This paper addresses the feasibility of virtual holonomic constraints (VHCs) in the context of motion planning for underactuated mechanical systems with a single degree of underactuation. While existing literature has established a widely accepted definition of VHC, we argue that this definition is overly restrictive and excludes a broad class of admissible trajectories from consideration. To illustrate this point, we analyze a periodic motion of the Planar Vertical Take-Off and Landing (PVTOL) aircraft that satisfies all standard motion planning requirements, including orbital stabilizability. However, for this solution -- as well as for a broad class of similar ones -- there exists no VHC that satisfies the conventional definition. We further provide a formal proof demonstrating that the conditions imposed by this definition necessarily fail for a broad class of trajectories of mechanical systems. These findings call for a reconsideration of the current definition of VHCs, with the potential to significantly broaden their applicability in motion planning.

The problem of realizing rotary propeller motion of a devil-stick in the vertical plane using forces purely normal to the stick is considered. This problem represents a nonprehensile manipulation task of an underactuated system. In contrast with previous approaches, the devil-stick is manipulated by controlling the normal force and its point of application. Virtual holonomic constraints are used to design the trajectory of the center-of-mass of the devil-stick in terms of its orientation angle, and conditions for stable propeller motion are derived. Intermittent large-amplitude forces are used to asymptotically stabilize a desired propeller motion. Simulations demonstrate the efficacy of the approach in realizing stable propeller motion without loss of contact between the actuator and devil-stick.

The problem of designing and stabilizing impact-free, energy-conserving gaits is considered for underactuated, point-foot planar bipeds. Virtual holonomic constraints are used to design energy-conserving gaits. A desired gait corresponds to a periodic hybrid orbit and is stabilized using the Impulse Controlled Poincar\'e Map approach. Numerical simulations for the case of a five-link biped demonstrate convergence to a desired gait from arbitrary initial conditions.

In this work, we present a flexible method for explaining, in human readable terms, the predictions made by decision trees used as decision support in liver transplantation. The decision trees have been obtained through machine learning applied on a dataset collected at the liver transplantation unit at the Coru\~na University Hospital Center and are used to predict long term (five years) survival after transplantation. The method we propose is based on the representation of the decision tree as a set of rules in a logic program (LP) that is further annotated with text messages. This logic program is then processed using the tool xclingo (based on Answer Set Programming) that allows building compound explanations depending on the annotation text and the rules effectively fired when a given input is provided. We explore two alternative LP encodings: one in which rules respect the tree structure (more convenient to reflect the learning process) and one where each rule corresponds to a (previously simplified) tree path (more readable for decision making).

Virtual coaching has rapidly evolved into a foundational component of modern clinical practice. At a time when healthcare professionals are in short supply and the demand for low-cost treatments is everincreasing, virtual health coaches (VHCs) offer intervention-ondemand for those limited by finances or geographic access to care. More recently, AIpowered virtual coaches have become a viable complement to human coaches. However, the push for AIpowered coaching systems raises several important issues for researchers, designers, clinicians, and patients. In this paper, we present a novel Figure 1: The figure shows four main domains of a successful framework to guide the design and development of virtual coaching virtual health coach throughout a data science pipeline.