Gaussian process regression (GPR) models are becoming increasingly tightly integrated into robotic systems, particularly in the context of robot model predictive control (MPC) operating in complex environments. Because data generated by robots are typically collected online and exhibits heteroscedasticity (i.e., the noise variance depends on the input), traditional GPR may not be suitable. Thus, an incremental heteroscedastic GPR (IHGPR) method is proposed, which takes advantage of incremental sparse spectrum GPR (I-SSGPR) and the framework of improved most likely heteroscedastic GPR (improved MLHGPR). The predictive distribution is not only in an explicit form but also differentiable, rendering a plug-and-play solution for optimization-based control. The efficacy of the proposed approach is demonstrated through a series of empirical evaluation experiments, highlighting its time efficiency and capacity to accurately capture heteroscedastic signals. To illustrate its versatile applicability in robotic system control, we integrate IHGPR into a robust MPC (RMPC) method to online fit the state-and input-dependent heteroscedastic stochastic disturbances and present the applicability and efficiency through simulation results.

Learning from Demonstrations (LfD) methods are applied to transfer human skills to robots from expert demonstrations, enabling them to perform complex tasks. However, existing methods often struggle to handle such long-horizon human skills as cleaning or wiping stains on the surface, which involve multiple periodic and transitional movement primitives. To address this limitation, this paper proposes a novel framework for segmenting, learning, and generalizing multi-periodic human skills, enabling robots to effectively learn different movement primitives and execute these skills in new environments. Specifically, the framework introduces an unsupervised learning method to segment long-horizon human demonstrations into periodic and discrete movement primitives. Further, a novel type of discrete dynamical movement primitives, namely transitional movement primitives, is employed to enhance the fluidity of combining different periodic movement primitives in skills. These primitives collectively form a lightweight state machine during task execution, where state transitions are governed by visual perception, thereby enabling generalization to long-horizon tasks composed of arbitrary numbers of periodic subtasks. To validate the effectiveness of the proposed approach, we conduct extensive experimental evaluations, including step-by-step validation of each method in simulation and the implementation of the entire presented framework in the real world. The results confirm that the proposed framework accurately learns and generalizes multi-periodic human skills, providing a feasible solution for transferring complex multi-periodic demonstrations to robots in practical applications. The project website can be found at: https://nkrobotlab.github.io/LAMPS/

Aerial robots have demonstrated significant potential in suspended cargo transportation, especially in industries such as logistics and food delivery. Due to the underactuated and nonlinear dynamics of the cable-suspended system, directly tracking a given trajectory with a multicopter without modifying its controller often leads to significant payload swing. This compromises the safety and stability of the cargo. To address the aforementioned issue, this paper proposes an online trajectory refinement method for a variable-length cable-suspended aerial transportation robot, independent from the control layer. By incorporating payload swing angle information, the reference trajectory is refined in real-time, effectively suppressing payload oscillations during transportation. Specially, Lyapunov techniques and LaSalle’s invariance theorem are employed to rigorously guarantee the feasibility of the designed trajectory refinement scheme. Finally, hardware experiments are conducted to validate the effectiveness and superiority of the proposed method. The results demonstrate that the refined trajectory not only enables precise positioning of the multicopter, but also effectively suppresses payload oscillations during transportation, significantly enhancing the safety and reliability of the aerial cargo delivery.

Autonomous Aerial Vehicles (AAVs), particularly quadrotors, have gained substantial attention in recent years due to their high agility, substantial convenience, and significant potential in hazardous missions such as military surveillance and disaster relief. This paper focuses on the aerial throwing problem, aiming to develop a time-optimal method for air-dropping cable-suspended payloads. The contributions of the paper are: 1) a fast approach is presented to streamline the quadrotor’s state management by directly mapping and planning at the quadrotor state space (position, velocity, acceleration); 2) a clearly defined initial guess is provided for aerial suspended throwing tasks, which speeds up the planning process. This methodology not only enhances the convenience of quadrotor navigation, but also fosters a more direct and efficient control scheme. The efficacy and feasibility of the proposed method are validated through both numerical simulations and practical experiments, demonstrating the potential for rapid and accurate payload throwing with cable-suspended systems. Note to Practitioners—This study is driven by the need to enhance aerial payload throwing task in hazardous scenarios, such as disaster relief and military surveillance where precision and speed are crucial. While quadrotors serve as agile platforms for such operations, existing methods lack a rapid planning approach that can directly plan at the quadrotor state space (position, velocity, acceleration). Our work introduces a warm start strategy, which significantly hastens the planning process, enabling faster throwing of cable-suspended payloads. Future extensions of this work could focus on integrating adaptive elements that respond to environmental feedback in real-time, thus broadening the practical applicability of the method in real-world conditions.

Landing a quadrotor on a mobile platform moving with various unknown trajectories presents special challenges, including the requirements of fast trajectory planning/replanning, accurate control, and the adaptability for different target trajectories, especially when the platform is non-cooperative. However, previous works either assume the platform moves along a predefined trajectory or decouple planning from control which may cause a delay in tracking. In this work, we integrate planning and control into a unified framework and present an efficient off-policy Meta-Reinforcement Learning (Meta-RL) algorithm that enables a quadrotor (agent) to land on a mobile platform with various unknown trajectories autonomously. In our approach, we disentangle task-specific policy parameters by a separate adapter network to shared low-level parameters and learn a probabilistic encoder to extract common structures across different tasks. Specifically, during meta-training, we sample different trajectories from the task distribution, and then the probabilistic encoder accumulates the necessary statistics from past experience into the latent variables that enable the policy to perform the task. At meta-testing time, when the quadrotor is faced with an unseen trajectory, the latent variables can be sampled according to past interactions between the quadrotor and the mobile platform and held constant during an episode, enabling rapid trajectory-level adaptation. We assume similar tasks share a common low-dimensional structure in the representation of the policy network and the task-specific information is learned in the head of the policy. Accordingly, we further propose a separate adapter net as a supervised learning problem. The adapter net learns the weights of the policy’s output layer for each meta-training task given by the environment interactions from the agent. When adapting to a new task during meta-testing, we fix the shared model layers and predict the head weights for the new task using the trained adapter network. This ensures that the pretrained policy can efficiently adapt to different tasks, which boosts the out-of-distribution performance. Our method can directly control the pitch, roll, yaw angle, and thrust of the quadrotor, yielding a fast response to the trajectory change. Simulation results show the superiority of our method both in success rate and adaptation efficiency over other RL algorithms on meta-testing tasks. The real-world experimental results compared with traditional planning and control algorithms demonstrate the satisfactory performance of our autonomous landing method, especially its robustness in adapting to unknown dynamics.Note to Practitioners—Given the challenge posed by the motion uncertainty when a quadrotor lands on a mobile platform with an unknown trajectory, there hasn’t been a well-established solution, as far as we know. This paper introduces meta-reinforcement learning, incorporating a latent variable encoder to extract common features from training tasks, and designing an adapter network to enhance the ability of policy networks to adapt to new tasks, thereby enhancing the landing performance of the agent. The proposed method demonstrates promising results in both simulation and experiments.

The unmanned aerial manipulator system has shown great application potential in rotor blade repairing, bridge inspection, and goods delivery. Allowing additional alternatives in tasks, dual-arm always provides more flexibility, versatility, and manipulability compared to a single arm. Unfortunately, the inherent defects of unignorable nonlinearities and complex dynamic coupling between the multirotor and the manipulator have limited the practical application of dual-arm aerial manipulator systems. It is noteworthy that the dynamic coupling between the multirotor UAV (unmanned aerial vehicle) and the dual-arm manipulator is much more complicated than the case of the single-arm, and may degrade the control performance significantly as the CoM (center of mass) of the system changes with the movement of the manipulator. To this end, this paper presents a novel control method based on dual-arm movement compensation. Specifically, the kinematic and dynamic model of the system is first established, based on which the force effect of the manipulator exerting on the multirotor UAV is estimated by the disturbance observer and then compensated. By using Lyapunov techniques, it is proven that the error signal can converge asymptotically. As far as we know, this paper presents the first controller design for dual-arm aerial manipulator systems with rigorous stability analysis. Finally, the effectiveness and robustness of the proposed method are verified through a significant number of comparison experiments, and the results of these experiments demonstrate that the proposed method can reduce the positioning error obviously compared to the comparison methods. Taking the PID method as the benchmark for comparison, it is obvious that the proposed method exhibits the greatest reduction in both maximum and average errors compared to the baseline method, indicating superior control precision than the other comparison methods. For the result of the proposed method in$\bm x$-direction, one can find a substantial reduction ranging from 16.69% to 38.57% for the maximum error, and 22.24% to 45.66% for the mean error. Shifting focus to the$\bm y$-direction, the error reduction for the proposed method is even more remarkable, ranging from 68.10% to 81.80% at maximum, and 66.31% to 86.33% for the mean error. As for the$\bm z$-direction, the error reduction by the proposed method remained significant, ranging from 50.67% to 86.38% at maximum, and with a mean error reduction of 33.11% to 80.39%.Note to Practitioners—This paper is motivated by the problem of executing such tasks as load transportation and coordinate manipulation for aerial robots in flight. By integrating the dual-arm manipulator, the flexibility, versatility, and manipulability of the unmanned aerial manipulator system is further extended. However, the uncertain center of mass of the system during operation may badly increase the control difficulty of the dual-arm aerial manipulator system. Moreover, the strong nonlinearity and complex coupling existing between the multirotor and the manipulator also induce urgently solved problems in practical aerial manipulation tasks. To this end, this paper proposes a novel dual-arm movement compensation based control scheme by utilizing an elaborately designed disturbance observer to deal with the unestimated part of disturbance exerting on the multirotor by arm operation. With rigorous theoretical analysis, the convergence of the error signal is proven. Additionally, groups of hardware experiments further verify the effectiveness and robustness of the suggested control method. In future studies, we will improve the autonomy level of the system by integrating onboard sensors.

By utilizing a suspension cable to connect the payload with the quadrotor, transport tasks can be accomplished while preserving the unmanned aerial vehicle’s agility and maneuverability, particularly in environments that are impassable for ground vehicles. Equipping onboard visual sensors and utilizing image-based visual servoing techniques, the application range of aerial transportation systems is poised to be significantly expanded in scenarios like autonomous landing and goods release. Unfortunately, within the system, there exist multiple layers of dynamic couplings between image features, quadrotor rotation, translation, and payload motion. These intricacies give rise to numerous difficulties in achieving smooth anti-swing transportation. To overcome the aforementioned difficulties, this paper presents the first image-based visual servoing control scheme for the aerial transportation system with variable-length cable. Specifically, the image moments defined on the rotated virtual image plane are taken as the image features, whose dynamics is independent of the quadrotor rotational motion. Subsequently, a generalized virtual image feature signal is introduced by organically combining the cable length and payload swing angles with the image feature, which is further exploited in the anti-swing control scheme design. The equilibrium point of the overall closed-loop system is proved to be asymptotically stable through Lyapunov techniques and LaSalle’s Invariance Theorem. Hardware experiments are conducted on a self-built aerial transportation platform to verify the proposed controller’s basic and functional performance in terms of rapid anti-swing and accurate target position and cable length tracking. Note to Practitioners—This paper is motivated by the requirement to improve the autonomy level and payload swing suppression ability of the aerial transportation system through visual servoing techniques. By installing onboard monocular camera and the cable length adjustment mechanism, the application scope of the aerial transportation system can be significantly expanded. However, due to the “double” underactuated characteristic, the visual features couple with both the quadrotor motion and the payload motion, hence, it is quite challenging to realize visual servoing control for cable-suspended aerial transportation systems with simultaneous payload swing suppression and quadrotor positioning. Accounting for the foregoing problems, this paper proposes an image-based visual servoing anti-swing control scheme. With the elaborately constructed generalized virtual image feature signal, the designed controller could improve the anti-swing ability with a completed theoretical analysis. Furthermore, two groups of hardware experiments are conducted to validate the effectiveness of the suggested control method. In future studies, we intend to design more effective control scheme for payload delivery issue with consideration of the visibility of the mobile platform.

Polygonal collision avoidance (PCA) is short for the problem of collision avoidance between two polygons (i.e., polytopes in planar) that own their dynamic equations. This problem suffers the inherent difficulty in dealing with nonsmooth boundaries and recently optimization-defined metrics, such as signed distance field (SDF) and its variants, have been proposed as control barrier functions (CBFs) to tackle PCA problems. In contrast, we propose an optimization-free smooth CBF method in this article, which is computationally efficient and proved to be nonconservative. It is achieved by three main steps: a lower bound of SDF is expressed as a nested Boolean logic composition first, then its smooth approximation is established by applying the latest log-sum-exp method, after which a specified CBF-based safety filter is proposed to address this class of problems. To illustrate its wide applications, the optimization-free smooth CBF method is extended to solve distributed collision avoidance of two underactuated nonholonomic vehicles and drive an underactuated container crane to avoid a moving obstacle, respectively, for which numerical simulations are also performed.

As a low-cost cargo delivery manner, cable-suspended aerial transportation system is highly regarded by researchers. However, existing works seldom consider the relative distance adjustment between the payload and the multirotor, which greatly limits the application scope, such as tunnel traversing or payload releasing. In addition, treating the hook and the payload as a single point mass while ignoring the hook effect results in an inaccurate description of the dynamic model. To address the aforementioned problems, the dynamic model of the variable-length cable-suspended aerial transportation system is established accurately through Lagrange's equation with consideration of the motion of the multirotor, the payload, and the hook. Subsequently, an adaptive control method is presented through energy-based analysis, and swing angle related fuzzy rules are established to dynamically adjust the control parameters, which can simultaneously achieve multirotor positioning, payload hoisting/lowering, and hook/payload swing suppression. Moreover, the cable length is constrained within a feasible range by an elaborately designed auxiliary control signal. Lyapunov techniques and LaSalle's invariance theorem are utilized to prove the asymptotic convergence of the closed-loop system. Finally, a series of simulations are conducted to verify the control performance of the designed method.

With excellent maneuver performance and flexibility, quadrotor unmanned aerial vehicles (UAVs) are widely used in aerial transportation. However, the aerial transportation system with dual quadrotors exhibits high degrees of freedom, strong nonlinearities, and complex state couplings, which makes it more difficult to realize simultaneous quadrotor positioning and cargo swing suppression. Compared with the traditional description of cargo swing dynamics with four angles in the previous work, the spatial swing angle is introduced in a more intuitive way to reflect the swing dynamics of the cargo. On this basis, the dynamic model of the system is established according to Lagrange's equations. Then, a nonlinear adaptive controller is proposed, in which a dynamic compensation term is introduced to compensate for the lateral forces along the cables, and a spatial swing angle-related term is designed to enhance cargo swing damping. Meanwhile, considering the influence of unknown air resistance on quadrotors and cargo during transportation, an adaptive term is applied. Subsequently, Lyapunov techniques and LaSalle's invariance principle are used to prove the stability of the closed-loop system. Finally, based on the self-built general experimental platform, both indoor and outdoor experiments have been carried out to validate the practicability and effectiveness of the proposed method.

Recently, it is becoming increasingly possible to apply aerial transportation systems to real-world applications. However, current research works on cable-suspended transportation systems present practical limitations due to the fixed-length cable. With the introduction of the cable adjustment mechanism, various complicated tasks, such as limited space crossing, offshore sample collection, and even landing the payload on a mobile platform, can be accomplished by actively changing the distance between the quadrotor and the payload. In order to complete the aforementioned tasks, a trajectory tracking control method is in urgent need for the variable-length-cable-suspended aerial transportation systems. To this end, an adaptive tracking control approach with the consideration of unknown resistance coefficients is designed in this article. Subsequently, Lyapunov techniques and Barbalat's Lemma are utilized to prove the convergence for the equilibrium point of the closed-loop system. Finally, hardware experiments are meticulously conducted based on a self-built experimental platform, which verify the satisfactory performance of the proposed method in antiswing aerial transportation and payload landing onto the mobile platform.

The aerial transportation system is a kind of nonlinear underactuated mechatronic system, which suspends the cargo beneath the rotorcraft’s fuselage and undertakes two basic missions of rotorcraft positioning and cargo swing suppression. Currently, most available methods need simplifications such as the near hovering hypothesis and dimension reduction operations, which may badly degrade the control performance when state variables get far away from the equilibrium point. In addition, integral terms, which can eliminate the steady errors, are not reflected in controller design and stability analysis processes. To tackle the aforementioned issues, this article provides a novel nonlinear control approach with an elaborately constructed integral term for aerial transportation systems, which not only achieves satisfactory antiswing and positioning performance but also reduces steady errors in practical flight. Meanwhile, the actuating constraint is taken into consideration so as to avoid saturation problems. Without linearization operations, we prove the closed-loop asymptotic stability of the equilibrium by the explicit Lyapunov-based analysis. As far as we know, this article is the first solution for controller design with the consideration of both steady errors elimination and actuating constraints. Finally, several groups of hardware experimental results are provided to validate the effectiveness of the presented control scheme.Note to Practitioners—This article is motivated by the requirement of effective control schemes for aerial transportation systems. The unexpected cargo swing motion may lead to safety accidents; thus, the dual objective of swing suppression and rotorcraft positioning is the focus of research. Nevertheless, with underactuated property, the cargo swing motion cannot be directly controlled. Up until now, at the cost of model accuracy, most existing methods utilize the simplified models in near hovering state or 2-D transverse plane to reduce the control difficulty. Accounting for the foregoing problems, this article presents a novel control scheme with improved antiswing and positioning performance. With an elaborately constructed integral term, the designed controller could improve the positioning accuracy of the rotorcraft with the guaranteed theoretical analysis. Moreover, to avoid the problem of actuator saturation, the control inputs are restricted in allowable ranges during the transportation process. All these aspects are verified by rigorous theoretical analysis and groups of hardware experiments in different conditions. In future studies, we will apply the suggested control scheme in practical applications.

Rotorcrafts, with satisfactory maneuver performance and ability under complex terrains unreachable for ground robots, are playing important roles for goods transportation. In this article, we focus on the control of the cable-suspended transportation way due to its lower costs and more agility of the rotorcraft's rotational motion. Compared with traditional crane systems and single rotorcrafts without loads, the aerial transportation system presents “double” underactuated property, stronger system nonlinearity, and more complex dynamic coupling, which are huge challenges for control schemes design. Meanwhile, aerial transportation usually suffers from external disturbances and uncertainties presented with aerodynamic damping coefficients and rope length. Additionally, overshoots of the rotorcraft's position are potential threats for flight safety, especially in confined and complex environments. To address these problems, a novel adaptive control scheme is designed, which ensures effective rotorcraft positioning and payload swing suppression with restricted overshoot amplitudes. Asymptotic results are obtained with rigorous theoretical derivations provided by the Lyapunov-based stability analysis and LaSalle's invariance theorem. Real-time experiments are performed to validate the effectiveness of the proposed control scheme even in the presence of external disturbances. To the best of our knowledge, this is the first method designed for aerial transportation systems which achieves simultaneous rotorcraft positioning and swing suppression, together with insurance for overshoot restriction even in the presence of parametric uncertainties.

To meet real-world production demands, two or more cranes are used to cooperatively complete transportation tasks. Dual boom cranes (DBCs) are widely used in large construction sites owing to their strong load capacity. However, for typical nonlinear underactuated multi-crane systems, most of the existing control methods focus on the overhead crane systems with simpler dynamic characteristics and not enough attentions are paid to DBCs with stronger coupling and more complex dynamics. Based on the existing model, geometric constraints are analyzed to obtain the relationship between the higher-order derivatives of state variables, which can simplify the dynamic model of DBCs reasonably. The dynamic relationship between the boom pitch angles and the payload attitude is analyzed accurately. Moreover, the oscillation period of DBCs is obtained, and an extra insensitive input shaper is designed by rigorous mathematical derivation. Finally, simulation results verify that the input shaping control method has a satisfactory anti-swing ability and can realize accurate positioning.