A Study on Control of a Six-Legged Walking Robot with Four Joint Legs

Abstract

In nature, many animals have legs for locomotion. Legged locomotion is intrinsically proper for movements on rough-uneven terrains. The legged system is well adaptive to uneven terrains that the wheeled system or the tracked system isn’t well adaptive to, i.e. the legged system can adjust the legs according to the level changes of uneven terrains, and it can move over obstacles and holes The objective of this dissertation is the study on controlling a six-legged walking robot (6LR) with four joint legs. In this dissertation, to do this task, the following problems are considered. The first is to present the four joint leg kinematic modeling of the 6LR. The second is to present a tracking controller of one leg to track a desired position based on a differential kinematic control of algorithm and backstepping method using Lyapunov function. The third is to present omnidirectional walking control method of the 6LR. The fourth is to present a terrain adaptation method of the 6LR while it is walking. And the last one is to present a path tracking controller of 6LR based on backstepping control using Lyapunov stability to track the path generated by potential function method. The following tasks are done to solve these problems. First, the stability and walking gaits of the legged robot is stated. The tripod walking gait is chosen for the 6LR in this dissertation. The walking cycle of the tripod gait is presented. Tripod gait is designed with swing phase and retract phase. The kinematics of one leg of the 6LR is presented to understand its behavior. The Denavit-Hartenberg (DH) convention is adopted to define the modeling parameters which allow the construction of the forward kinematics function by composition of the individual coordinate transformation. Second, since it is difficult to solve inverse kinematics problem because of its complexity, a differential kinematics control algorithm is proposed to solve the inverse kinematics problem. A proposed controller is designed to control the end effector of one leg to track a desired position based on backstepping method using Lyapunov stability. Third, the omnidirectional movement capability of the 6LR is achieved by designing a moving path for the end effector of each leg based on a given orientation and a step distance. According to tripod step cycle, three swing legs lift up, move horizontally and forward with desired orientation angle and step distance, other three retract legs move horizontally and backwards while retract legs contact the ground and make the 6LR propel. And the step cycle continues while swing legs become retract legs and retract legs become swing legs. Fourth, a terrain adaptation method with bounded uncertainty is proposed. The objective of the terrain adaptation is to make 6LR walk while it is maintaining the body parallel to the even ground. The leg transfer trajectories are modified to achieve adaptability to irregular terrain. The end effector of the leg lifts up as high as possible to avoid collision in the uncertain terrain and it moves down until it touches the ground. Two controllers for balancing the roll angle and pitch angle of the 6LR are designed based on backstepping method using Lyapunov stability. Fifth, potential function method is used as a path planner to generate a path for the 6LR to follow. The potential function and its gradient are introduced. The potential function is composed of attractive and repulsive potential function. The attractive potential represents that the goal attracts the robot. The repulsive potential represents that the obstacles repel the robot. The combination of repulsive and attractive forces directs the 6LR from the start position to the goal position while it is avoiding obstacles. By the gradient descent algorithm, the 6LR follows the inverse direction of gradient of the potential function and generates a path for the 6LR. A controller is designed based on backstepping method using Lyapunov stability for the 6LR to track the generated path. Sixth, to implement the proposed controllers, a real six-legged robot is developed with several interconnected devices such as: servomotors, sensors, Micro Control Unit (MCU), etc. The IMU sensor is used for measuring the 6LR attitude. The touch sensor is installed by using the torque direction data provided by the servomotor. The sensors’ data are processed by MCU and send to a computer via bluetooth. Based on the control algorithm, the computer computes the angle of each joint and sends to MCU. The MCU controls the servomotors. Finally, simulation results of omnidirectional walking are presented. The experiments of omnidirectional walking and terrain adaptation are presented to verify the effectiveness of the proposed controllers. Simulation results of potential function method and gradient descent algorithm are presented to verify the effectiveness of the proposed algorithm. Simulation results of path tracking controller are presented to verify the effectiveness of the proposed controllers. Keywords: Multi-legged Robot, DH Convention, Analytical Jacobian, Redundant Manipulator, Lyapunov Function, Potential Function, Gradient Decent