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In this paper, we develop a novel and safe control design approach that takes demonstrations provided by a human teacher to enable a robot to accomplish complex manipulation scenarios in dynamic environments. First, an overall task is divided into multiple simpler subtasks that are more appropriate for learning and control objectives. Then, by collecting human demonstrations, the subtasks that require robot movement are modeled by probabilistic movement primitives (ProMPs). We also study two strategies for modifying the ProMPs to avoid collisions with environmental obstacles. Finally, we introduce a rule-base control technique by utilizing a finite-state machine along with a unique means of control design for ProMPs. For the ProMP controller, we propose control barrier and Lyapunov functions to guide the system along a trajectory within the distribution defined by a ProMP while guaranteeing that the system state never leaves more than a desired distance from the distribution mean. This allows for better performance on nonlinear systems and offers solid stability and known bounds on the system state. A series of simulations and experimental studies demonstrate the efficacy of our approach and show that it can run in real time. Note to Practitioners —This paper is motivated by the need to create a teach-by-demonstration framework that captures the strengths of movement primitives and verifiable, safe control. We provide a framework that learns safe control laws from a probability distribution of robot trajectories through the use of advanced nonlinear control that incorporates safety constraints. Typically, such distributions are stochastic, making it difficult to offer any guarantees on safe operation. Our approach ensures that the distribution of allowed robot trajectories is within an envelope of safety and allows for robust operation of a robot. Furthermore, using our framework various probability distributions can be combined to represent complex scenarios in the environment. It will benefit practitioners by making it substantially easier to test and deploy accurate, efficient, and safe robots in complex real-world scenarios. The approach is currently limited to scenarios involving static obstacles, with dynamic obstacle avoidance an avenue of future effort. 

This paper describes a multi-objective ESC strategy that determines Pareto-optimal control parameters to jointly optimize wind turbine loads and power capture. The method uses two optimization objectives calculated in real time: (a) the logarithm of the average power and (b) the logarithm of the standard deviation of a measurable blade load, tower load or the combination of these loads. These two objectives are weighted in real-time to obtain a solution that is Pareto optimal with respect to the power average and the standard deviation of chosen load metric. The method is evaluated using NREL FAST simulations of the 5-MW reference turbine. The results are then evaluated using energy capture over the duration of the simulation and damage equivalent loads (DEL) calculated with MLife.