A minimum attention control law for ball catching

Area of Science:

• Robotics and Control Systems
• Computational Neuroscience
• Applied Mathematics

Background:

• Digital control systems often require high levels of discretization, increasing computational load and implementation costs.
• Quantifying 'control attention' is crucial for optimizing control laws, with rate of change concerning state and time being a key metric.
• Existing control strategies may not adequately address efficiency and robustness in discretized environments.

Purpose of the Study:

• To develop and present an attention-minimizing control law for target tracking tasks, specifically ball catching.
• To quantitatively measure and minimize the 'attention' of a control law using Brockett's attention criterion.
• To explore the connection between this attention criterion and established principles in human motor control.

Main Methods:

• Derivation of a Linear Quadratic Regulator (LQR)-based minimum attention tracking control law.
• Assumption of optimal control as a sum of linear time-varying feedback and time-varying feedforward terms.
• Efficient optimization over symmetric positive-definite matrices for control law computation.

Main Results:

• The derived control law is stable and efficient to compute.
• Numerical experiments on ball catching demonstrated familiar human motor control features, like open-loop to closed-loop transitions.
• The attention-minimizing control law showed improved robustness against spatiotemporal discretization.

Conclusions:

• The developed control law effectively minimizes attention, reducing implementation costs and enhancing robustness.
• The findings align with theories of human motor control in tasks like ball catching.
• The control laws are generalizable to various tracking problems, especially those with limited communication resources.