Method of command control for a robot manipulator

The method according to claim I wherein, starting from a commanded end-effector destination shift Δxc:=(Δxt,Δxr) at a time Ti, wherein and Δxtε 3 and Δxrε 3 each represent, respectively translational and rotational components of the commanded end-effector destination shift;

• Δxlmax and Δxrmax, respectively each define a maximum scalar-value Cartesian position offset of the end effector per sample time ΔT, a desired Cartesian translational or rotational end-effector destination shift Δxld is given by:
• Δ ⁢ ⁢ x t d := { Δ ⁢ ⁢ x t if ⁢ ⁢ [LeftBracketingBar] Δ ⁢ ⁢ x t [RightBracketingBar] ≤ Δ ⁢ ⁢ x t max Δ ⁢ ⁢ x t ⁢ [LeftBracketingBar] Δ ⁢ ⁢ x t [RightBracketingBar] Δ ⁢ ⁢ x t max otherwise ⁢ ⁢ Δ ⁢ ⁢ x r d := { Δ ⁢ ⁢ x r if ⁢ ⁢ [LeftBracketingBar] Δ ⁢ ⁢ x r [RightBracketingBar] ≤ Δ ⁢ ⁢ x r max Δ ⁢ ⁢ x r ⁢ [LeftBracketingBar] Δ ⁢ ⁢ x r [RightBracketingBar] Δ ⁢ ⁢ x r max otherwise ,
• wherein quantity |x| of a vector x is determined by a Euclidian norm [LeftBracketingBar] x [RightBracketingBar] := ( ∑ i ⁢ x i 2 ) ,
• and whereby the desired end-effector destination shift is given by Δxd:
• =(Δxld,Δxrd);
• and wherein the criteria, energy criteria, reference-position criteria, and acceleration criteria, are weighted according to prevalent problem-specific requirements by allocating three predetermined numerical values αj, βj, γj , to each axis j, the value αj serving in the weighting of an energy criterion that evaluates a difference between two adjacent, calculated articulation positions of axis j;
• and the value βj serving in weighting of a criterion that evaluates deflection of the predetermined articulation position qj from a reference value qref,j, and the value γj serving in the weighting of a criterion which evaluates acceleration behavior in form of an articulation speed offset of the articulation axis qj, which is predetermined by the operator as are the physical articulation stops qmin, qmax of the manipulator, which relate to path limitations, and the articulation speed limitations {dot over (q)}max and the articulation acceleration limitations {umlaut over (q)}max,
• and wherein, upon an attainment of output value;
• an allowable optimum articulation position offset Δqi is calculated for a desired end-effector destination shift Δxdi at the time Ti−1 during the time interval ΔT, via an algorithm of inverse kinematics progressing during an initialization phase and a subsequent optimization phase, whereby a desired value is provided to articulation regulators from qsolli+1:=qsolli+Δqi and the articulation regulators are correspondingly shifted with qsolli during the time interval ΔT, and
• wherein an allowable articulation position offset comprises the articulation position value being updated with Δq to satisfy the physical articulation stops qmin, qmax corresponding to qmin≦qsoll+Δq≦qmax and wherein Δq satisfies the articulation speed limitations {dot over (q)}max corresponding to |Δqi|≦{dot over (q)}maxΔT;
• and
• wherein the limitations of the articulation accelerations during an approach of articulation positions to the physical articulation stops are maintained reliably, and the type of optimum quality of Δqi os determined by an operator through the quality-criterion weighting α, β, γ;
• and
• wherein the sampling time ΔT corresponding to ΔT≧max (Δtq, Δtr) is dimensioned such that the computation time Δtq for calculating an optimum allowable articulation position offset Δq and the adjustment time Δtr, which the regulators require for adapting the axial positions to the desired values qsoll lies within the time span ΔT.

An apparatus for controlling a robot, in an environment of robotic physical motion limits, to move a point on the robot from a current first position vector qi to a second position vector qi+1;

• wherein the robot has ndof robotic joint articulations or degrees of freedom;
• the apparatus comprising:
• a computer including software and being coupled to the robot and to an input device for inputting a control command to the computer, the command further comprising a desired end-effect destination shift Δxd, and
• wherein the software solves a kinematic equation based on use of a Jacobi Matrix J(q) having ndof columns to perform a calculation the second position vector qi+1 from the inputted destination shift Δxd and the first position vector qi;
• the calculation further comprising:
• (a) calculating a scalar energy criterion
• (q−qi)T diag(αj(q−qi)
• wherein αj are first non-negative weighting values and j=1, . . . , ndof;
• calculating a scalar reference-position deflection criterion
• (q−qphf ref)T diag(βj)(q−qref)
• wherein βj are second non-negative weighting values and j=1, . . . , ndof and qref is an articulation reference position value that is predetermined such that a sequence of the position vectors qi runs near this reference position value;
• calculating a scalar acceleration criterion
• (q−2qi+q1−1)T diag(γj)(q−2qi+qi−1)
• wherein γj are third non-negative weighting values and j=1, . . . ndof;
• calculating an additional criterion further comprising the negative of a scalar parameter p satisfying a kinematic equation
• p·Δxd=J(qi) (q−qi)
• and an inequality 0≦p≦1, whereby p is an attained fraction of the commanded end- effect destination shift Δxd;
• and
• (b) summing the energy criterion, the reference-position criterion, the acceleration criterion, and the additional criterion to obtain a scalar quality function f(q);
• (c) determining secondary conditions comprising the kinematic equation, the inequality 0≦p≦1, physical path limitations qmin and qmax, a maximum articulation speed qmax, and a maximum articulation acceleration qmax;
• (d) starting from the first position vector qi, iteratively repeating optimization steps to obtain a series of intermediate position vectors, the optimization steps further comprising:
• (d1) determining the active and inactive secondary conditions in the intermediate position vector;
• (d2) taking a gradient of the quality function f(q) to obtain an optimization vector oriented in a descent direction of the quality function f(q);
• (d3) projecting the optimization vector in a tangent space of active secondary conditions, whereby the optimization vector is orthogonal to a set of gradients of active secondary constraint conditions;
• (d4) scaling a magnitude of the optimization vector according to a set of inactive secondary constraint conditions to obtain a scaled optimization vector;
• (d5) obtaining a sum vector by adding the scaled optimization vector to the intermediate position vector;
• and
• (d6) evaluating the sum vector to determine if the sum vector lies generally at a minimum of the quality function;
• and
• (d7) if the sum vector does not lie generally at the minimum, then
• repeating the optimization steps starting from a new intermediate vector equal to the sum vector plus the preceding intermediate vector;
• and
• (e) if the sum vector lies generally at the minimum, then outputting to the robot the second position vector qi+1.

In a method of command control, by a programmer, for interactive path guidance of a kinematically-redundant manipulator based on end-effector destination shifts from the programmer, in connection with a calculation of articulated-position values according to an algorithm of inverse kinematics, the method including steps of:

• providing a manual control device;
• calculating a new articulation position (qi+i) from an end-effector destination shift command from the control device and a current articulation position actual value (qi) of the manipulator;
• the calculating step including as calculating factors a quality function (f(q)), which is parametrized by non-negative weighting values (αj, βj) and path limitations through physical articulation stops (qmin, qmax), a maximum articulation speed ({dot over (q)}max), and a kinematic equation represented by the Jacobi Matrix;
• calculating an energy criterion from
• (q−qi)t diag(αj)(q−qi);
• calculating a reference-position criterion from
• (qref)t diag(βi)·(q−qref);
• predetermining by the new articulation position new values for an articulation regulator, with the quality function being a sum of the energy criterion and the reference-position criterion;
• determining a value qref as a predetermined articulation-position value such that a sequence of calculated articulation-position values (qi) runs near a value of the reference-position criterion;
• determining an allowable optimization vector, beginning with one of the articulation-position values qi as a starting point, on the basis of the quality function with respect to all active secondary conditions that indicate which path limitations have been attained;
• scaling the allowable optinization vector according to inactive secondary conditions that indicate which path limitations have not been attained;
• adding the scaled optimization vector to the articulation-position value calculated in the previous step of the iteration;
• and
• evaluating an optimum quality of the articulation-position values based on the quality function and the secondary conditions activated in the newly-calculated articulation position;
• the improvement wherein:
• the non-negative weighting values include a weighting value γj;
• the calculating factors include a maximum articulation acceleration (qmax);
• the calculating step includes calculating an acceleration criterion from
• (−2qi−qi−1)t diag(γi)·(q−2qi−qi−1);
• and
• calculating an additional criterion further comprising the negative of a scalar parameter p satisfying a kinematic equation
• p·Δxd=J(qi) (q−qi)
• and an inequality 0≦p≦1, whereby p is an attained fraction of a commanded end-effector destination shift Δxd.