Kinodynamic Motion Planning for an X4-Flyer

Kinodynamic Motion Planning for an X4-Flyer

Kimiko Motonaka (Okayama University, Japan), Keigo Watanabe (Okayama University, Japan) and Shoichi Maeyama (Okayama University, Japan)
Copyright: © 2015 |Pages: 20
DOI: 10.4018/978-1-4666-7387-8.ch015


This chapter describes kinodynamic motion planning and its application. Kinodynamics is the discipline that tries to solve kinematic constraints and dynamical constraints simultaneously. By using kinodynamic motion planning, control inputs can be generated in a much simpler way, compared to the conventional motion planning that solves kinematics and dynamics separately. After briefly overviewing the kinodynamic motion planning, its application to a flying robot is described in detail.
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“Kinodynamics” consists of the words “kinematics” and “dynamics”, and it means the research area that considers and solves the kinematics and dynamics simultaneously. In most of conventional motion planning, dynamical constraints are generally solved by designing control inputs according to the result of kinematic constraints, after first solving kinematic constraints by using path planning. However, kinodynamic motion planning is aimed at solving the kinematic constraints and dynamical constraints simultaneously to generate a control input by using the current states of the controlled object (Donald, Xavier, Canny, & Reif, 1993). Kinodynamic motion planning is useful for generating the control input more simply because it can define the control input in one step by considering the kinematics and dynamics simultaneously after the controller is designed. Therefore, many kinodynamic motion planning methods are proposed up to now. For example, “Randomized Kinodynamic Planning” was proposed by LaValle and Kuffner (1999), where the path toward an arbitrary target point is calculated by a random search method considering the dynamics of a robot. In this method, the searched path is reasonable and a natural route, which can be tracked by the assumed robot, because the velocity and form of the robot are also considered in a state space. Moreover, a method for generating an avoidable and realistic trajectory for the cooperation of multi-robots is also proposed in Jufeng et al. (2005) by combining the kinodynamic motion planning and the optimal control.

A method of using “Harmonic potential field (HPF)” was proposed as one of kinodynamic motion planning. An HPF is a smooth potential field that has no stationary points. By using its gradient vector, it is guaranteed that a kinematic trajectory can reliably reach an arbitrary target point from anywhere in the potential field while avoiding obstacles. When using the gradient of an HPF for the kinodynamic motion planning, damping forces are required for preventing that the controlled object deviates from the gradient direction. Using the viscous damping forces as damping forces is the simplest method, but the method always keeps the controlled object be converged with a slow speed.

From the above point of view, Masoud (2010) introduced the “nonlinear anisotropic damping forces (NADFs)” as an alternative to viscous damping forces. The NADFs can consider the direction of the gradient vector and they decelerate the controlled object only when it deviates from the gradient vector. Masoud also proposed “clamping control” for suppressing an overshoot or oscillation, and it is confirmed that these methods are useful for the control of a point mass.

Key Terms in this Chapter

Motion Planning: Planning problem which is raised when the robot moves automatically. It plans how to move for the robot.

X4-Flyer: One of a VTOL type aerial robot. It can fly by rotating four propellers which are mounted on the end of the crossed frame.

Harmonic Potential Field: A potential field which has no stationary points.

Kinodynamics: The word which combined “kinematics” and “dynamics”.

Kinodynamic Motion Planning: Motion planning which is aimed at solving the kinematic constraints and dynamical constraints simultaneously.

VTOL: Aerial robots that can hover, take off, and land vertically.

UAV: Unmanned Aerial Vehicle. The robots which can fly in the air without human riding.

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