This paper presents a control framework designed to enhance the stability and robustness of legged robots in the presence of uncertainties, including model uncertainties, external disturbances, and faults. The framework enables the full-state feedback estimator to estimate and compensate for uncertainties in the whole-body dynamics of the legged robots. First, we propose a novel moving horizon extended state observer (MH-ESO) to estimate uncertainties and mitigate noise in legged systems, which can be integrated into the framework for disturbance compensation. Second, we introduce a three-level whole-body disturbance rejection control framework (T-WB-DRC). Unlike the previous two-level approach, this three-level framework considers both the plan based on whole-body dynamics without uncertainties and the plan based on dynamics with uncertainties, significantly improving payload transportation, external disturbance rejection, and fault tolerance. Third, simulations of both humanoid and quadruped robots in the Gazebo simulator demonstrate the effectiveness and versatility of T-WB-DRC. Finally, extensive experimental trials on a quadruped robot validate the robustness and stability of the system when using T-WB-DRC under various disturbance conditions.

This paper proposes a novel tube-based geometric model predictive control (GMPC) framework on Lie groups for robust and real-time trajectory tracking control of robot manipulators under uncertainties. The proposed method directly computes joint torques from task-space error dynamics, eliminating inverse kinematics and ensuring efficient torque-level control. To guarantee constraint satisfaction and robustness, the tube-based GMPC is formulated to constrain the actual system trajectory within a bounded tube surrounding the nominal path, ensuring both feasibility and input-to-state stability. A disturbance observer is employed to estimate external disturbances, while a weighted whole-body controller is integrated to enhance disturbance rejection and increase the control frequency. The effectiveness of the proposed algorithm is validated through numerical simulation and experimental studies using an industrial robot manipulator. The comparative results demonstrate the stability and robustness of the proposed scheme in manipulator trajectory tracking control.

In this article, we address the problem of prescribed-time distributed convex optimization (DCO) for a class of networked Euler-Lagrange systems (NELSs) operating over undirected connected graphs. By utilizing position-dependent measured gradient values of local objective functions and facilitating local information exchanges among neighboring agents, we construct a set of auxiliary systems that collaboratively seek the optimal solution. The prescribed-time DCO problem is then reformulated as a prescribed-time stabilization challenge of an interconnected error system. We propose a prescribed-time small-gain criterion to characterize the prescribed-time stabilization of the system, presenting a novel approach that enhances effectiveness beyond existing asymptotic or finite-time stabilization methods for interconnected systems. Based on this criterion and the auxiliary systems, we design innovative adaptive prescribed-time local tracking controllers for the subsystems. The prescribed-time convergence is achieved through the introduction of time-varying gains that increase to infinity as time approaches the prescribed deadline. The Lyapunov function, along with prescribed-time mapping, is employed to establish the prescribed-time stability of the closed-loop system and the boundedness of internal signals. Finally, the theoretical results are validated through a numerical example.

This paper presents a robust monocular visual SLAM system that simultaneously utilizes point, line, and vanishing point features for accurate camera pose estimation and mapping. To address the critical challenge of achieving reliable localization in low-texture environments, where traditional point-based systems often fail due to insufficient visual features, we introduce a novel approach leveraging Global Primitives structural information to improve the system’s robustness and accuracy performance. Our key innovation lies in constructing vanishing points from line features and proposing a weighted fusion strategy to build Global Primitives in the world coordinate system. This strategy associates multiple frames with non-overlapping regions and formulates a multi-frame reprojection error optimization, significantly improving tracking accuracy in texture-scarce scenarios. Evaluations on various datasets show that our system outperforms state-of-the-art methods in trajectory precision, particularly in challenging environments.

In this paper, we propose a prescribed-time synchronization (PTS) algorithm for networked Euler-Lagrange systems subjected to external disturbances. Notably, the system matrix and the state of the leader agent are not accessible to all agents. The algorithm consists of distributed prescribed-time observers and local prescribed-time tracking controllers, dividing the PTS problem into prescribed-time convergence of distributed estimation errors and local tracking errors. Unlike most existing prescribed-time control methods, which achieve prescribed-time convergence by introducing specific time-varying gains and adjusting feedback values, we establish a class of${\mathcal {K}}_{T}$functions and incorporate them into comparison functions to represent time-varying gains. By analyzing the properties of class${\mathcal {K}}_{T}$and comparison functions, we ensure the prescribed-time convergence of distributed estimation errors and local tracking errors, as well as the uniform boundedness of internal signals in the closed-loop systems. External disturbances are handled and dominated by the time-varying gains that tend to infinity as time approaches the prescribed time, while the control signal is still guaranteed to be bounded. Finally, a numerical example and a practical experiment demonstrate the effectiveness and innovation of the algorithm. Note to Practitioners—This paper aims to address the issue of prescribed-time synchronization for networked Euler-Lagrange systems. Existing research on asymptotic and finite-time convergence reveals that the settling time for synchronization is significantly influenced by the system’s initial values and controller parameters, making it challenging to be freely pre-designed. In contrast, our proposed prescribed-time synchronization algorithm ensures that all Euler-Lagrange systems achieve synchronization within a prescribed time. The effectiveness of our algorithm has been validated through numerical simulations and physical experiments. In practical applications, our algorithm can be utilized for cooperative control in robotic manipulators and drones. Compared to traditional PD controllers, our proposed algorithm not only offers the advantage of arbitrary settling time configuration in cooperation but also ensures faster response speeds and higher control accuracy, owing to the incorporation of time-varying gains.

This paper investigates the prescribed-time cooperative output regulation (PTCOR) for a class of linear heterogeneous multi-agent systems (MASs) under directed communication graphs. As a special case of PTCOR, the necessary and sufficient condition for prescribed-time output regulation of an individual system is first explored, whereas only sufficient conditions are developed in the literature. A PTCOR algorithm is subsequently developed, composed of prescribed-time distributed observers, local state observers, and tracking controllers, utilizing a distributed feedforward method. This approach converts the PTCOR problem into the prescribed-time stabilization problem of a cascaded subsystem. The criterion for the prescribed-time stabilization of the cascaded system is proposed, differing from that of traditional asymptotic or finite-time stabilization of a cascaded system. It is proven that the regulated outputs converge to zero within a prescribed time and remain at zero afterward, while all internal signals in the closed-loop MASs are uniformly bounded. Finally, the theoretical results are validated through two numerical examples.

This article addresses the distributed prescribed-time convex optimization (DPTCO) problem for high-order nonlinear multiagent systems (MASs) under undirected connected graphs. A cascade design framework is proposed that divides the DPTCO implementation into distributed optimal trajectory generator design and local reference trajectory tracking controller design. The DPTCO problem is then transformed into the prescribed-time stabilization problem of a cascaded system. Using changing Lyapunov functions and time-varying state transformations with sufficient conditions, we establish criteria for prescribed-time stabilization and prove the boundedness of internal signals in closed-loop MASs. The framework addresses robust DPTCO for chain-integrator MASs with disturbances through the introduction of novel sliding-mode variables and time-varying gains. It also solves adaptive DPTCO for strict-feedback MASs with parameter uncertainty via backstepping method and descending power state transformation. Two numerical examples verify the theoretical results.

Load forecasting is critical to the task of energy management in power systems, for example, balancing supply and demand and minimizing energy transaction costs. There are many approaches used for load forecasting such as the support vector regression (SVR), the autoregressive integrated moving average (ARIMA), and neural networks, but most of these methods focus on single-step load forecasting, whereas multistep load forecasting can provide better insights for optimizing the energy resource allocation and assisting the decision-making process. In this work, a novel sequence-to-sequence (Seq2Seq)-based deep learning model based on a time series decomposition strategy for multistep load forecasting is proposed. The model consists of a series of basic blocks, each of which includes one encoder and two decoders; and all basic blocks are connected by residuals. In the inner of each basic block, the encoder is realized by temporal convolution network (TCN) for its benefit of parallel computing, and the decoder is implemented by long short-term memory (LSTM) neural network to predict and estimate time series. During the forecasting process, each basic block is forecasted individually. The final forecasted result is the aggregation of the predicted results in all basic blocks. Several cases within multiple real-world datasets are conducted to evaluate the performance of the proposed model. The results demonstrate that the proposed model achieves the best accuracy compared with several benchmark models.

In this article, an optimal surrounding control algorithm is proposed for multiple unmanned surface vessels (USVs), in which actor-critic reinforcement learning (RL) is utilized to optimize the merging process. Specifically, the multiple-USV optimal surrounding control problem is first transformed into the Hamilton-Jacobi-Bellman (HJB) equation, which is difficult to solve due to its nonlinearity. An adaptive actor-critic RL control paradigm is then proposed to obtain the optimal surround strategy, wherein the Bellman residual error is utilized to construct the network update laws. Particularly, a virtual controller representing intermediate transitions and an actual controller operating on a dynamics model are employed as surrounding control solutions for second-order USVs; thus, optimal surrounding control of the USVs is guaranteed. In addition, the stability of the proposed controller is analyzed by means of Lyapunov theory functions. Finally, numerical simulation results demonstrate that the proposed actor-critic RL-based surrounding controller can achieve the surrounding objective while optimizing the evolution process and obtains 9.76% and 20.85% reduction in trajectory length and energy consumption compared with the existing controller.

This article aims to propose a general control strategy for coordination of multiple nonholonomic agents in three dimensional space. For real-world applications, since the field sensor equipped on the mobile agents for local information detection and estimation has some limited detecting range, it is necessary to guarantee that the nearby agents must stay within this range of the onboard sensor. This is called sensory connectivity maintenance. A function termed as coordination function with sensory connectivity maintenance (CFSCM) is defined to describe the performances of the coordination as well as the sensory connectivity status between the agents. Then, a general control strategy is designed based on the proposed CFSCM for spatial coordination of multiple nonholonomic agents with sensory connectivity maintenance. Moreover, the applications of the proposed control strategy for formation with omnidirectional sensors and flocking with directional sensors are shown, respectively. Finally, some numerical examples are conducted to validate the theoretical analysis.

Safe corridor-based Trajectory Optimization (TO) presents an appealing approach for collision-free path planning of autonomous robots, because its convex formulation can guarantee global optimality. The safe corridor is constructed based on the obstacle map, however, the non-ideal perception induces uncertainty, which is rarely considered in the context of trajectory generation. In this paper, we propose Distributionally Robust Safe Corridor Constraints (DRSCCs) to consider the uncertainty of the safe corridor. Then, we integrate DRSCCs into the trajectory optimization framework using Bernstein basis polynomials. Theoretically, we rigorously prove that the proposed trajectory optimization problem is equivalent to a convex quadratic program, which is computationally efficient to deploy onto real robots. The simulation results show that our method enhances navigation safety by significantly reducing the infeasible motions compared to the baseline. Moreover, the proposed approach is validated through two robotic applications, a micro Unmanned Aerial Vehicle (UAV) and a quadruped robot Unitree A1.

This paper presents a collaborative quadrotor-quadruped robot system for the manipulation of a cable-towed payload. In particular, we aim to solve the challenge from the unknown dynamics of the cable-towed payload. To this end, we first propose novel dynamic models for both the quadrotor and the quadruped robot, taking into account the nonlinear robot dynamics and the uncertainties associated with the cable-towed load. Moreover, we design observers for the hybrid interaction between the robots and the payload. Theoretically, the convergence of these observers is analyzed using Lyapunov functions under mild technical assumptions. Finally, we seamlessly integrate the dynamics models and the observers into a distributed Model Predictive Control (MPC) framework with kinematics limitations and collision avoidance constraints. The proposed system is validated through challenging field experiments in indoor and outdoor environments, involving push disturbances, varying and unknown payloads, uneven terrains, etc.

In this paper, we propose a reactive planning system for quadruped robots based on prescribed-time control. The navigation of the quadruped robot is fundamentally depicted as omnidirectional movements, while a feedback control law is formulated to address any deviations the robot may encounter. In particular, our proposed feedback control system is theoretically proven to achieve convergence within a predefined finite time that is specified by the user. To further compute the optimal convergent time and the local goal state, we present a high-level planning node encompassing terrain-aware kinodynamic search and spatiotemporal trajectory optimization, which can generate collision-free, smooth, and efficient trajectories. The effectiveness of our proposed framework is validated through both numerical simulation and real-robot experiments in indoor and outdoor environments, including scenarios with cluttered obstacles, slopes, and external disturbances.

This paper presents a Kalman filter based LiDAR-Inertial-Leg Odometry (KLILO) system for legged robots to navigate in challenging environments. In particular, we employ the iterated error-state extended Kalman filter framework on manifolds to fuse measurements from the inertial measurement unit (IMU), LiDAR, joint encoders, and contact force sensors in a tightly coupled manner. To assess the performance of KLILO, we build a dataset that encompasses intricate environments with challenging conditions such as dynamic objects and deformable terrains. The results demonstrate that our algorithm can provide efficient and reliable localization in all tests. It exhibits an average improvement of around 40% in positioning accuracy compared to the baselines. Furthermore, we validate KLILO in a challenging navigation task on a real robot, where the LiDAR encounters ineffective measurements.

Quadruped robots demonstrate robust and agile movements in various terrains; however, their navigation autonomy is still insufficient. One of the challenges is that the motion capabilities of the quadruped robot are anisotropic along different directions, which significantly affects the safety of quadruped robot navigation. This paper proposes a navigation framework that takes into account the motion anisotropy of quadruped robots including kinodynamic trajectory generation, nonlinear trajectory optimization, and nonlinear model predictive control. In simulation and real robot tests, we demonstrate that our motion-anisotropy-aware navigation framework could: (1) generate more efficient trajectories and realize more agile quadruped navigation; (2) significantly improve the navigation safety in challenging scenarios. The implementation is realized as an open-source package at https://github.com/ZWT006/agile_navigation.

Calibrating unknown transformation relationships is an essential task for multirobot cooperative systems. Traditional linear methods are inadequate to decouple and simultaneously solve the unknown matrices due to their intercoupling. This article proposes a novel dual-robot accurate calibration method that uses convex optimization and Lie derivative to solve the dual-robot calibration problem simultaneously. The key idea is that a convex optimization model based on dual-robot transformation chain is established using Lie representation of special Euclidean group in 3 dimensions [SE(3)]. The Jacobian matrix of the established optimization model is explicitly derived using the corresponding Lie derivative ofSE(3). To balance the influence of the magnitudes of the rotational and translational optimization variables, a weight coefficient is defined. Due to the closure and smoothness of Lie group, the optimization model can be solved simultaneously using Newton-like iterative methods without additional orthogonalization processing. The performance of the proposed method is verified through simulation and actual calibration experiments. The results show that the proposed method outperforms the previous calibration methods in terms of accuracy and stability. The actual experiments are used to compare the proposed method with two existing calibration methods, and the mean measurement error of a certified ceramic sphere is reduced from 0.9205 and 0.5363 to 0.4381 mm, respectively.

In this paper, we present a fully distributed framework for multiple quadruped robots in environments with obstacles. Our approach utilizes Model Predictive Control (MPC) and multi-robot consensus protocol to obtain the distributed control law. It ensures that all the robots are able to avoid obstacles, navigate to the desired positions, and meanwhile synchronize the gaits. In particular, via MPC and consensus, the robots compute the optimal trajectory and the contact profile of the legs. Then an MPC-based locomotion controller is implemented to achieve the gait, stabilize the locomotion and track the desired trajectory. We present experiments in simulation and with three real quadruped robots in an environment with a static obstacle.

This article considers quadruped locomotion control in the presence of uncertainties. Two types of structured uncertainties are considered, namely, uncertain friction constraints and uncertain model dynamics. Then, a min-max optimization model is formulated based on robust optimization, and a robust min-max model predictive controller is proposed by recurrently solving the optimization model. We prove that the min-max optimization model is equivalent to a convex quadratic constrained quadratic program by exploiting the structure of uncertainties. Moreover, a two-stage optimization algorithm is proposed to solve the optimization problem efficiently, allowing for the deployment of the controller onto the real robot. The results show that the proposed optimization algorithm can improve solving frequency by$\sim$11× compared with Gurobi. The proposed controller is able to stabilize quadruped locomotion in challenging scenarios where the uncertainties are caused by significant disturbances and unknown environments.

Four-legged animals are able to change their gaits adaptively for lower energy consumption. However, designing a robust controller for their robot counterparts with multi-modal locomotion remains challenging. In this paper, we present a hierarchical control framework that decomposes this challenge into two kinds of problems: high-level decision-making for gait selection and robust low-level control in complex application environments. For gait transitions, we use reinforcement learning (RL) to design a gait policy that selects the optimal gaits in different environments. After the gait is decided, model predictive control (MPC) is applied to implement the desired gait. To improve the robustness of the locomotion, a model adaptation policy is developed to optimize the input parameters of our MPC controller adaptively. The control framework is first trained and tested in simulation, and then it is applied directly to a quadruped robot in real without any fine-tuning. We show that our control framework is more energy efficient by choosing different gaits and is more robust by adjusting model parameters compared to baseline controllers.

This paper is concerned with the fixed-time cooperative relay tracking control problem for a set of planar agents in a surveillance network. The plane is partitioned into multiple “capture regions” by using the Voronoi partition according to agents' positions. Once an evader enters into a new capture region, one agent of the tracer team stops and the tracking mission is relayed to another one who is in charge of the new region. As a result, an impulsive model is proposed to describe the problem and a distributed fixed-time cooperative relay control strategy is provided that is not dependent on initial condition. Numerical simulations are provided to demonstrate the validness of the cooperative relay tracking scheme.