Robot control utilizing cubic spline interpolation

A method of providing joint trajectories between joint space target points to achieve end effector motion of a computer controlled articulated robot manipulator responsive to feedrate commands comprising the steps of:

• tying a polynomial representing a spline between each consecutive pair of joint space target points using a normalized time which decreases to zero at the end point of each spline;
• providing the coefficients of each of the polynomials to an interpolator;
• providing the time desired for the robot joint to move from one joint space target point to the next to the interpolator;
• determining how many times a position command can be generated along each spline in the time desired for the robot joint to move from one joint space target point to the next;
• determining a fractional time which is the reciprocal of the number of times the position command can be generated;
• changing the fractional time in direct proportional to the feedrate command;
• subtracting the fractional time from the remaining normalized time each time the position command is to be generated;
• generating position commands repeatedly using the gradually decreasing normalized time;
• setting the normalized time equal to zero when the normalized time remaining is less than the fractional time;
• generating the final position command of each of the splines using a normalized time of zero;
• and
• sending the position commands position as they are generated to the servo control associated with the robot joint, to control robot joint motion.

A method of providing joint trajectories between joint space target points to achieve end effector motion of a computer controlled articulated robot manipulator comprising the steps of:

• reading a first block of points comprising at least three consecutive target points along the desired joint trajectory;
• determining an initial estimate of the slope at the block end point by tying the next to the last point and the last point of the block with a quadratic polynomial;
• reading the next block of points comprising at least three consecutive target points along the desired joint trajectory, said next block having as a first point the next to the last point of the first block, the second point of the next block is the same as the last point of the first block, whereby the two blocks overlap;
• improving the estimate of the slope at the end point of the first block by splining a polynomial between the next to the last point in the first block and the second point in the next block and splining a polynomial between the second and third point in the next block, with continuity in acceleration at the first block end point;
• providing the coefficients of the polynomial tying the first and second points in the next block to an interpolator;
• providing the time desired for the robot joint to move from the first and second point in the next block;
• generating position commands in the interpolator periodically, between the first and second point of the next block;
• and
• sending the position commands to the servo control associated with a robot joint to control the robot joint motion.