U5 Motion Planning
5.1.- Motion planning.
In the joint stepping method, itis assumed
that the initial and final positions of the joint are
known to the initial and final settings of the final
effector by solving the problem of reverse position
explained in Chapter 6. So the
basic problem is how to select a path between an
initial position and a joint end with the interval
that is allowed for the movement between the two.
In the literature, several methods have been
proposed to solve the problem. A simple
one that is based on the polynomial functions
of time. Suppose that for some articulation,
the nicial angle i is q0 in a time t x 0 and the end
angle is q' at a time t't', that is,
kinematics
q(0) s q 0 ; and q(t f ) s q f
predict the movement of the
final effector in The
Cartesian space. There are also cases where
some specific trajectory of the end effector
is required. By mplo axis,in arc welding, the
electrode must precisely follow a seam. In
these cases, we want to gene a path in terms
of the variablesof position and orientation,
that is, the configuration of the end
effector.
5.3.- Cartesian space planning.
Se considers that x is the vector of the
operational space variables that exprey the
position and orientation of the
manipulator's final effector,generating a path
in the operational space represents
determining a function x (t), tomand or the
system of the final effector from l to the initial location
to the end at a time t- along a given path with a
specific law of movement time. To do this,first of
all consider the positionof the fin effector
system. As a result, the guidance will be
given.
11.3.1 Primitive routes
For thedefi nition of primitive routes, it is
convenient to refer to the parametric
description routes in space. Suppose that p is
the three-dimensional vector and f(s) is
acontinuous vector function definida in the
range [yes, yes]. Consider the equation
5.4.- Position and orientation paths.
5.2 Planning of joint spaces.
When a trayectoria is generated between two
robot configurations by means of a method of joint
variables, com or described in the
previous subsection, it is sometimes difficult to
The algorithm should generate a path that,
with respect to the aforementioned gene
rales requirements, will also be able to
optimize at any performance index when it
moves the articulation from one position to