Maximum Hands-Off Control: A Paradigm of Control Effort Minimization

In this paper, we propose a new paradigm of control, called a maximum hands-off control. A hands-off control is defined as a control that has a short support per unit time. The maximum hands-off control is the minimum support (or sparsest) per unit time among all controls that achieve control objectives. For finite horizon control, we show the equivalence between the maximum hands-off control and L1-optimal control under a uniqueness assumption called normality. This result rationalizes the use of L1 optimality in computing a maximum hands-off control. We also propose an L1/L2-optimal control to obtain a smooth hands-off control. Furthermore, we give a self-triggered feedback control algorithm for linear time-invariant systems, which achieves a given sparsity rate and practical stability in the case of plant disturbances. An example is included to illustrate the effectiveness of the proposed control.Comment: IEEE Transactions on Automatic Control, 2015 (to appear

Characterization of maximum hands-off control

Maximum hands-off control aims to maximize the length of time over which zero actuator values are applied to a system when executing specified control tasks. To tackle such problems, recent literature has investigated optimal control problems which penalize the size of the support of the control function and thereby lead to desired sparsity properties. This article gives the exact set of necessary conditions for a maximum hands-off optimal control problem using an $L_0$-(semi)norm, and also provides sufficient conditions for the optimality of such controls. Numerical example illustrates that adopting an $L_0$ cost leads to a sparse control, whereas an $L_1$-relaxation in singular problems leads to a non-sparse solution.Comment: 6 page

Real Time Animation of Virtual Humans: A Trade-off Between Naturalness and Control

Virtual humans are employed in many interactive applications using 3D virtual environments, including (serious) games. The motion of such virtual humans should look realistic (or ‘natural’) and allow interaction with the surroundings and other (virtual) humans. Current animation techniques differ in the trade-off they offer between motion naturalness and the control that can be exerted over the motion. We show mechanisms to parametrize, combine (on different body parts) and concatenate motions generated by different animation techniques. We discuss several aspects of motion naturalness and show how it can be evaluated. We conclude by showing the promise of combinations of different animation paradigms to enhance both naturalness and control