# Fuzzy Logic-Based Controller for Bipedal Robot
## 4 The IDPD, IDPID Controller for Bipedal Robot  
As shown, the bipedal robot was an underactuated system having seven generalized coordinates, of which six were controllable joint coordinates. The non-driven coordinate \(\theta_{1}\) was related to the robot's relative equilibrium condition. The relative equilibrium condition was guaranteed if \(\theta_{1}\) remained unchanged or changed within a range such that the robot was still moving along the designed trajectory. The robot lost its relative equilibrium if \(\theta_{1}\) changed greatly, leading to the robot falling or completely deviating from the designed trajectory. Thus, the underactuated system of the biped robot was different from other underactuated systems. That is, when the uncontrollable coordinates deviated greatly, the controlled coordinates also became out of control. As preliminarily mentioned above, among the factors affecting the relative equilibrium condition of bipedal robots, the moments that drive the controlled joints are also directly affected. The problem was to find control algorithms with which the driving moments were calculated to ensure both the motion laws of the controlled joints and at the same time contribute to ensuring the relative equilibrium conditions. The most common and popular controller in the industry is a controller based on two closed feedback loops consisting of an inner feedback loop, to  
Figure 10: Some robot gaits with different levels of lowering of the center of mass.  
calculate Inverse Dynamics, and an outer loop that applies Proportional Derivative control law (Inverse Dynamics + PD), or Proportional Integral Derivative (Inverse Dynamics + PID). These controllers are also commonly applied in robotics engineering. For the convenience of presentation, we abbreviate the controller Inverse Dynamics + PD or Inverse Dynamics + PID as IDPD or IDPID, respectively. With the motion trajectory of the bipedal robot designed to satisfy the ZMP point principle or the relative equilibrium condition as stated, applying the control law IDPD, IDPID was convenient and easy. However, with these controllers, the driving moments were calculated based on the equations, and so it was not flexible to adjust the driving torque to contribute to increasing the robot's ability to ensure the relative equilibrium condition.  
In his natural walk, man adjusts himself based on natural reflexes trained from natural \"inferences\" from the first steps.  
The fuzzy logic-based controller (hereinafter referred to as the fuzzy controller) was based on natural human reasoning, so it had the flexibility to adjust the interactions reasonably. Specifically, the fuzzy controller was built by a reasonable fuzzy rule system based on natural human inference, allowing it to adjust the driving torques to ensure the control goal. The use of a fuzzy controller for a bipedal robot is presented in Section 5.  
Below, the IDPD and IDPID controllers that were applied to bipedal robots are presented. In the simulation calculations, first of all, the assumption that the dynamic model is accurately determined and that the motion trajectory is designed to ensure the relative equilibrium condition was applied to the IDPD controller. Next, in the dynamical model of the robot, it was assumed that there were noisy or uncertain forces, such as friction and/or damping at the joints. In this case, the IDPD controller needed to have additional noise cancellation capability, so with the addition of the integral component in the control law, the IDPD controller became the IDPID controller and was applied for simulation calculations.