2D Behavior Models for Adjusting Quadratic-Cost Weightings and Directly Tuning Gains

Formal design procedures for choosing Q and R weighting matrices in a linear quadratic regulator, or a related quadratic optimization, typically provide only a starting point in an iterative applied design procedure for identifying a solution that will best trade off all the real-world objectives while meeting constraints. Furthermore, directly tuning the control gains about an optimal control solution may also provide a practical way of finding a solution that better meets real-world trade-offs, especially useful for applications where one would like real-time tuning for changing situations. When exploring the effects of more than two design parameters, whether they be cost-functional weightings and/or control gains, people may resort to trial and error in the (generally) high-dimensional space. Instead, this paper presents a way to explore large parts of the solution space by adjusting or tuning only two portion parameters. Moreover, we can easily understand the effects of changing the two portions by drawing parallels between robot and human behavior; thus this work refers to the portions as behavior traits. The two traits adjust the cost-functional weightings in the proposed general behavior model. In the proposed specific behavior model, the traits tune the control gains directly. The methods limit the exploration to the space of near-optimal solutions, which should allow even an untrained operator to safely adjust a control system in real-time in an appealingly intuitive manner. Simulations show how this applied design procedure would work for optimal and near-optimal designs of a nonlinear control for a single robot link. A discussion draws parallels to understandings of human behavior, with the aim of providing a path to easing human-machine interactions.