1. Nonlinear Control of Manipulators

2. Nonlinear and Time-Varying System
Local linearization
Derives linear model that is approximation of the nonlinear equation of an operating point
Well-suited when nonlinearities are not severe
Not well suited for manipulator control problem

3. Nonlinear and Time-Varying System
Linearizing control law
Cancels the nonlinearity so that the overall closed loop system is linear
Partitioned control law
Model-based portion: contains model of the nonlinearity
* feedback linearization
Servo portion: same with the linear control

4. Nonlinear and Time-Varying System
(Example 1)
Open-loop equation
Model-based portion
Servo portion

5. Nonlinear and Time-Varying System
(Example 2)
Open-loop equation
Model-based portion
Servo portion

6. Nonlinear and Time-Varying System
(Example 3)
Open-loop equation
Model-based portion
Servo portion

7. Multi-Input, Multi-Output Control System
MIMO
Model-based portion
Servo portion
☞ linearizing and decoupling

8. Control Problem for Manipulators
Manipulator dynamics
Partitioned control scheme
Model-based
Servo law
: friction terms

9. Control Problem for Manipulators
Practical issues
Time required to compute the model
Inaccuracy in the manipulator model

10. Practical Considerations
Feedforward nonlinear control
Servo law
Inner loop
Run-time
Model based portion
Outside loop
Pre-calculation and stored (offline) => feedforward
Not decoupling control law

11. Practical Considerations
Dual-rate computed-torque implementation
Servo law
Fast rate (250 Hz)
Model based portion
Pre-computed or computed by background processor
Slow rate (60 Hz)
* Computed-torque control