With the increasingly prominent role of high-resolution remote sensing data in supporting the digital economy and intelligent industries, on-orbit assembly of large space optical systems has become a critical pathway to overcome launch vehicle constraints and achieve large-aperture detection. However, during on-orbit assembly, the manipulator is required to simultaneously satisfy multiple objectives, including replicating standardized paths, avoiding non-cooperative obstacles, and precisely passing through key waypoints. Existing global methods are limited by the real-time bottleneck of high-dimensional search, while local methods lack global consistency guarantees. Although Dynamic Movement Primitives (DMPs) possess parametric trajectory representation capabilities, they struggle to reconcile the inherent conflict between path shape accuracy and safe obstacle avoidance under multi-objective constraints. Therefore, how to synergistically optimize path passing accuracy and obstacle avoidance safety for manipulators in dynamic, unstructured space environments has become a core challenge constraining the effectiveness of on-orbit autonomous assembly for large-aperture optical systems.
In a recent study published in Space: Science & Technology , the team led by Liu Yinnian from the Shanghai Institute of Technical Physics, Chinese Academy of Sciences, proposed a hierarchical path planning method based on joint optimization of internal and external parameters of Dynamic Movement Primitives. The study employs DMPs to generate global assembly paths as the foundational representation. At the inner level, Policy Improvement with Path Integrals (PI²) is adopted to optimize the shape parameters of DMPs, enabling the manipulator end-effector to precisely pass through predefined assembly waypoints. At the outer level, Model Predictive Control (MPC) is introduced to perform rolling-horizon optimization of the external perturbation terms of DMPs, adjusting obstacle avoidance responses based on the real-time clearance between the end-effector ellipsoidal envelope and obstacle spheres, thereby simultaneously ensuring path passing accuracy and safe avoidance of non-cooperative obstacles. Simulation and Gazebo physical platform experimental results demonstrate that the proposed method achieves minimum obstacle avoidance clearances of 0.078 m and 0.018 m in static and dynamic obstacle scenarios, respectively, with waypoint passing errors as low as 0.006 m. In contrast, the reference path without internal and external parameter optimization collides with both obstacles and already-assembled modules (with minimum clearance reaching negative values), validating the necessity and robustness of the proposed framework. This research provides a structured and scalable path planning solution for on-orbit autonomous assembly of large optical inspection systems, offering significant engineering application value for enhancing the autonomous operation capability of space robotic systems in complex mission environments.
First, this paper focuses on the path planning problem for on-orbit autonomous assembly of large-aperture space optical systems and proposes a hierarchical planning framework based on joint optimization of internal and external parameters of Dynamic Movement Primitives (DMPs). Constrained by launch vehicle capabilities, large-aperture primary mirrors cannot be launched as an integrated whole, making robot-assisted on-orbit assembly a critical pathway to overcome this bottleneck. However, during on-orbit assembly, the manipulator is required to simultaneously satisfy multiple constraints, including replicating standardized paths, avoiding non-cooperative obstacles, and precisely passing through key assembly waypoints. Conventional global methods are limited by the real-time performance bottleneck of high-dimensional search, while local methods lack global consistency. As illustrated in Fig. 1, DMPs model desired motions as spring-damper systems with nonlinear forcing terms, and generate arbitrarily complex-shaped trajectories through the weighted superposition of Gaussian basis functions, providing a structured parametric representation for path planning. Fig. 2 illustrates the distribution of basis functions and the principle of weighted summation, where the trajectory shape can be modulated by adjusting the weight coefficients of different basis functions. The internal parameters of DMPs (such as shape weights, stiffness, and damping) determine the geometric characteristics of the trajectory, while the external parameters (e.g., perturbation terms generated by artificial potential fields) are employed to respond to changes in the external environment. This framework decouples the two objectives—path passing accuracy and obstacle avoidance safety—into two optimization layers, namely the inner and outer layers, providing a clear solution structure for multi-objective coordination.
Second, this paper elaborates on the inner-layer waypoint passing optimization method and its validation results. At the inner level, the study employs the Policy Improvement with Path Integrals (PI²) algorithm to optimize the shape parameter weights of DMPs. By injecting Gaussian noise into the parameter space, multiple candidate trajectories are generated, and the weights are updated through probability-weighted averaging based on the cost function, enabling the end-effector to precisely pass through predefined assembly waypoints. As shown in Fig. 3, after the waypoints deviate from the reference trajectory by a specified distance in three-dimensional space, the absolute position error of the optimized trajectory at the waypoints is only 0.039 m (normalized error of 0.048), demonstrating the effectiveness of the method in driving the DMP trajectory to accurately pass through designated positions. Fig. 4 presents the convergence curve of the cost function during the iterative process of the PI² algorithm; as the number of iterations increases, the combined cost—comprising waypoint deviation and trajectory smoothness—continuously decreases and stabilizes, indicating favorable convergence characteristics of the optimization process. The inner-layer optimization also explicitly incorporates interference constraints between already-assembled and to-be-assembled modules into the cost function, employing an exponential enhancement-type penalty term to reinforce the approximation to assembly waypoints at specific instants. Simultaneously, a gating function is introduced to restrict parameter updates to the vicinity of the waypoints, preventing unnecessary distortion in trajectory segments far from the waypoints, thereby maintaining overall path smoothness while accomplishing critical waypoint passing.
Finally, this paper validates the effectiveness of the outer-layer obstacle avoidance strategy and the joint internal–external optimization approach through simulations and experiments on the Gazebo physical platform. At the outer level, the external perturbation term of DMPs is treated as the control input of Model Predictive Control (MPC). By predicting the future clearance between the end-effector ellipsoidal envelope and obstacle spheres, the scaling factor of the perturbation term is optimized in a rolling-horizon manner, achieving safe avoidance of both static and dynamic obstacles. Fig. 5 presents a comparison of three-dimensional trajectories under joint internal–external optimization: the internal parameters optimized by PI² drive the trajectory to pass through the waypoints indicated by the black dashed line, while the outer-layer MPC, after adjusting the external perturbation, enables the trajectory (red dashed line) to circumvent obstacles while maintaining waypoint passing accuracy—corresponding to different priority requirements, respectively. Fig. 6 shows the combined results of dynamic obstacle avoidance and waypoint passing, where the minimum clearance remains positive as the obstacle moves at a prescribed speed. In the Gazebo physical platform experiments, a UR5 manipulator carrying a hexagonal prism sub-mirror module successfully accomplishes both obstacle avoidance and waypoint assembly under both static and dynamic obstacle environments, with an absolute position error as low as 0.006 m. Fig. 7 compares the clearance curves with and without the optimization strategy; in the reference path without internal–external optimization, the end-effector sub-mirror collides with the obstacle (clearance reaching negative values) and also interferes with already-assembled modules, demonstrating the necessity of the proposed framework. This research provides a structured and scalable path planning solution for on-orbit autonomous assembly of large-aperture optical inspection systems.
Path Planning for Mirror Assembly in Optical Detection Systems:Internal and External Parameter Optimization of Dynamic Movement Primitives
7-Jul-2026