DEVELOPMENT OF A NEW SOLUTION METHOD FOR ROBOT KINEMATIC EQUATIONS

A NEW TECHNIQUE FOR SOLVING ROBOT KINEMATIC EQUATIONS WILL BE DEVELOPED WHICH WILL RESULT IN A CLOSED FORM EXPRESSION FOR THE JOINT COORDINATES AS FUNCTIONS OF END EFFECTOR POSITION AND ORIENTATION. THE TECHNIQUE IS NEITHER INTERATIVE NOR ANALYTIC. THE JOINT COORDINATES WILL BE MODELED AS NONLINEAR FUNCTIONS OF THE DESIRED POSITION AND ORIENTATION OF THE END EFFECTOR IN OBJECT SPACE. GIVEN ONLYEMPERICAL DATA ON JOINT COORDINATES FOR A SET OF CALIBRATIONPOINTS SPANNING THE SPACE OF A ROBOT'S WORK ENVELOPE, THE MODELS WILL ENABLE CALCULATION OF THE JOINT COORDINATES FOR ANY DESIRED OBJECT SPACE POSITION AND ORIENTATION. THIS ALGORITHM WILL NOT REQUIRE DERIVATION OF THE ROBOT'S KINEMATIC EQUATIONS OR ANY A PRIOR KNOWLEDGE OF THE REFERENCE COORDINATE SYSTEM OR END EFFECTOR IN USE. ONCE THE MODELS ARE DERIVED, EACH JOINT COORDINATE WILL REQUIRE ONLY ONE FUNCTION EVALUATION AND NO TRANSCENDENTAL FUNCTION CALLS. THE FUNCTIONS WILL BE DIFFERENTIABLE, ENABLING CALCULATION OF JOINT VELOCITIES GIVEN END EFFECTOR VELOCITY.THE ALGORITHM MAY ENABLE MORE SOPHISTICATED ROBOT DESIGN BY PROVIDING CLOSED FORM SOLUTIONS FOR ARCHITECTURES WHICH ARE TOO COMPLEX TO SOLVE USING EXISTING ANALYTIC TECHNIQUES.IT MAY ALSO PROVIDE A SIMPLE METHOD FOR MODELING FLEXIBLE MANIPULATORS AND MANUFACTURING ERRORS SUCH AS THE MISALIGNMENT OF AXES AND ORIGIN TRANSLATION.