Inverted pendulum model for turn-planning for biped robot

Abstract

Based on the inverted pendulum model, gait planning of biped robot is carried out, which makes it walk steadily and realizes steering in one step. Aiming at the stability of the turning poses of the humanoid robot, this paper studies the landing stability analysis of the robot, the planning and control of landing after turning, improves the inverted pendulum model, and introduces the turning angle to the model of trajectory generation. By this method, the robot can plan a more reasonable gait trajectory of the real robot when turning, and achieve a single-step sharp turn at any angle, thereby making the robot walk more smoothly. Based on ROS and V-rep, the robot simulation platform was constructed, the hardware experimental platform was self-made, and the feasibility of gait planning method was verified by simulation and experiments respectively. The experiment results showed that the turning error of the robot on the plane was less than 6°.

Introduction

The application of high-performance computing in robot simulation has greatly promoted the development of robotics. Simulation is very important in the robot design process for fast algorithm verification. In the field of robotics, simulation generally includes kinematics simulation, dynamics simulation, and finite element simulation. The function of kinematics simulation is to observe the range of motion of each joint of the robot, and the visualization function of the working range of the robot. Dynamics simulation determines the mechanical arm force balance, the highest motion speed determination, and so on. Finite element simulation is mainly used to calculate the load or gravity deformation, and can also be used to calculate the temperature field distribution of the robot. The robot simulation software uses the robot 3D integrated development environment V-rep, using its computational modules (inverse kinematics, physics/dynamics, collision detection, minimum distance calculation, path planning, etc.) and distributed control architecture (infinite number of controls) Scripting, threading or non-threading, combined with the Vortex physics engine to improve the accuracy of motion, rotation and collision, and to simulate the dynamics of the robot [1], [2], [3].

Owing to the characteristics of low energy consumption and human-like walking of the dynamic biped robot, many research institutions and scholars are constantly researching [4] since the 90’s. In 1997, Professor A. Goswami, Chief scientist of American Honda Research Institute, initially and systematically studied the theory of dynamic passive biped robot, proposed the model of Compass-like biped robot, and carried out numerical simulation and dynamic analysis. The research indicates the advantages of the dynamic biped robot that it consumes low energy and has less Degree of Freedoms (DoFs) to control [5]. This kind of robots can realize personified natural gaits, and rationally convert the potential and kinematic energy into equivalent driving energy in the movement process by means of few energy inputs, which realizes the stable periodic motion of the dynamic biped robot with multiple working conditions and multiple tasks [6], [7].

The advanced humanoid robots mainly include: $ASIMO$, $HRP-4c$, $wabian-2$, $huboqrio$, etc. [8]. $ASIMO$ is $1.3$ m in height, and $48\mathrm{kg}$ in weight, with a total of $54$ DoFs [9], with the ‘i-walk’ walking technology developed by Honda Company, and walking speed is up to $9$ KM/H [10]; $HRP-4c$ is $1.58$ m in height, and $43\mathrm{kg}$ in weight, with a total of $42$ DoFs, besides it can capture the human walking by the simulating motion capturer and realizes the walking similar to human [11]; $WABIAN-2$ is $1.5$ m in height, and $67\mathrm{kg}$ in weight, with two legs of 14 DoFs, which are driven by motors with harmonic reducer [12].

The linear inverted pendulum model has been widely used in gait control of anthropomorphic robots. Based on this model, the trajectory of the center of mass on the coronal and sagittal planes is planned to achieve stable walking of the robot [13], [14]. By this planning mode, the robot can move stably all around. However, small robots tend to perform better in the straight walk, while cornering is clumsy. The reason is that when generating the turning trajectory, most of the current robots first plan the gait trajectory of straight walking and then change the implementing trajectory into turning trajectory according to the turning angle [15]. In view of the complexity and real-time performance of the current robot turning algorithm, this paper proposes an algorithm for one-step turning at any angle. The simulation work of the algorithm is realized based on high-performance computing, and finally verified on the actual robot [16], [17].

The rest of this article is organized as follows: In the second section, the linear inverted pendulum model is introduced. The third section introduces the current robot steering trajectory planning method and proposes a one-step steering method. The fourth section introduces the simulation and robot hardware experimental platform and performs the robot steering experiment. The fifth section is the conclusion.