# Kinodynamic Motion Planning for a Two-Wheel-Drive Mobile Robot

Kimiko Motonaka (Kansai University, Japan)
DOI: 10.4018/978-1-5225-2993-4.ch014

## Abstract

Since a nonholonomic system such as a robot with two independent driving wheels includes complicated nonlinear terms generally, it is hard to realize a stable and tractable controller design. However, about a dynamic control method for the motion planning, it is guaranteed that a nonholonomic-controlled object can always be converged to an arbitrary point using a control method based on an invariant manifold. Based on it, the method called “kinodynamic motion planning” was proposed to converge the states of the two-wheeled mobile robot to the arbitrary target position while avoiding obstacles by combining the control based on the invariant manifold and the HPF. In this chapter, how to combine the invariant manifold control and the concept of the HPF is explained in detail, and the usefulness of the proposed approach is verified through some simulations.
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## Introduction

Recently, many robots are working in our living environment. Especially, a mobile robot with two independently driven wheels has been commonly used for transportation or giving service to human. For these robots, autonomous locomotion is important, and there are many kinds of researches about an obstacle avoidance or a path planning for it.

For the smooth moving of the robot in a living environment, it is desirable to consider the kinematic constraint (generated from the constraint based on an obstacle or target position) and the dynamic constraints (generated from the dynamic characteristics of the controlled object). Therefore, the method called “kinodynamic motion planning” was proposed by Donald, Xavier, Canny, and Reif (1993) to solve this problem. The kinodynamic motion planning aims to design the control input so that the kinematic constraints generated from the environment and the dynamic constraints generated from the dynamic characteristics of the controlled object are both considered simultaneously. Now, there are many researches about kinodynamics (Rimon, 1998; Hsu, 2002; Peng, 2005). However, most of these methods do not generate the control input in real time reflecting the current state of the robot but calculate the all of the control input in advance. This is unfavorable when the overshoot occurs and it needs to correct the state of the robot in an actual environment. Masoud (2010) realized the kinodynamic motion planning for a point mass by combining two control inputs: one is generated by considering the dynamics of the controlled object and the other is based on the gradient information of the potential field called harmonic potential field (HPF) which is generated from the boundary information of the environment. In this chapter, the method to extend and apply the kinodynamic motion planning based on the HPF to the two-wheeled mobile robot is described.

The kinodynamic motion planning using the HPF is achieved by adding the gradient information of an HPF to the control input that has considered the dynamic characteristics of the controlled object. To apply the kinodynamic motion planning based on an HPF to some controlled object, at first, it needs the control input that considers the dynamic model of the controlled object. Here, the stabilizing control to the origin using an invariant manifold is given as one of the methods to control the two-wheeled mobile robot. The controller based on the invariant manifold can reliably stabilize the controlled object to the origin kinematically and dynamically (Tsiotras, Corless, & Longuski, 1993). However, that method can stabilize the controlled object to the origin only. In the case of the robot works in the actual environment, the robot is required to move onto not only the origin but also the arbitral target position. To converge the controlled object to a non-zero desired point, Goto, Watanabe, and Maeyama (2014) extended the controller based on the invariant manifold by using an error model (2014). This extended method is suitable to combine the controller based on the HPF. By combining these controllers, the kinodynamic control can be achieved and the controlled object can reach the desired target position with the desired state while avoiding obstacles. In the following sections, the model of the two-wheeled mobile robot, the controller using an invariant manifold, the controller using the HPF, how to combine them, and some experiment and results are described.

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