On Path Planning and Obstacle Avoidance for Nonholonomic Platforms with Manipulators: A Polynomial Approach

Abstract

A planning methodology for nonholonomic mobile platforms with manipulators in the presence of obstacles is developed that employs smooth and continuous functions such as polynomials. The method yields admissible input trajectories that drive both the manipulator and the platform to a desired configuration and is based on mapping the nonholonomic constraint to a space where it can be satisfied trivially. In addition, the method allows for direct control over the platform orientation. Cartesian space obstacles are also mapped into this space in which they can be avoided by increasing the order of the polynomials employed in planning trajectories. The additional parameters required are computed systematically, while the computational burden increases linearly with the number of obstacles and the system elements taken into account. Illustrative examples demonstrate the planning methodology in obstacle-free and obstructed environments.

A Review of Robotics Technologies for On-Orbit Services

“…Most of the abovementioned methods are time consuming. A computationally inexpensive method developed for terrestrial mobile manipulator systems was extended for potential use in space robotics [97] but it has not been validated yet.…”

Analysis and Design of a Two-Wheeled Robot With Multiple User Interface Inputs and Vision Feedback Control

“…There are many discussions in the literature to address these difficulties [17][18][19][20][21]. This research utilized two different control methods, which will be discussed in the following sections, to address this difficulty.…”

“…There are many path planning algorithms discussed in the literature [13,20,24,25]. Path planning was not the primary focus of this research; therefore, the path-planning method described by Papadopoulos [21] was used because it is relatively simple to implement and computationally inexpensive. The entire derivation of this method need not be discussed here, but Papadopoulos built on a method described earlier by Pars to define a transformation from Cartesian space to some other space of the form (26) where only two differentials appear [26].…”

“…The entire derivation of this method need not be discussed here, but Papadopoulos built on a method described earlier by Pars to define a transformation from Cartesian space to some other space of the form (26) where only two differentials appear [26]. Papadopoulos then developed a nonlinear time functions to describe a path in this new space and to transform the path back into Cartesian space [21]. This transformation is given by (27) where is the distance from the center of mass of the robot to some point off of the center of mass in the x-direction.…”

The Comparative Assessment of Modeling and Control of Mechanical Robot Manipulators

“…It steers a platform and its accompanying manipulator from an initial state to a final one, without violating the nonholonomic constraints (Sheng & Qun, 2006). In most studies of trajectory planning for mobile manipulators the end effector trajectory is specified and the optimal motion planning of the base is considered (Mohri et al, 2001), or integrated motion planning of the base and the end effector is carried out (Papadopoulos, et al, 2002). However, because of designing limitation or environmental obstacle in majority of practical application of mobile manipulators especially in repetitive applications, the platform must follow a specified pose trajectory.…”