Motion planning is one of the most important areas of robotics research. The complexity of the motion-planning problem has hindered the development of practical algorithms. This paper surveys the work on gross-motion planning, including motion planners for point robots, rigid robots, and manipulators in stationary, time-varying, constrained, and movable-object environments. The general issues in motion planning are explained. Recent approaches and their performances are briefly described, and possible future research directions are discussed.

Gross motion planning—a survey

The authors describe a method for coordinating the trajectories of two robot manipulators so as to avoid collisions between them. It is assumed that the robots' environment is known and that the robots' paths can thus be planned in advance but that there may be significant variations in the execution time of some of the path segments. The goal is to allow the motions of each manipulator to be planned nearly independently and to allow the execution of the path segments to be asynchronous. The coordination is achieved by introducing explicit coordination commands into the path. The key problems in coordinating trajectories are to avoid collisions between the two robots and to avoid deadlock, that is, situations where each manipulator is waiting for the other to proceed. >

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Deadlock-free and collision-free coordination of two robot manipulators

This paper focuses on the collision-free coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical programming, consists of identifying collision segments along each robot's path, and then optimizing the robots' velocities along the collision and collision-free segments. First, for each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding two-point boundary value problems. The collision avoidance constraints for pairs of robots can then be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations, which provide schedules that give lower and upper bounds on the optimum; the upper bound schedule is designed to provide continuous velocity trajectories that are feasible. The approach is illustrated with coordination of multiple robots, modeled as double integrators subject to velocity and acceleration constraints. An application to coordination of nonholonomic car-like robots is described, along with implementation results for 12 robots.

https://link.springer.com/content/pdf/10.1007%2F978-3-540-45058-0_14.pdf

Coordinating Multiple Robots with Kinodynamic Constraints Along Specified Paths

Large-scale 3D printing by a team of mobile robots

This study of robot motion planning in dynamic domains presents algorithms for generating motion in an environment that changes over time. Their computational costs are also analyzed. The ability to plan motion in a dynamic domain is of critical importance to an autonomous robotic system that must operate in the presence of moving obstacles or other robots. The most important feature of the book is the presentation of algorithmic solutions to geometric aspects of dynamic motion planning problems which are of fundamental importance in robotics. Topics discussed include planning in time-dependent environments, generation of time-minimal paths in three dimensions, and the co-ordination of multiple mobile agents. The book can serve as a reference for those working on spatial reasoning and autonomous robotic systems.

Motion Planning in Dynamic Environments

The paper describes an approach to the solution of the find path problem, including obstacle avoidance in multirobot systems. The design of multirobot systems requires an overall approach where not only parts of the structure, including the hierarchy are considered, but a complete concept, including the dynamics of the robots, has to be developed. In this paper the structure of these systems is based on the nonlinear con trol approach. The method for real-time pathfinding itself uses a systematic design procedure for multirobot systems, which includes the hierarchical coordinator. This hierarchical coordinator is designed for real-time collision avoidance, where the collision avoidance strategy is based on an analyti cally described avoidance trajectory that serves for collision detection as well as avoidance. The efficiency of the new approach for real-time pathfinding is demonstrated by several cases of practical interest, such as collision avoidance between three robots, interaction of three stationary...

E. Freund

Papers

Real-time pathfinding in multirobot systems including obstacle avoidance