## 1.1 TRAJECTORY CONTROL

• Given a set of points, we must move at given speeds.

### 1.1.1 Resolved Rate Motion Control

• When the robot motion is important (such as welding applications), the resolved rate method may be useful

• This method requires a good model of the manipulator.

• The figure below shows an incremental interpolator, based on resolved rate motion control. ### 1.1.2 Cartesian Motion System

• The figure below illustrates a system for making motions in cartesian space (straight line). ### 1.1.3 Model Reference Adaptive Control (MRAC)

• To compensate for overly complex, or changing systems we can use an adaptive controller ### 1.1.4 Digital Control System

• It is more common to use computers to control operations • The computer must examine sensors, then decide how to change outputs to actuators. But, computers can only do one thing at once, so the approach is limited by CPU speed.

• Note the controlling computer still needs a control algorithm such as PID, resolved rate, MRAC, etc.

• e.g. to control a simple robotic arm with proportional control • Some sensors, such as encoders can return binary numbers to the computer, instead of analog voltages, this leads to more accurate, noise resistant position measurements.

• The main functions of the control computer are,

1. plans and interpolates a path from the start, to the endpoint in world coordinates.

2. Transforms path points from world to joint coordinates

3. Receives a signal about a completed move, and signals next moves on a path.

4. Executes other motions, not directly driving motion.

• There are two servo loops for each joint,

- the inner loop may consist of an amplifier (voltage or current), a joint drive, and a tachometer for velocity feedback.

- the outer loop may consist of incremental encoder, counter or microprocessor,

- Microprocessor samples the contents of the counter (equal to the BRUs) and transfers this to the computer. The computer compares the counter contents with a program reference to produce the system error. The error signal is fed each ms (for example) to a D/A converter which supplies a voltage proportional to the required axis velocity.

• Advantages,

- complex calculations for control are possible

- software is easy to change for new control laws

- the controller can be adapted easily to new operating conditions

- the computer does not need retuning, reducing the amount of maintenance required

- faults can be easily detected

• Disadvantages,

- the computer may be unable to calculate fast enough

- the computer is generally less reliable