40. ROBOTIC PATH PLANNING METHODS

ABSTRACT:

The main goal in the control of robots is to achieve human flexibility. Unfortunately humans are very complex systems, and this is carried over to the design of robots. Thus, for any apparently simple task like motion, there are some very complex control problems. When the robot must move between two points, it must consider the control of motors, possible collisions, and physical limitations. These problems have been solved in a number of different ways, and these solutions tend to follow certain trends. In fact, without generalizations, the number of solutions is so diverse, that they tend to overwhelm the search for a simple solution. A formal survey of path planning techniques will allow a knowledgeable overview of path planning.

May 18th,1989.

40.1 INTRODUCTION:

There are a number of different ways to classify the robotics problems. Various features of a problem may determine which type of path planning strategy will work best. Two fundamental classifications suggested by Fu, Gonzalez, and Lee [1987, Pg.150] are Obstacle Constraint and Path Constraint. Obstacle Constraints indicate that there are some points in space which are already occupied, and are not free for the robot to pass through. Path Constraints are usually provided as points on a path which the robot must follow. From these two suggestions there is a control strategy diagram which may be drawn,

Figure 1.1 Control Strategies for Manipulators [Fu,Gonzalez & Lee,1987]

page 691

These basic strategies form the basis for most approaches to robotic path planning. Positional Control is a simple motion controller using joint interpolated motion, or point to point motion. Path Tracking is moving through a prespecified set of points on a path. All of the strategies in this diagram affect the methods used to plan paths, thus from this point it is best to discuss some requirements of the system.

40.1.1 ROBOT APPLICATIONS

Many authors suggest, in their papers, that there are a set of tasks to which a robot may be applied. The earlier work in Artificial Intelligence suggested many approaches to solving problems, which involves splitting them into tasks. It is relatively easy to list a few ’commonly expected’ path planning tasks for a robot.

-Grasping and Releasing objects.

-Moving from place to place.

-Following prespecified paths.

-Following moving objects.

-Working with other manipulators.

-Exerting Forces (i.e.. pushing, pulling and holding).

-Exert Torques.

-Collecting Data.

-Using tools.

Items on this list have been approached by various authors. A paper describing the integrated approach of all these items is yet to be seen, although some combinations have been documented. The ideal situation would be a good general method which incorporates all of these features.

40.1.2 ROBOTIC CONSTRAINTS

Robots are machines, and as machines they are subject to all of the constraints of mechanics. Thus when dealing with many joints (prismatic or revolute) the physical limits of manipulator motion become evident. For the best solution, the limits of joint and actuator positions, velocity, acceleration, and jerk must be considered. The physical nature of the device also means that there are dimensions which must be considered, thus kinematics and collision avoidance come into play. When a robot makes any move, it expends energy to accelerate, hold and brake. This also means that the energy efficiency of the manipulator should be optimized, by reducing unnecessary expenditures of energy. Most importantly, if robots are to be cost effective, then their speed is of concern. In a high production situation, a cycle time that is 10% faster could save millions of dollars. Thus, time of path traversal can most often be the most important path planning factor.

MEASURES OF PERFORMANCE:

-Time for Path Traversal.

-Velocity of Manipulator Links or joints.

-Energy.

-Actuator Forces.

page 692

-Proximity to Obstacles. CONSTRAINTS:

-Joint Positions, Velocities, Accelerations and Jerks.

-Actuator Forces and Dynamics.

-Kinematics (this includes singularities).

-Collisions with Obstacles.

-Time, when moving obstacles are involved.

Considering these factors, the problem may be formulated as a classical optimization problem, as many authors have done. These approaches usually produce good results, at the expense of computation time. Other methods are being found which trade off some of the completeness of the optimization to find solutions quickly.

40.1.3 THE OPTIMIZATION PROBLEM OF PATH PLANNERS

To aid the description of the path planning problem, a generalized statement of the optimization criteria will be given. This will be presented for both the Measure of Performance and Constraints. The first most important Measure of Performance is time for the path. To find this, and other factors, a number of relations will be derived. First assume that the path is made up of a number of discrete segments (trajectories). These segments are linked together to form the path of motion. Motion along the path will then have a few characteristics, and these provide the basis for some equations.

E = the total path energy cost (including kinetic, potential, friction).

Local Path Time: ti =˜ si˜ /˜ vi˜

n

Global Path Time: T = S ˜ si˜ /˜ vi˜ i=1

Local Path Length = ˜ si˜

n Global Path Length: D = S ˜ si˜

i=1

Local Energy Input = ei

n

page 693

Global Energy Input: E = Σ ei

i=1

Feasible is defined as D, P, T, E are all non-infinite.

Local Optimization involves optimizing some function of si, vi & ei.

Global Optimization involves optimizing some function of T, D and E.

Collision avoidance involves altering si so that the path segments avoid obstacles. vi is used to produce the best velocity through a path segment. ei is a factor which is determined from energy input, less energy output (including friction loses). One, or any, of si, vi, ei, or n may be altered when attempting to find an alternate path. These are the only factors describing the path, and they may be found in various ways by themselves. The other factors involving forces, torques, and obstacle proximity must be determined in a similar way that is specific to the manipulator.

An example of how to derive, and apply, optimization techniques to an actual system is in order. To find a value for these parameters for a single link manipulator we would have to define a few variables