Multi-Pendulum Synchronization Using Constrained Agreement Protocols

Abstract

This paper considers the problem of coordinating multiple pendula attached to mobile bases. In particular, the pendula should move in such a way that their motion is synchronized, which calls for two problems to be solved simultaneously, namely a constrained optimal control problem for each pendulum, and a constrained agreement problem across the network of pendula. A novel way of manipulating the initial conditions in the consensus equation is presented that will solve the latter of these problems, and simulation results are presented that support the viability of the proposed approach.

Less Is More: Mixed-Initiative Model-Predictive Control With Human Inputs

“…We will formulate task completion in terms of making the system reach a set of target states X f ⊂ R n , and achieving this with direct human control may, for a various of reasons, not be feasible, desirable, or necessary. This part of the task will thus be offloaded to an automatic controller, as proposed in [20]. The problem we address in this paper is ultimately to devise a controller that drives the system in such a way that both the state constraints are satisfied (low-level task) and the human operator's "intentions" for the system behavior (high-level task) are respected as much as possible.…”

Human-in-the-Loop: Terminal constraint receding horizon control with human inputs

“…However, if part of the task is to satisfy certain linear state constraints, commanding the system to do so may not be a trivial task. On the other hand, it is certainly possible to design an automatic controller that can handle the task of satisfying linear state constraints, as in [8]. However, the problem we wish to address in this paper is to implement a controller that drives the system in such a way that both the state constraint is satisfied and the human operators intentions for the system behavior are respected as much as possible.…”

“…In order to demonstrate the viability of the presented problem formulation and optimal control law, we apply the control law to a MATLAB simulation of the two masscart-pendula synchronization problem, as discussed in [8]. However, in this problem, a human operator is issuing force commands to one mass-cart-pendulum, while another human issues commands to the other.…”