Stable dynamic systems enable robotic systems to plan and execute complex geometric motions in unstructured environments. However, in certain scenarios, such as precision assembly tasks, the constrained operational workspace of robotic arms, along with the presence of obstacles, may lead to unintended collisions. Furthermore, motion precision plays a crucial role in determining the success rate of such tasks. To address these challenges, we propose a novel Safe-Critical Dynamic System (SC-DS) framework. The SC-DS framework consists of a stable dynamic system and an obstacle avoidance controller. The stable dynamic system is formulated in a parametric nonlinear form, which enhances performance in terms of accuracy. Additionally, control barrier functions (CBF), corresponding to complex constraint spaces, are learned from demonstration data. By utilizing these learned CBFs, an obstacle avoidance controller is designed to ensure that the system trajectory remains within the learned safety boundaries. Moreover, the controller adaptively extends the effective range of control inputs, thus mitigating replication errors due to input limitations. Experimental results, both in simulation and with a physical robot, demonstrate that the SC-DS framework effectively reproduces trajectories with both stability and safety, outperforming existing methods in terms of overall task performance.Note to Practitioners—This study is motivated by the need to develop a safer and more precise skill-learning framework for practical applications, such as service robots and assembly robots. We propose the SC-DS framework, which integrates the challenges of uncertain environments into the learning of precise motion skills, ensuring both accuracy and safety in trajectory generation. This framework is particularly suitable for applications requiring strict performance and safety standards. By incorporating safety constraints directly into the learning process, our method provides a robust solution that effectively addresses robot-environment interactions, including obstacles, disturbances, and varying conditions. Our research enhances the reliability of dynamic system-based learning frameworks and offers practical tools for real-world applications, ensuring robots perform tasks efficiently while maintaining safety. Practitioners can leverage this framework to improve safety and maintain high-precision skill learning, ensuring effective handling of real-world challenges.

Imitation learning is an important method for the human-robot skill transfer. However, ensuring that skills learned through imitation remain effective in different environments is a challenge. This article addresses the challenge by proposing a stable autonomous dynamic system that can effectively handle obstacles and disturbances while maintaining trajectory accuracy. We introduce an energy-approximated dynamic subattractor (EADA) method that enhances disturbance resistance by dynamically selecting subattractors through Neum (an energy function derived from demonstration data). By combining velocity modulation algorithms with EADA, the system achieves global stability, precise obstacle avoidance, autonomous trajectory recovery, and rapid response. The proposed framework effectively handles complex scenarios, including environments with multiple obstacles, dynamic obstacles, and disturbances. We validate the proposed approach through simulations on the LASA dataset and real-world robotic experiments (both single-arm and dual-arm robots), demonstrating its effectiveness in achieving smooth and accurate obstacle avoidance trajectories with generalization capability.

Learning an autonomous dynamic system (ADS) encoding human motion rules has been shown as an effective way for human motion skills transfer. However, most existing approaches focus on goal-directed motion skills transfer, and the study on periodic motion skills transfer is rare. One popular approach for periodic motion skills transfer is learning periodic dynamic movement primitive (DMP); however, periodic DMP is sensitive to spatial disturbances due to the introduction of the phase parameters. To solve this issue, this brief presents a novel approach to learn an ADS with a stable limit cycle without introducing phase parameters. First, a data-driven Lyapunov function (energy function) is learned, such that one of its level surfaces is consistent with periodic human demonstration trajectories. Then, an ADS is learned by sequentially solving energy function-related constrained optimization problems. With a proper design of constraint functions, we can ensure that the trajectory generated by the ADS will converge to an energy function-level surface, of which the shape is similar to periodic human demonstration trajectories. Experiments are conducted to show the effectiveness of the proposed approach (PA).

In this article, a hierarchical predictive control (PC) algorithm is designed for visual servoing mobile robot systems. At the kinematic level, the image-based visual servoing model of a wheeled mobile robot is established. By defining the corresponding performance index of the PC, an iterative linear quadratic regulator (iLQR) is used to obtain the velocity controller and to provide reference velocity for dynamics. In dynamics, a data-driven PC controller based on the Gaussian process (GP) is proposed to obtain the torque controller with unknown dynamics. The input-to-state practical stability (ISpS) of the system based on the proposed data-driven PC method is proved by introducing reasonable assumptions. The corresponding theorem also analyzes the maximum upper bound of GP inference error. Finally, the effectiveness of the proposed hierarchical controller is verified by simulations and experiments.

In this paper, using the ball and beam system as an illustration, a control scheme is developed on human-robot collaboration, i.e., a two-level hierarchical framework is proposed to establish a robust human-robot collaboration (HRC) policy. On the high level, a deep reinforcement learning (DRL) algorithm is presented to plan the desired beam rotational velocity. The low level is constructed by a human-intention perception module and a robust collaboration policy design module. For the first module, a probabilistic model is fitted by using the Gaussian process regression (GPR) approach to predict human-hand velocities, and prediction results follow Gaussian distributions where mean values and variances represent predicted human-hand velocities and corresponding prediction confidences, respectively. For the second module, a robust collaboration policy is established by fusing a proactive policy and a conservative policy, where the proactive policy is used to control the robot to achieve the desired beam rotational velocity by using the predicted human-hand velocities. The conservative policy is designed to ensure the collaboration safety. The weighted parameters for fusion are adaptively tuned based on the prediction precision and confidence. Experiments are conducted on controlling ball position on a beam jointly by a human and a robot with vision data, and experimental results show the effectiveness of the designed robust collaboration policy. Note to Practitioners—Predicting human future behaviors and moderating robot behaviors accordingly is a long-standing problem for human-robot collaboration (HRC) tasks, such as assembling, transporting, etc. Existing approaches generally regard human behaviors as noises or only build simple human models without prediction confidence. This paper proposes a learning-based hierarchical framework that will derive a robust and safe HRC policy considering human behaviors, prediction confidence, and task-related optimality. The framework is validated by a representative experiment where human and robot are asked to jointly control a ball and beam system.

Learning a stable autonomous dynamic system (ADS) encoding human motion rules has been shown as an effective way for demonstration learning. However, the stability guarantee may sacrifice the demonstration learning accuracy. This article solves the issue by learning a stability certificate, represented by a neural energy function, on the demonstration set. We propose a polarlike space analysis approach to derive parameter constraints to guarantee the unique-minimum property of the neural energy function, which is essential for it to be a cogent stability certificate. Then, the neural energy function is learned to capture the demonstration preferences via constrained optimization algorithms. With the learned neural energy function, a globally asymptotically stable ADS with predefined position constraint is further formulated. We also quantitatively analyze the generalization ability of the learned ADS by utilizing the substantial flexibility of the neural energy function. The effectiveness of the proposed approach is validated on the LASA dataset and two representative robotic experiments.

This paper proposes a quadratic programming (QP)-based variable impedance control (VIC) algorithm to solve contact-rich trajectory tracking problems with impedance, position and velocity constraints. To the best of our knowledge, the impedance constraints which are significant to ensure the worst contact compliance have never been considered in other previous works. To handle the impedance constraints of the VIC algorithm, a novel impedance model where the impedance parameters are directly served as the control input is established. The impedance-constrained VIC design problem is then formulated as a QP problem which can be efficiently solved. To handle the position and velocity constraints, a complementary force is introduced into the novel impedance model. The complementary force will appear to prevent the constraints violation when the robot approaches the constrained area. The design problem of the complementary force is also transformed into a QP problem. Combing these two QP solutions, the VIC algorithm with both impedance, position and velocity constraints can be obtained. Finally, various experiments are conducted to show the effectiveness of the proposed QP-based constrained VIC algorithm.