## 1 Introduction  
The use of drones across a multitude of industries, including military, delivery, monitoring, and agriculture, has become increasingly prevalent in recent years. One significant challenge faced by companies in these sectors is the limited capacity of traditional transportation infrastructure, particularly within urban areas, as the demand for commercial deliveries continues to escalate. In response, drone delivery systems have been proposed as a potential solution to alleviate traffic congestion by taking advantage of the vertical airspace above a city's roadways while also addressing pressing environmental and noise pollution concerns [1]. Companies like Amazon and Google have, therefore, started looking for alternative delivery strategies--for instance, using unmanned aerial vehicles or autonomous drones [2]. In fact, autonomous drone delivery modes are anticipated to play a significant role in the future of the logistics sector, both for the last-mile delivery of small packages and for the delivery of fast food and restaurant meals. Domino's Pizza, in collaboration with the New Zealand start-up Flirtey, has initiated trials for drone delivery services for pizzas and food [3]. Also, delivery robots have been increasingly adopted in various cities worldwide, mainly in response to customers' COVID-19-related concerns about staying at home during lockdowns and the potential risks faced by human delivery personnel during the pandemic [3]. Recently, there has been a growing focus in research on the transportation of loads, which stands out as one of the most prevalent activities carried out with unmanned aerial vehicles [4, 5]. However, to enable widespread drone use,significant changes need to be made to the current delivery-drone technology. For instance, when delivering food items such as pizza or hot syrup, it is crucial to isolate them from vibrations caused by heave, roll, and pitch movements. One solution to this problem is to utilize a stabilizing manipulator with three degrees of freedom (DOFs). Serial manipulators (SMs) and parallel manipulators (PMs) are two primary divisions of robot manipulators. PMs have multiple limbs that share the payload capacity, providing a higher capacity than SMs. Moreover, PMs are better at precise positioning compared to their serial counterparts [6; 7; 8]. Recent studies have focused on developing and studying parallel manipulators for applications such as ship stabilization, wheelchair control, and helicopter landing aboard ships. [PERSON] et al. [9] utilized an inverted 6-DOF parallel manipulator as a stabilizer for any vehicle encountering path-bump variations. PMs with 2R1T motion, namely, two independent rotations and one translation, have been investigated as well. [PERSON] et al. [10] studied the forward kinematics of a 3-SPR (in this paper, P, R, S, and U stand for prismatic, revolute, spherical, and universal joints, respectively) wave compensation counteract mechanism and compared it to the 3-PSR mechanism for marine ships with dynamic positioning systems. [PERSON] et al. [11] proposed a 3-PSR shipboard stabilization platform to mimic the fundamental DOFs of \"roll, pitch, and heave\" for wave replication to support the tethered unmanned aerial vehicles' (UAV) win payloads. [PERSON] et al. [12] studied the kinematics and dynamics of the 3-RRS mechanism for a torque-model-based PD controller to stop a disabled person who is using a typical electric wheelchair from tipping over. [PERSON] et al. [13] developed a mathematical model of the 3-RRS PM and performed position control over the physical model of the PM. [PERSON] et al. [14] proposed a kinematic control of a 3-SRR/SRU 3-DOF PM designed as a stabilization platform for helicopters landing aboard ships safely. Nevertheless, the dynamical model of the 3-SRR/SRU PM was not included in the control approach. Despite its simplicity, proportional-integral-derivative (PID) control is frequently used to control the position and/or orientation of parallel manipulators [15; 16].