Perfecting Periodic Trajectory Tracking: Model Predictive Control with a Periodic Observer ($Π$-MPC)

In Model Predictive Control (MPC), discrepancies between the actual system and the predictive model can lead to substantial tracking errors and significantly degrade performance and reliability. While such discrepancies can be alleviated with more complex models, this often complicates controller design and implementation. By leveraging the fact that many trajectories of interest are periodic, we show that perfect tracking is possible when incorporating a simple observer that estimates and compensates for periodic disturbances. We present the design of the observer and the accompanying tracking MPC scheme, proving that their combination achieves zero tracking error asymptotically, regardless of the complexity of the unmodelled dynamics. We validate the effectiveness of our method, demonstrating asymptotically perfect tracking on a high-dimensional soft robot with nearly 10,000 states and a fivefold reduction in tracking errors compared to a baseline MPC on small-scale autonomous race car experiments.

Dobby: A Conversational Service Robot Driven by GPT-4

This work introduces a robotics platform which embeds a conversational AI agent in an embodied system for natural language understanding and intelligent decision-making for service tasks; integrating task planning and human-like conversation. The agent is derived from a large language model, which has learned from a vast corpus of general knowledge. In addition to generating dialogue, this agent can interface with the physical world by invoking commands on the robot; seamlessly merging communication and behavior. This system is demonstrated in a free-form tour-guide scenario, in an HRI study combining robots with and without conversational AI capabilities. Performance is measured along five dimensions: overall effectiveness, exploration abilities, scrutinization abilities, receptiveness to personification, and adaptability.