本論文旨在使用本實驗室先前所設計之雙足機器人的控制系統架構、力量感測器與姿態感測器，實現雙足機器人之步態規劃。在機器人步態規劃方面，利用擺線輪廓曲線法和一個三次多項式為基礎規劃機器人的步態，且藉由MATLAB和anyKode Marilou軟體輔助模擬和驗證；在實作方面，在馬達控制迴路裡增加電流回授，使馬達具穩定的輸出力矩。在感測器部分，利用力量感測器量測機器人行走時的零力矩點，以確認步態規劃的可行性；利用姿態感測器量測機器人行走姿態，得到雙足機器人的動態姿態以供給日後回授之用。在論文中，吾人整合工業電腦PC104/+與數位訊號處理器TMS320F2812完成雙足機器人步態規劃之實現。使用PC/104+做為主控制器，以CAN為通訊介面對數位訊號處理器下達馬達控制命令，以完成各關節之角度控制，並以力量感測器系統與姿態感測器完成感測訊號的量測。

SUMMARY
The aim of this thesis is to use the control system, force sensors and attitude sensor on a previously built bipedal robot to design and realize the gait pattern planning. Gait pattern planning is based on the cycloidal profile and a cubic equation. It is simulated by MATLAB and verified through a robotic simulator, anyKode Marilou. In implementation, a current feedback in the motor control loop is added to improve the output torque response of the motor. The force sensors are used to measure the zero moment point to confirm the feasibility of the gait pattern. The attitude sensor is used to measure the walking robot’s gesture to provide a feedback signal for the future use. In this system, an industrial PC PC/104 + and digital signal processors are integrated for the control of the robot gait pattern planning. The PC/104+ is the main controller and a CAN bus communication interface is used to give the control command to each digital signal processor to control the motor. The force sensors and attitude sensor are used to measure states of the robot during control.
Keywords: Biped robot; gait pattern planning

INTRODUCTION
Research of biped robots has been developed for a long time. The robot’s walking can be classified into two methods, dynamic walking and static walking. The different between these two methods is dependent on the ground projection of CoM(Center of Mass). It is said in [1] “ When a human stands on the ground, the ZMP(Zero Momentum Point) coincides with the ground projection of CoM and the foot support polygon. On the other hand, when a human moves dynamically, the ground projection of CoM may exists outside the foot support polygon. However, the ZMP never exists outside the support polygon.” Because of this concept, most of researcher used the ZMP method in walking. Although the ZMP never exists outside the support polygon, the robot may fall down because of the unstable area in the foot support polygon. If the ZMP exists at the edge of foot support polygon which is the unstable area, the robot will rotate about the point. So, the main purpose of the ZMP method is to keep the ZMP inside the stable area. In this thesis, biped robot’s locomotion is based on the cycloidal profile and a cubic equation. The gait pattern planning method will introduce later. In addition to gait planning, we need to know if the ZMP is inside the foot support polygon. In order to make the robot walk stably, we have to make sure the ZMP always stays in the stable area. There are two ways to sense the ZMP which will be discussed later.
MATERIALS AND METHODS
In gait pattern planning, we can divide it into two parts, forward stepping and CoM lateral transferring. First part, forward stepping is based on a cycloidal profile to determine the robot’s foot stepping forward trajectory. To do so, the foot stepping forward trajectory is determined as shown in Figure 1.

Figure 1 Foot forward stepping trajectory.
The equation of the trajectory can be expressed by
.
(1 1)

As shown in this equation, we only need to decide the distance of a foot step and a period time of a step, and then we can get the foot forward stepping trajectory. The trajectory of the foot upward raising is determined as shown in Figure 2.

Figure 2 Foot upward raising trajectory.
The equation of the trajectory can be expressed by

(1 2)

As shown in this equation, we only need to decide the height of a foot step and a period time of a step, and then we can get the foot upward raising trajectory.
Secondly, CoM lateral transferring is based on a cubic equation. Before the robot stepping forward, the robot must transfer its CoM to the other foot to keep the robot standing. Therefore, a smooth trajectory is used to be the CoM lateral transferring equation which can be expressed by
.
(1 3)

Then we combine these two parts to be the one step gait pattern of the robot as shown in Figure 3.

Figure 3 One step gait pattern.
Based on this method, we designed a complete 21-second gait pattern as shown in Figure 4.
Figure 4 21-second gait pattern.

RESULTS AND DISCUSSION
After gait pattern planning, we used inverse kinematic to calculate the angle of each joint, and calculate the ZMP to make sure if the gait pattern planning is appropriate. In this thesis, the ZMP is obtained by an inertial measurement unit in simulation. According to [1], we only need the robot’s acceleration to calculate the ZMP of the robot on a rigid ground. The equation of computing the ZMP in [1] is expressed by

(1 4)

(1 5)
The result of the ZMP calculation is shown in Figure 5. As shown in Figure 5, we can see the square is the robot’s foot, and the blue line is the ZMP trajectory. The ZMP trajectory is always inside the foot support polygon, so the gait pattern is appropriate.

Figure 5 The result of the ZMP calculation.

CONCLUSION
This thesis used the cycloidal profile and a cubic equation to design the gait pattern of the bipedal robot. In gait pattern planning, the rotation angle of each joint was calculated by inverse kinematic, simulated by MATLAB, and robotic simulator, anyKode Marilou, to verify the gait pattern planning. In this system, the industrial PC PC/104 + was the main controller and the digital signal processor was the motor controller. The communication between main controller and motor controllers used a CAN bus interface to give the control command to each digital signal processor to control the motor and realize the gait pattern planning.
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