###### Abstract  
This paper studies an adaptive control strategy for a 2-axes gimbal structure loading device for a stair-climbing delivery robot. The properties of the loading device change depending on the luggage, and the loaded luggage cannot be specified. It is difficult to design an appropriate controller with fixed PID gains. To optimize the controller regardless of luggage condition, the adaptive control strategy is conducted by system identification and gain scheduling. The system identification estimates the parameters of the dynamic equations. The gain scheduler optimizes the PID controller using the estimated parameters. The system identification technique is based on the least-squares method. The accuracy of system identification is improved by a null-space solution. The gain scheduler consists of surface functions defined by interpolation of the optimized PID gains. The system identification techniques are verified by simulation, comparing a specific system assumed as a real system and the estimated system. The experiments using the motion platform verify the adaptive control strategy. This proposed control strategy adapts the controller to the system of the loading device. adaptive control; gimbal structure; loading device; system identification; PID gain scheduling Article Adaptive Control Strategy of a 2-Axes Gimbal Structure Loading Device for a Stair-Climbing Delivery Robot. 1  
Agnb  
The dynamic equation of the loading device changes depending on the properties of the luggage such as mass, moments of inertia, or position of the center of gravity. The luggage cannot be specified, and this makes it difficult to design an appropriate controller. The fixed gains or simple gain scheduler can cause the divergence or long settling time. To optimize the controller for the system in real time, the proposed control strategy includes a system identification and a gain scheduler. The system identification estimates the parameters of the dynamic equations with the only movement of the loading box and torque of the motor. The gain scheduler is composed of surface functions of the estimated parameters, and the surface function is made with optimized PID gains. In this paper, the 2-axes gimbal structure loading device is interpreted as two independent pendulum systems. There was various preceding research related to the system identification of a pendulum. A study presented an inverted pendulum system identification using an artificial neural network [1]. Deployed were the Fuzzy T-S identification strategy [2], genetic algorithms [3], and modified practical swarm optimization algorithms [4]. In the other study, the friction coefficient and moment of inertia of the pendulum were identified by the prediction error method [5]. A study proposed the optimization of the controller of a motor for an inverted pendulum with system identification [6]. The proposed system identification technique is based on the least-squares method and estimates unknown parameters of the dynamic equation of the loading device in real-time [7]. At the first, the dynamic equation of the loading device is divided into the known parameters and unknown parameters. The least-squares method-based system identification estimates the unknown parameters by calculating them which minimizes the error function between the motions of a real system and the estimated dynamic equation. The proposed system identification technique can estimate the dynamic equation that produces equal motion with the real loading device in real-time. The technique needs only one IMU and an encoder of the motor without other sensors. However, since the solutions of calculating a dynamic equation are innumerable, the estimated unknown parameters sometimes have large errors. This would be a problem for the gain scheduler that uses the estimated unknown parameters as the variables. The desired solution can be obtained by adding a null-space solution to the general solution. For example, some studies plan the working path of the robot arm with a null-space solution [8; 9].