Matrix Lie groups are an important class of manifolds commonly used in control and robotics, and the optimization of control policies on these manifolds is a fundamental problem. In this work, we propose a new approach for trajectory optimization on matrix Lie groups using an augmented Lagrangian-based constrained Differential Dynamic Programming (DDP). The method involves lifting the optimization problem to the Lie algebra in the backward pass and retracting back to the manifold in the forward pass. In contrast to previous approaches which only addressed constraint handling for specific classes of matrix Lie groups, the proposed method provides a general approach for nonlinear constraint handling for generic matrix Lie groups. We evaluate the effectiveness of the proposed DDP method in handling constraints in a simple mechanical system characterized by rigid body dynamics in SE(3), assessing computational efficiency compared to existing optimization solvers, and optimizing trajectory performance in a realistic quadrotor scenario.

Building machines capable of efficiently collaborating with humans has been a longstanding goal in artificial intelligence. Especially in the presence of uncertainties, optimal cooperation often requires that humans and artificial agents model each other’s behavior and use these models to infer underlying goals, beliefs or intentions, potentially involving multiple levels of recursion. Empirical evidence for such higher-order cognition in human behavior is also provided by previous works in cognitive science, linguistics, and robotics. We advocate for a new paradigm for active learning for human feedback that utilises humans as active data sources while accounting for their higher levels of agency. In particular, we discuss how increasing level of agency results in qualitatively different forms of rational communication between an active learning system and a teacher. Additionally, we provide a practical example of active learning using a higher-order cognitive model. This is accompanied by a computational study that underscores the unique behaviors that this model produces.

Building simulation environments for developing and testing autonomous vehicles necessitates that the simulators accurately model the statistical realism of the real-world environment, including the interaction with other vehicles driven by human drivers. To address this requirement, an accurate human behavior model is essential to incorporate the diversity and consistency of human driving behavior. We propose a mathematical framework for designing a data-driven simulation model that simulates human driving behavior more realistically than the currently used physics-based simulation models. Experiments conducted using the NGSIM dataset validate our hypothesis regarding the necessity of considering the complexity, diversity, and consistency of human driving behavior when aiming to develop realistic simulators.