No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
On controlling robots with redundancy in an environment with obstacles
Abstract
This paper presents a method to solve the problem of obstacle avoidance for a redundant manipulator so that it closely tracks the desired end-effector trajec-lory and simultaneously avoids workspace obstacles. The proposed method introduces the describing Cunction J to indicate whether collision occurs between the robot and obstacles. The obstacle avoidance task is achieved by Cormulating the performance criterion J > J m ,,, (J m ;" represents the minimal distance between the redundant robot and obstacles), and by using configuration control lo ensure that this criterion is satisfied. The cafculation oC J function is only related to some vertices which are used to generate and model the robot and obstacles, and the computational times are nearly linear with the total number of vertices. The configuration control algorithm which achieves end-effector motion and obstacle avoidance does not require either a complex dynamic model or complicated inverse kinematics transformations of the robot. Several simulation cases for a four-link planar manipulator are given to prove that the proposed collision-free trajectory planning scheme is efficient and practical.
... hlodel-based detection has usually been used off-liue as a cornponcut of path planning and simulation systems and, as such, has not had the requirement for real-time performance, These detection methods are capable of mocleling complex manipulators and obstacles aud can exhaustively search for nearest obstacles (e.g. [6,7]). Oftentimes, desig~,s for real-time collision avoidance have used sensor-basecl obstacle detectiou (e.g. ...
This paper describes the approach and algorithms developed for
real-time model-based obstacle detection and distance computation for
the NASA Ranger Telerobotic Flight Experiment. Objects of interest, such
as manipulator arms or the ranger vehicle and solar arrays, are modeled
using a small set of component types: edges, polygonal faces and
cylindrical links. Link positions are computed using standard forward
kinematics, and distances between object components are computed
directly using equations derived from geometry. Prioritized lists of
potential obstacles for each manipulator link eliminate needless
distance computations and assure that the most likely obstacles are
checked, even if the computation is terminated early due to real-time
constraints. A test program, utilizing a 3D graphical simulation and
providing a graphical user interface for operator control, has been
developed and used to test and demonstrate obstacle detection. An
earlier paper (1996) described how the obstacle detection results are
utilized for collision avoidance
The development of a vision-only intelligent interface for
dexterous robots is described, capable of tracking operator motions:
evaluating trajectory feasibility, and providing visual feedback to the
operator. This interface analyses the operator's arm motion for safety,
and then converts it into trajectory commands for a mechanical arm.
Potentially dangerous situations, such as singularity and self
collision, are displayed to the operator as graphical icons superimposed
over the robot video images. The paper summarizes the main features of
the current implementation, presents the approach developed for
singularity identification and describes the performance of the
demonstration prototype
This paper describes an online approach to whole-arm collision
avoidance for the NASA Ranger Telerobotic Flight Experiment. Using a
geometric world model, minimum distances and nearest points between
parts of the active dexterous 7-DOF manipulator and potential obstacles
are computed by the Ranger obstacle detection software. Obstacle data is
then used to compute virtual repulsive forces which perturb the
operator-commanded manipulator Cartesian motions in order to avoid
collisions. The virtual forces are computed at the tool-tip for
end-effector position perturbation, at the wrist for end-effector
orientation perturbation, and on the upper and lower arm links for arm
angle perturbation. The paper also describes the software development
environment, utilizing a 3D graphical simulation and providing a
graphical user interface for display and operator command. Results of
several test runs illustrating end-effector position and orientation
perturbation, as well as arm angle perturbation, are presented
The method of multibody systems is discussed with respect to the computerized generation of symbolical equations of motion. The kinematics are presented in an inertial frame and, additionally, in an often very useful moving reference frame. The dynamics include not only spring and damper forces, but also integral forces and contact forces typical for vehicle applications. The equations of motion are found by d’Alembert’s principle and Jourdain’s principle featuring generalized coordinates and generalized velocities, holonomic and nonholonomic constraints. It is also shown how constraint forces, necessary for the modeling of contact and friction, can be computed using a minimal number of equations. Finally, the symbolical formalism NEWEUL is introduced.
In this study, global planning of a collision-free trajectory (simultaneous planning of geometric path and its time para meterization) involving potential functions and direct kinematic and dynamic equations of the manipulator is presented. This planning is based on using the necessary conditions of min imum for an integral type criterion. General transversality conditions corresponding to the boundary ones (resulting from the task to be performed) are derived. Thus, closed systems of boundary dependences fully specifying differential equations, which arise from the necessary conditions of extreme for the above criterion, are obtained. As a result, this system renders it possible to reduce the collision-free trajectory planning problem to a two-point boundary value problem. A numerical example involving a manipulator of three-revolute kinematic pairs of the Vth class is considered.
Collision avoidance is an absolutely essential requirement for a robot to complete a task in an environment with obstacles. For kinematically redundant robots, collision avoidance can be achieved by making full use of the redundancy. In this article, the problem of determining collision-free joint space trajectories for redundant robots in an environment with multiple obstacles is considered, and the “command generator” approach is employed to generate such trajectories. In this approach, a nondifferentiable distance objective function is defined and is guaranteed to increase wherever possible along the trajectory through a vector in N(J), the null space of Jacobian matrix J. Algorithms that implement this nondifferentiable optimization problem are fully developed. It is shown that the proposed collision-free trajectory generation scheme is efficient and practical. Extensive simulation results of a four-link robot example are presented and analyzed.
The article presents a new and simple solution to the obstacle avoidance problem for redundant robots. In the proposed approach, called configuraiton control, the redundancy is utilized to configure the robot so as to satisfy a set of kinematic inequality constraints representing obstacle avoidance, while the end-effector is tracking a desired trajectory. The robot control scheme is very simple, and uses on-line adaptation to eliminate the need for the complex dynamic model and parameter values of the robot. Several simulation results for a four-link planar robot are presented to illustrate the versatility of the approach. These include reaching around a stationary obstacle, simultaneous avoidance of two obstacles, robot reconfiguration to avoid a moving obstacle, and avoidance of rectangular obstacles.
Iterative algorithms for detecting the collision of convex objects
whose motion is characterized by a path in configuration space are
described. They use as an essential substep the computation of the
distance between the two objects. When the objects are polytopes in
either two-dimensional or three-dimensional space, an algorithm is given
which terminates in a finite number of iterations. It either determines
that no collision occurs or locates the first collision point on the
path. For practical problems it appears that the computational time is
short and grows only linearly in the total number of vertices of the two
polytopes. Numerical examples are presented
A simple approach for controlling the manipulator configuration
over the entire motion, which is based on augmentation of the
manipulator forward kinematics, is presented. A set of kinematic
functions is defined in Cartesian or joint space to reflect the
desirable configuration. The user-defined kinematic functions and the
end-effector Cartesian coordinates are combined to form a set of
task-related configuration variables as generalized coordinates for the
manipulator. A task-based adaptive scheme is then utilized to control
directly the configuration variables so as to achieve tracking of some
desired reference trajectories throughout the robot motion. This
accomplishes the basic task of desired end-effector motion, while
utilizing the redundancy to achieve any additional task through the
desired time variation of the kinematic functions. Simulation results
for a direct-drive two-link arm are given to illustrate the proposed
control scheme. The scheme has also been implemented for real-time
control of three links of a PUMA 560 industrial robot, and experimental
results are presented and discussed. The simulation and experimental
results validate the configuration control scheme, and demonstrate its
capabilities for performing various realistic tasks
Optimal planning of collision-free trajectory of redundant manipulators
- R Colbaugh
Colbaugh R. et al (1989).
Obstacle avoidance for redundant robots using configuration control, Journal 0/ Robolic Sy-. lIem.t, Vol. 6, No. 6, pp.121-744.
Galid:i M.(1992).
Optimal planning of
collision-free trajectory of redundant manipulators, The Intern. J. 0/ Robolic, Re-.tearc:h, Vol. II, pp.549-559.
Computer generation of equation of motion , Computer aided ana/y-.ti, and oplimizalion 0/ mechanical -,y.tylem dynamic
- W Schiehlen
Schiehlen W.(1984) : Computer generation of
equation of motion, Computer aided ana/y-.ti, and oplimizalion 0/ mechanical -,y.tylem
dynamic" Springer. Verlag, pp. 18~215.