wider class of energy-based Lyapunov function candidates. This paper extends KPES to deal with a special class of Lyapunov function candidates whose arguments depend nonlinearly on the momentum. Based on this extension, we propose a nonsingular terminal sliding mode controller that achieves finite time convergence of the closed-loop system with an energy-based Lyapunov function. Due to the passivity-based approach, the proposed controller guarantees Lyapunov stability of the closed-loop system even if the discontinuous control input is replaced with a continuous one to alleviate chattering. A numerical example demonstrates the effectiveness of the proposed method.

In this research, we investigate a system identification method based on deep neural networks for nonlinear Model Predictive Control (MPC), focusing on efficiently managing massive multi-output systems. This method involves the direct synthesis of state estimators and output predictors represented by neural networks from experimental data. The integration of these components with the Levenberg-Marquardt optimization method, coupled with the use of automatic differentiation, enables efficient realization of nonlinear MPC. In this research, we propose a specific architecture for the state estimator and output predictor, designed to suit multi-output systems. This approach is applied to a miniature four-wheeled vehicle equipped with a 1D camera, which generates 160-pixel image outputs. The experimental application to this test vehicle demonstrates the method's capability in effectively managing complex, multi-output systems. Copyright (C) 2024 The Authors.

In this work, we propose a passivity-based super-twisting controller for mechanical port-Hamiltonian systems. The authors have proposed a passivity-based sliding mode controller based on kinetic-potential energy shaping (KPES) which allows us to embed a subsystem whose dimension is the same as that of the input into the closed-loop system. This paper extends KPES to incorporate a higher-order subsystem in the closed-loop system, which enables us to obtain the subsystem that has the same structure as the super-twisting algorithm (STA). Passivity-based control provides a variety of Lyapunov function candidates for interconnected physical systems, while the STA achieves second-order sliding mode control. Therefore, the proposed method is expected to offer a way to integrate the two methods, passivity-based control and second-order sliding mode control, and to allow us to design sliding mode control systems with a variety of energy-based Lyapunov functions. The effectiveness of the proposed method is verified through a numerical example.

Learning dynamical systems in a sample-efficient way is important for model-based control. Active learning which sequentially selects the most informative data to sample is capable of greatly reducing sample complexity. The active learning problem for dynamical systems is hard as we can not arbitrarily draw samples from the system’s state space under constraints of system dynamics. The existing approaches model the dynamical systems using Bayesian linear regression or Gaussian processes which can not be applied to complex dynamical systems with high-dimensional state spaces. In this article, we propose a new method to actively learn dynamical systems using Bayesian neural networks which allow for modeling high-dimensional systems with complex dynamics. By maximizing the accumulated differential entropies along the trajectory, the proposed method iteratively searches for the most informative action sequence which will yield informative samples when applied to the real system. With random exploration and model-based reinforcement learning as baselines, we verify the superiority of the proposed method via accuracy of one-step and multi-step predictions, the control performance, the exploration efficiency of the state space on numerical benchmarks.

This paper proposes a new type of subspace state-space system identification method for nonlinear dynamical systems, which generates a model consisting of a state estimator and a predictor that can be directly used for model predictive control (MPC). The main feature of the proposed method is that it uses a neural network with a bottleneck layer between the state estimator and predictor to represent the input-output dynamics, and it is proven that the state of the dynamical system can be extracted from the bottleneck layer based on the observability of the target system. The training of the network is shown to be a natural nonlinear extension of the subspace state-space system identification method established for linear dynamical systems. This correspondence provides interpretability and optimality to the resulting model based on linear control theory. The usefulness of the proposed method and the interpretability of the model are demonstrated through an illustrative example of MPC.

This paper proposes a nonlinear system identifi-cation method for constructing models that provide not only point estimates but also distribution. The method is based on a nonlinear system identification method using the concepts of bottleneck structured neural networks and subspace system identification, and further applies the concept of variational autoencoders. The validity of the proposed method is confirmed through numerical examples.

This paper proposes a fault tolerant control (FTC) design with a fault detection (FD) scheme for oscillatory failure cases (OFC) within the framework of “The Joint Airbus-Stellenbosch University Industrial Benchmark.” The FD scheme consists of an observer using “Nonlinear Autoregressive models with eXogenous input” (NARX) model, a signal processing part, and an FD algorithm. The proposed FTC design smoothly switches controllers by adjusting weights according to a sigmoid function using a reconfiguration scheme. The parameters in both schemes are optimized by grid search based on the metrics set to evaluate performance. These schemes have the advantage of the ease of industrial use because they have a simple structure, and parameters can be tuned in a systematic way. Simulation results show that the proposed FD scheme's ability to detect OFC meets the benchmark's prescriptions regardless of the defined turbulence or load factor input. The robustness of the proposed FD scheme was evaluated using a Monte Carlo method by varying the parameters of the actuator model to confirm the limit value of the OFC amplitude that can be robustly detected.

This letter proposes a passivity based integral sliding mode controller for mechanical port-Hamiltonian systems. Recently, passivity based sliding mode control (PBSMC) has been proposed for mechanical and electro-mechanical systems. This method has properties of both sliding mode control (SMC) and passivity based control. However, the robustness of the closed-loop system is not guaranteed in the reaching phase. For this problem, integral sliding mode control (ISMC), which eliminates the reaching phase, has been proposed. This letter proposes a unified control method of passivity based control and integral sliding mode control based on the idea of PBSMC. In order to achieve ISMC in the port-Hamiltonian form, an integral term of the sliding variable of PBSMC is firstly added to the system equation. Next, by adding an appropriate potential function to the Hamiltonian function, the dynamics of ISMC is obtained. The proposed method is more robust than PBSMC and ensures Lyapunov stability even if the resulting feedback controller is replaced by its continuous approximation to alleviate the chattering phenomena. The effectiveness of the proposed method is demonstrated by a numerical example.

Finite impulse response (FIR) models have attracted much attention in system identification in recent years. However, finite impulse response models have many parameters, and it is sometimes difficult to identify them under conditions with limited computational resources. This paper considers a finite impulse response model with a reduced number of parameters. In particular, supposing the purpose of the model is to estimate the unit step response at a given time, it is shown that one of the desirable models for this purpose is a model in which the impulse response values are piecewise constants. The statistical properties of such a piecewise-constant FIR model obtained by system identification are clarified. The usefulness of the proposed method is confirmed through numerical examples.

Usually learning dynamical systems by data-driven methods requires large amount of training data, which may be time consuming and expensive. Active learning, which aims at choosing the most informative samples to make learning more efficient is a promising way to solve this issue. However, actively learning dynamical systems is difficult since it is not possible to arbitrarily sample the state-action space under the constraint of system dynamics. The state-of-the-art methods for actively learning dynamical systems iteratively search for an informative state-action pair by maximizing the differential entropy of the predictive distribution, or iteratively search for a long informative trajectory by maximizing the sum of predictive variances along the trajectory. These methods suffer from low efficiency or high computational complexity and memory demand. To solve these problems, this paper proposes novel and more sample-efficient methods which combine global and local explorations. As the global exploration, the agent searches for a relatively short informative trajectory in the whole state-action space of the dynamical system. Then, as the local exploration, an action sequence is optimized to drive the system’s state towards the initial state of the local informative trajectory found by the global exploration and the agent explores this local informative trajectory. Compared to the state-of-the-art methods, the proposed methods are capable of exploring the state-action space more efficiently, and have much lower computational complexity and memory demand. With the state-of-the-art methods as baselines, the advantages of the proposed methods are verified via various numerical examples.

This paper proposes a new Newton method for solving finite time ℓ 1 -optimal control problems with a boundary condition on the terminal state. In the proposed algorithm, the error between the terminal state and its desired value is described as a nonlinear function of the input sequence. The algorithm then updates the input towards the ℓ 1 -optimal Newton direction to find a root of the nonlinear error function. The resulting root is an ℓ 1 -optimal input sequence satisfying the boundary condition. The advantage of this method is that the error converges at least linearly and at most quadratically in finding an ℓ 1 -optimal feasible solution. Additionally, we propose a continuation based method that relaxes the convergence condition of the proposed algorithm. The applicability of the proposed method is confirmed through a numerical example of transfer orbit generation for a satellite.