Aradhana Nayak

Aradhana Nayak, Ravi N. Banavar

Almost-global orientation trajectory tracking for a rigid body with external actuation has been well studied in the literature, and in the geometric setting as well. The tracking control law relies on the fact that a rigid body is a simple mechanical system (SMS) on the $3-$dimensional group of special orthogonal matrices. However, the problem of designing feedback control laws for tracking using internal actuation mechanisms, like rotors or control moment gyros, has received lesser attention from a geometric point of view. An internally actuated rigid body is not a simple mechanical system, and the phase-space here evolves on the level set of a momentum map. In this note, we propose a novel proportional integral derivative (PID) control law for a rigid body with $3$ internal rotors, that achieves tracking of feasible trajectories from almost all initial conditions.

Aradhana Nayak, Ravi N. Banavar

Tracking the unactuated configuration variable in an underactuated system, in a global sense, has not received much attention. Here we present a scheme to do so for a pendubot - a two link robot actuated only at the first link. We propose a control law for almost-global asymptotic tracking (AGAT) of a smooth reference trajectory for the unactuated second joint of the pendubot. The control law achieves almost-global tracking for any smooth reference trajectory specified for the unactuated joint. Further, we generalize the proposed scheme to an n-link system with as many (or more) degrees of actuation than unactuation, and show that the result holds.

Lorenzo Baraldi, Zifan Zeng, Chongzhe Zhang et al.

The rapid progress in embodied artificial intelligence has highlighted the necessity for more advanced and integrated models that can perceive, interpret, and predict environmental dynamics. In this context, World Models (WMs) have been introduced to provide embodied agents with the abilities to anticipate future environmental states and fill in knowledge gaps, thereby enhancing agents' ability to plan and execute actions. However, when dealing with embodied agents it is fundamental to ensure that predictions are safe for both the agent and the environment. In this article, we conduct a comprehensive literature review of World Models in the domains of autonomous driving and robotics, with a specific focus on the safety implications of scene and control generation tasks. Our review is complemented by an empirical analysis, wherein we collect and examine predictions from state-of-the-art models, identify and categorize common faults (herein referred to as pathologies), and provide a quantitative evaluation of the results.

Aradhana Nayak, Ravi Banavar

In this article, we propose a control law for almost-global asymptotic tracking (AGAT) of a smooth reference trajectory for a fully actuated simple mechanical system (SMS) evolving on a Riemannian manifold which can be embedded in a Euclidean space. The existing results on tracking for an SMS are either local, or almost-global, only in the case the manifold is a Lie group. In the latter case, the notion of a configuration error is naturally defined by the group operation and facilitates a global analysis. However, such a notion is not intrinsic to a Riemannian manifold. In this paper, we define a configuration error followed by error dynamics on a Riemannian manifold, and then prove AGAT. The results are demonstrated for a spherical pendulum which is an SMS on $S^2$ and for a particle moving on a Lissajous curve in $\mathbb{R}^3$.