## 1 Introduction  
Conventional serial robots typically consist of multiple rigid links interconnected by actuated joints. Most commercially available models in three-dimensional space offer four to seven degrees of freedom. However, these traditional robots often struggle to perform tasks in narrow or confined areas, which limits their use in certain industries and impacts their commercial viability. Hyper-redundant robots, also known as snake robots, have attracted growing attention for their ability to maneuver around obstacles in confined spaces [1]. Over the past few decades, extensive research has produced numerous configurations and mechanisms for diverse applications, including search-and-rescue operations [2; 3; 4; 5; 6], maintenance tasks, and minimally invasive medical procedures [7; 8; 9; 10]. Their lightweight design, associated with continuum robots, also makes them potential candidates for planetary exploration and space satellite maintenance [11; 12; 13]. Despite their advantages, the high dimensionality of highly redundant serial robots makes controlling and planning motion challenging. In previous works, we introduced two innovative designs to address the complexities associated with the kinematics, actuation and dynamic modeling of these robots. The first was a minimally actuated reconfigurable track robot [14], which simplified kinematics and actuation. The second was the minimally actuated serial robot (MASR) [15; 16], featuring a serial robot with a mobile actuator (MA) that traversed its links to rotate its joints. The MASR combined the advantages of minimally actuated and hyper-redundant robots by offering enhanced reliability, reduced weight, lower costs, increased modularity, and simplified modeling due to its kinematic chain properties. These robots are particularly well-suited for applications where low weight is prioritized over high speed, such as in space exploration and agriculture. Despite these advances, the design of the 3D MASR presented unresolved challenges, particularly concerning its kinematics. One key issue remained the determination of an optimal solution for the MASR's specific inverse kinematics (IK) problem, which involves finding an IK solution for the desired gripper position in Euclidean space by optimizing the MA's movement to activate the joints and sequentially determine the final position. IK methods are generally divided into analytical and numerical approaches. While analytical methods offer closed-form solutions, they are often impractical for complex and redundant robots like the 3D MASR [17]. Numerical methods, typically based on least squares and gradient descent, apply to a broader range of kinematic chains [18], but they suffer from inconsistent convergence rates and are highly dependent on the initial guess. Over time, various data-driven learning methods have been investigated to tackle complex IK challenges [19]. Notably, neural networks (NNs) can manage intricate kinematic systems and deliver real-time predictions [20; 21; 22]. However, these data-driven IK techniques are designed specifically for traditional manipulators. To respond to these issues, we present an upgraded 3D MASR robot with several mechanical enhancements. The new arm supports 3D movement through a rotating work-plane joint and features a unique prismatic joint, both of which utilize high-torque, precise worm gears. These improvements enhance the robot's strength, functionality, speed, reliability, and accuracy. In addition, the MA now includes a gripper, thus allowing for seamless object translation along the links without requiring arm rotation.