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We propose a new concept named subschedulability to relax schedulability conditions on task sets in the context of scheduling and control co-design. Subschedulability is less conservative compared to schedulablity requirement with respect to network utilization. But it can still guarantee that all tasks can be executed before or within a bounded time interval after their deadlines. Based on the subschedulability concept, we derive an analytical timing model to check the sub-schedulability and perform online prediction of time-delays caused by real-time scheduling. A modified event-triggered contention-resolving MPC is presented to co-design the scheduling and control for the sub-schedulable control tasks. Simulation results are demonstrated to show the effectiveness of the proposed method. 

We analyze a human and multi-robot collaboration system and propose a method to optimally schedule the human attention when a human operator receives collaboration requests from multiple robots at the same time. We formulate the human attention scheduling problem as a binary optimization problem which aims to maximize the overall performance among all the robots, under the constraint that a human has limited attention capacity. We first present the optimal schedule for the human to determine when to collaborate with a robot if there is no contention occurring among robots' collaboration requests. For the moments when contentions occur, we present a contention-resolving Model Predictive Control (MPC) method to dynamically schedule the human attention and determine which robot the human should collaborate with first. The optimal schedule can then be determined using a sampling based approach. The effectiveness of the proposed method is validated through simulation that shows improvements.