A Unified Methodology for Motion Planning with Uncertainty for 2D and 3D Two-Link Robot Arm Manipulators

Abstract

Most of the work on robot path planning revolves around two basic models: the model with complete information (often called the "Piano Mover's Problem") and the model with incomplete information (called here the "South Pole Search Problem'). The approach of dynamic path planning introduced in Lumelsky and Stepanov (1987) and Lumelsky (1987) is based on the latter model and produces nonheuristic (provable) algorithms for simple robot arm manipulators operating in an environment with unknown obstacles of arbitrary shapes. The algorithms assume local on-line input information coming from the arm sensors. Unfortunately, the existing techniques require that each kinematic configuration be considered separately, which results in different algorithms for different kinematics. In this paper, a unified methodology is presented for designing dynamic path planning algorithms for two-and three-dimensional two-link arm manipulators. The approach is independent of the specifics of the kinematic configuration and imposes no constraints on the shape of the arm links or obstacles in the environment. The methodology exploits some important topological characteristics of the configuration space. However, no explicit computation of obstacles in the configuration space ever takes place, which results in fast real-time algorithms. l . IntroductionDepending on the underlying models, algorithms for robot path planning and collision avoidance fall into one of two categories. In one model, often called the model with complete information, or the &dquo;Piano Mover's Model&dquo; [see, e.g., Schwartz and Sharir (1987) and Lozano-P6rez ( 1983)], complete information about the environment is assumed. In the second model, also considered in this paper and called the &dquo;South Pole Search Problem,&dquo; the information about the environment is incomplete and appears on-line, typically from the robot sensors.In Lumelsky and Stepanov (1987), theory has been developed for designing nonheuristic (&dquo;exact,&dquo; provable) path planning algorithms for a point automaton operating in a planar environment filled with unknown obstacles. In the accepted model, each obstacle is a simple closed curve of arbitrary shape. The automaton knows its current and the target positions and is capable of sensing an obstacle, on contact or at a distance, and of moving along the obstacle boundary. The automaton plans its path continuously (dynamically); that is, at any point of its path, the automaton generates its next position based on its current position relative to the target and on the incoming sensory data. Accordingly, the approach is called &dquo;Dynamic Path Planning.&dquo; Because of the uncertainty involved, no optimality of the path can be guaranteed; instead, the objective is to generate a &dquo;reasonable&dquo; path.

Connectivity graphs on two‐dimensional surfaces and their application in robotics

“…cl Now let us define a connectivity graph 9 for the torus similar to Definition 3.1, except that the one generic path used in the definition is replaced with the three of a complete set. That is, the connectivity graph is formed by the obstacle boundaries together with the portions of a complete set of generic paths outside of obstacles.…”

“…For fixed and 02, there exist two 'elbow positions' for e4: the up-elbow position corresponds to e4 > 0, and the down-elbow position to O4 < 0 two degrees of freedom, and its configuration space presents a torus. It is shown in [9] that the configuration space of all two-link planar or spatial robot arm manipulators with prismatic or revolute joints presents a compact subset of a torus with obstacles being simple closed curves on the surface of the torus, and in [20] that the configuration space of a certain class of three-link robot arm manipulators can be deformed into a 2D compact surface.…”

Communication-Based Motion Planning

“…Path planning is used for a range of applications from optimal-path navigation [1], [2] to exploration [3], [4] to the movement of robotic arms in manufacturing plants [5], [6]. Many different constraints have been explored, including formations of robots, kinematic properties of vehicles, and robotic sensors and communication.…”

Path planning among unknown obstacles: the case of a three-dimensional Cartesian arm

“…In the case of a two-link two-or three-dimensional robot arm manipulator operating among planar or spatial obstacles, the configuration space (C-space) formed by its joint variables is a two-dimensional manifold, in which the arm maps into a point and obstacles map into simple closed curves. It has been shown that in such cases, the same approach, with some modifications, can also be applied [3]. The algorithms do not require any explicit computations of the unknown obstacles in work space or configuration space, and they guarantee convergence.…”