Method of command control for a robot manipulator

Details Method of command control for a robot manipulator Method of command control for a robot manipulator

1998-06-19

2001-01-30

Sheikh, Ayaz R. (Department: 2781)

Data processing: generic control systems or specific application

Specific application, apparatus or process

Robot control

C700S250000, C700S251000, C700S262000, C700S263000, C700S244000, C318S568110, C318S568120, C318S646000, C318S628000, C318S648000, C708S442000, C708S625000

Reexamination Certificate

active

06181983

ABSTRACT:

FIELD OF THE INVENTION
The present invention relates to a method of command control for a manipulator, based on end-effector destination shifts (&Dgr;x
d
) commanded by a programmer or a superordinate task with the aid of a manual control ball or the like, in combination with a calculation of articulation position values according to an algorithm of inverse kinematics.
REVIEW OF THE RELATED TECHNOLOGY
Methods of command control of a manipulator based on end-effector destination shifts, in combination with a calculation according to an algorithm of inverse kinematics using the Jacobi Matrix, are known from Siciliano, B., Sciavicco, L.: “Modeling and Control of Robot Manipulators,” McGraw-Hill Companies (1996), pp 95 to 101, and from Vukobratovic, M., Kircanski, N.: “Kinematics and Trajectory Synthesis of Manipulation Robots,” Springer-Verlag, Tokyo, 1986, pp 105 to 122.
In this context, a method of inverse kinematics is obtained for kinematically non-redundant manipulators, albeit in a partial space of the working area that contains non-singular positions. Since singular configurations, i.e., articulator positions in which the Jacobi Matrix experiences a reduction in priority, do occur in practice, this method has only limited application, because the operation being performed with the manipulator (interactive path guidance, force control) must be aborted or delayed when a singular configuration (singularity) is approached.
In this context, a method is known that includes a calculation of a generalized inverse of the Jacobi Matrix. This method possesses a few advantageous properties, but is also associated with a number of disadvantages. For example, a smoothness of the calculated articulation path and low wear of the robot drive are attained through minimization of the local articulation position offset &Dgr;q (local energy criteria). In addition, the spacing between the articulation positions and the physical articulation stops is taken into consideration through the optimization of global criteria in the zero space of the Jacobi Matrix. Disadvantages of this method are that it cannot guarantee that path limitations will be maintained with physical articulation stops, and unstable behavior occurs in singular robot positions due to a (generalized) inversion of the Jacobi Matrix, and inefficient robot path courses are possible when conflicting local and global criteria exist.
In another known method, in which a calculation of the transposed Jacobi Matrix is performed, the commanded end-effector destination is attained iteratively corresponding to a representation of reverse kinematics as an optimization problem. An advantageous feature of this method is a stable behavior in singular robot positions, because the Jacobi Matrix is not inverted.
However, there is no guarantee that path limitations can be maintained through physical articulation stops and maximum articulation speeds. Superordinate heuristics must be constructed to meet these requirements, which then results in errors in the real end effector position compared to the desired end effector position. Inefficient path courses result in the form of interference movements of the end effectors, because the Cartesian linear movement commanded by the manual control ball cannot be transferred exactly to the end effector of the manipulator.
Moreover, the robot drive is subjected to high material wear due to abrupt passage through singular robot positions and because of a generally insufficiently smooth articulation path, since neither the weighted local articulation position offset nor the local articulation speed offset (local energy and acceleration criteria) have been optimized. A further negative consequence is a low convergence speed, i.e., a reduced ability to operate in real time, because no practical optimum strategy is known for determining the positively-defined Cartesian stiffness matrix.
DE 33 44 633 C2 describes a real-time control in which the redundant articulations that are not necessary for the movement of an end effector are noted for calculating the articulation speed, which simplifies the calculation of the inverse Jacobi Matrix. This type of calculation is performed for at least one of the articulation combinations. The speeds for each articulation are then determined through averaging of the calculated articulation speeds. A weighting of the articulation speeds thus takes place in this prior art.
U.S. Pat. No. 5,430,643 also describes a real-time method, in which the inverse Jacobi Matrix is calculated. The method known from this U.S. patent document also takes into consideration weight values for the articulation speeds, as well as path limitations for at least a graphic simulation of the robot's movements.
The German patent application 197 03 915.4 and U.S. application Ser. No. 08/017,485 propose a method in which an interactive path guidance of a kinematically redundant manipulator can be performed efficiently, with the advantage of an accordingly less complex and thus more user-friendly parametrization. The only disadvantage of this method is that it is not suitable for force control purposes since no uniform measurement exists to indicate which percentage of the desired end-effector destination shift can be attained; also, the method places a lower priority on attaining the best possible end-effector destination shift.
SUMMARY OF THE INVENTION
It is an object of the invention to provide a method of inverse kinematics command control for an interactive path guidance, and/or as a modular component of a superordinate task (e.g., force control) of a manipulator with an optimized acceleration behavior, with which path limitations can be reliably maintained through physical articulation stops and maximum allowable articulation speeds to ensure the accuracy of the determined solution with respect to the allowable path limitations, and with which the stress on the manipulator drive device is kept to a minimum by optimizing the acceleration behavior of the articulation axes.
In accordance with the invention, which relates to a method of command control for a manipulator of the above type, this object is accomplished in that
a new articulation position (q
i+1
) of the manipulator is calculated, beginning with a commanded end-effector destination shift and the current actual value (q
i
) of the articulation position of the manipulator,
with consideration of a quality function (f(q) ) to be minimized, which is parametrized by non-negative weighting values (a&agr;
j
, &bgr;
j
, &ggr;
j
),
and with consideration of path limitations through physical articulation stops (q
min
, q
max
), maximum articulation speed ({dot over (q)}max), maximum articulation acceleration ({umlaut over (q)}max) in an environment of physical articulation stops, and the kinematic equation, which is represented by the Jacobi Matrix (J (q)), which articulation position predetermines the new values for the articulation regulators, with the quality function (f(q)) being the sum of energy criterion, reference-position criterion, acceleration criterion and an additional criterion,
the energy criterion being calculated from
(q−q
i
)
t
diag(a
j
)(q−q
i
)
the reference-position criterion being calculated from
(q−q
ref
)
t
diag(&bgr;
j
j)(q−q
ref
),
the value q
ref
being a predetermined articulation position value that is determined such that the sequence of calculated articulation position values (q
i
) runs near this reference position value;
the acceleration criterion being calculated from
(q−2q
i−1
)
t
diag(&ggr;
j
)(q−2q
i
+q
i−1
),
and
the additional criterion from −p, with the scalar parameterp satisfying the kinematic equation p·&Dgr;x
d
=J(q
i
(q−q
i
) and the inequality 0≦p≦1; p·100 being the attained percentage of the commanded end-effector destination shift (&Dgr;x
d
),
beginning with an articulation-position value q
i
as the starting point, an allowable optimization vector is determined on the basis of the quality function with respect to all activ

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