A Fast and Smooth Walking Pattern Generator for Biped Robots

Abstract

In order to solve inverse kinematics of a multi-DOF (degree of freedom) mechanism, many methods have been proposed with the Jacobian linearization method. When solving inverse kinematics problems of the biped robot with this method, long computation time is required since the Jacobian matrix should be updated in order to solve the configuration for each different end-effector trajectory knot. In this chapter, two smooth trajectories are generated as target positions, one for swing leg’s ankle, and the other for center of gravity (COG). These generated knot points in the task space with appropriate distance to each other are used to solve inverse kinematics by the proposed modified Jacobian method—Fixed Leg Jacobian. It can guarantee that only one iteration is required to solve the configuration when it is away from singularity with a small position error (0.0712% of leg length). The proposed algorithm can generate the gait in real-time including singularity avoidance and joint limit avoidance. Simulations have been carried out. The results showed that the proposed method can generate a smooth gait for robot walking on real-time implementation. Compared with wheeled robots, legged robots have the advantage of being able to traverse uneven or sharp-height-changing environments. Nowadays, many vehicles, buildings and environments are designed for humans. Simple robots cannot enter and adapt to these places. Therefore, we must design complicated humanoid robots to do it. But when the designs become more complicated and with more DOFs, it is getting harder to control and generate the trajectories of them. The proposed algorithm can quickly generate smooth trajectories of the ankle and COG and solve inverse kinematics in order to achieve real-time control of biped robots. In this chapter, the focus is how to coordinate the swing leg, the fixed leg and the COG of the robot, and generate the gait in real-time. In the simulation, the robot has 24 DOFs, 6 in each leg (12 in two legs), 4 in each arm (8 in two arms), 2 in the torso and 2 in the head. The most important DOFs for balancing and walking are the twelve DOFs in the legs. DOFs in the fixed leg dominate the position of the COG, and the position of the ankle of the swing leg is given relative to the position of the ankle of the fixed leg in order to guarantee that the swing leg is in a proper position that it will not hit the fixed leg and touch the ground. The trajectories of the end-effectors planned with desired constraints are inputted to solve inverse kinematics, as shown in Fig. 1. Many researchers have proposed the solutions to the problem while solving Jacobian linearized inverse kinematics. They include the damped least square method (DLS) (Wampler, 1986) and the robust damped least square method (RDLS) (Nakamura &