Adaptive and Robust Control

A controller tuned for an empty gripper may struggle once the robot picks up a heavy part. Robust control is designed to work across a range of loads without knowing which one. Adaptive control instead estimates the load as it goes and retunes itself.

Controller Payload picked up at 5 s Adaptation rate

Two strategies

For a mass $m$ tracking $x_d(t)$, with tracking error $e = x - x_d$ and sliding variable $s = \dot e + \lambda e$:

$$\text{Adaptive: } u = \hat m(\ddot x_d - \lambda\dot e) - K s, \quad \dot{\hat m} = -\gamma\,s\,(\ddot x_d - \lambda\dot e) \qquad \text{Robust: } u = \bar m(\ddot x_d - \lambda\dot e) - \eta\,\operatorname{sat}(s/\phi)$$

What to notice

When the payload is added at 5 s, the fixed controller's error jumps and stays large. The robust sliding mode controller holds the error small for any mass in its design range, at the cost of using aggressive, switching effort, which is called chattering. The adaptive controller's error spikes briefly, then shrinks as its mass estimate, the amber line, climbs to the true value. A faster adaptation rate learns quicker but can get jittery with noise.