The Development of Nonlinear Model Reference PID Controller for a bipedal robot

This paper develops a new concept of a Nonlinear Model Reference PID controller for a biped robot with seven degrees of freedom. The controller consists of five second order differential equations, each in terms of the angle error of a single joint from the designed trajectory. The coefficients of each differential equation are specifiable giving the ability to specify the behavior of the biped in the presence of disturbances. Simulations are presented that show the ability of the biped robot with the Nonlinear Model Reference PID (NMRPID) controller to follow the designed trajectory in the presence of disturbances. From the experiments, NMRPID controller can reduce the errors of the trajectory when using the traditional PID controller from ±1.97 radians to ±0.0137 radians with the same gains. 1. Introduction The control techniques most used to control a bipedal robot are the PID control [1-3], optimal control [4], adaptive control [5], robust control, and inverse dynamics control [6-7]. There are many kinds of controllers that can be used to cause a bipedal robot to move along a desired trajectory. The simplest controller that can be used to control a bipedal robot is the PID controller. By selecting the PID gains by trial and error, the biped robot will move alone the designed trajectory. It is hard to select the PID gain because of the nonlinearity of the robot. The neural network controller is the alternative way to be used to control a bipedal robot. There are two major applications of the neural network technique that are used in the robot design. First, the neural network is used for the trajectory generation algorithm [8], and the second approach is a neural network controller [9-10]. By computing the leaning set for the neural network from a specific trajectory and robot structure, the neural network controller can cause the bipedal robot to follow desired trajectory. There is one major problem of the neural network approach. The neural network controller gain set is determined for a specific trajectory. It has to be relearned from a new learning data set when the trajectory is changed. Because the model of the robot is not a perfect representation of the robot, differences between the actual and designed trajectory angles, velocities, and accelerations occur. Disturbance that move the robot off the desired trajectory also generate differences between the actual and designed trajectory angles, velocities, and accelerations. In this research, a new trajectory following controller, the Nonlinear Model Reference PID (NMRPID) Controller [11], is developed that corrects for these errors and causes a bipedal robot to move along the designed trajectory. The bipedal joint angle torques is developed as a function of time from the designed trajectory. They are used as inputs to the trajectory reference model which outputs the designed trajectory angles, velocities, and accelerations. These are compared to the actual trajectory angles, velocities, and accelerations of the robot and the errors are inputted into the NMRPID controller to generate a torque correction. The controller is independent of the trajectory, so the controller does not have to learn a new trajectory algorithm each time the trajectory is changed. The error of each joint angle from the designed trajectory joint angle is described by a third order time invariant differential equation whose coefficients are independent of the robot. This gives the controls engineer the ability to determine how the robot will return to the desired trajectory if the robot moves off the desired trajectory. The bipedal robot which is selected for this paper is shown in Figure (1.1).