# Segmented Hybrid Impedance Control for Hyper-Redundant Space Manipulators
## 1 Introduction  
Space exploration depends on critical operations such as satellite inspection, refueling, repairs, orbital debris removal, and the construction and maintenance of orbital infrastructure. While astronauts have traditionally performed these tasks through spacewalks, such operations are inherently dangerous, requiring extensive planning and preparation. These constraints often make servicing missions prohibitively costly or impractical. Robotic servicing, particularly using hyper-redundant space manipulators (HRSMs), has emerged as a promising alternative due to the enhanced workspace and dexterity compared to traditional manipulators [1, 2, 3]. The historical approach to HRSMs has predominantly focused on developing methodologies to maintain environmental separation during operation. This paradigm is exemplified by [PERSON]'s pioneering work on real-time collision prevention for robotic systems, which introduced the artificial potential field methodology [4]. Further advancements came from [PERSON] and colleagues, who explored tunnel-constrained manipulator configurations through curvature function analysis [5]. The field's theoretical foundation wasenhanced by [PERSON] et al. 's investigation into fractional dynamics' chaotic behavior using the Fourier and wavelet analytical techniques [6]. Contemporary contributions include [PERSON] et al. 's development of synchronized trajectory planning for dual-arm space robotics [7], while [PERSON] et al. introduced a geometric solution to the inverse kinematics challenges in hyper-redundant systems, specifically targeting real-time human-interactive control applications [8]. The emergence of artificial intelligence has catalyzed novel approaches to manipulation and obstacle avoidance, particularly through neural networks and evolutionary computing [9; 10; 11; 12]. Notable recent developments include [PERSON] et al. 's adaptive neural synchronization framework for cooperative manipulation [13] and [PERSON] et al. 's optimization-based approach to space robot trajectory planning, utilizing particle swarm optimization techniques [14]. However, our research reveals a paradigm shift. Controlled interaction between HRSMs and their surroundings can actually enhance operational capabilities rather than limit them. Environmental contact, when properly managed, can provide additional support points and stability, potentially improving the overall precision and load-bearing capacity of the system, as investigated by [PERSON] et al. [15]. This approach is particularly relevant in scenarios where the hyper-redundant structure can leverage its extensive degrees of freedom to distribute the forces across multiple contact points, similar to how biological systems like snakes or tentacles utilize environmental interaction to enhance their mobility and manipulation capabilities. In this context, a hybrid impedance control with an object manipulation controller for HRSMs is developed. Conventional control methods and recent research exhibit significant limitations when managing multiple contact points, as they are primarily designed for single-point contact scenarios. In the dynamic conditions of space operations, single-point contacts often prove insufficient for maintaining stability, leading to potential slippage, imbalance, or unwanted rotations. This limitation becomes particularly critical when intermediate joints inevitably interact with the environment, highlighting the need for more comprehensive control strategies. Multi-point contact systems have emerged as a more robust alternative, offering enhanced stability through even force distribution across objects and providing essential redundancy in grasp stability. Multi-point contact impedance research in space manipulation has predominantly focused on the end-effector morphology. This focus emerged naturally from the challenge of grasping and manipulating objects in space, where end-effector-centric approaches have been highly investigated for both single- and multi-point contact scenarios.