Basak Sakcak

Vadim Weinstein, Basak Sakcak, Steven M. LaValle

We formulate five basic tenets of enactivist cognitive science that we have carefully identified in the relevant literature as the main underlying principles of that philosophy. We then develop a mathematical framework to talk about cognitive systems (both artificial and natural) which complies with these enactivist tenets. In particular we pay attention that our mathematical modeling does not attribute contentful symbolic representations to the agents, and that the agent's brain, body and environment are modeled in a way that makes them an inseparable part of a greater totality. The purpose is to create a mathematical foundation for cognition which is in line with enactivism. We see two main benefits of doing so: (1) It enables enactivist ideas to be more accessible for computer scientists, AI researchers, roboticists, cognitive scientists, and psychologists, and (2) it gives the philosophers a mathematical tool which can be used to clarify their notions and help with their debates. Our main notion is that of a sensorimotor system which is a special case of a well studied notion of a transition system. We also consider related notions such as labeled transition systems and deterministic automata. We analyze a notion called sufficiency and show that it is a very good candidate for a foundational notion in the "mathematics of cognition from an enactivist perspective". We demonstrate its importance by proving a uniqueness theorem about the minimal sufficient refinements (which correspond in some sense to an optimal attunement of an organism to its environment) and by showing that sufficiency corresponds to known notions such as sufficient history information spaces. We then develop other related notions such as degree of insufficiency, universal covers, hierarchies, strategic sufficiency. In the end, we tie it all back to the enactivist tenets.

Basak Sakcak, Kalle G. Timperi, Vadim Weinstein et al.

This paper addresses the lower limits of encoding and processing the information acquired through interactions between an internal system (robot algorithms or software) and an external system (robot body and its environment) in terms of action and observation histories. Both are modeled as transition systems. We want to know the weakest internal system that is sufficient for achieving passive (filtering) and active (planning) tasks. We introduce the notion of an information transition system for the internal system which is a transition system over a space of information states that reflect a robot's or other observer's perspective based on limited sensing, memory, computation, and actuation. An information transition system is viewed as a filter and a policy or plan is viewed as a function that labels the states of this information transition system. Regardless of whether internal systems are obtained by learning algorithms, planning algorithms, or human insight, we want to know the limits of feasibility for given robot hardware and tasks. We establish, in a general setting, that minimal information transition systems exist up to reasonable equivalence assumptions, and are unique under some general conditions. We then apply the theory to generate new insights into several problems, including optimal sensor fusion/filtering, solving basic planning tasks, and finding minimal representations for modeling a system given input-output relations.

Kshitij Tiwari, Basak Sakcak, Prasanna Routray et al.

This paper introduces mathematical models of \sensors\ for mobile robots based on visibility. Serving a purpose similar to the pinhole camera model for computer vision, the introduced models are expected to provide a useful, idealized characterization of task-relevant information that can be inferred from their outputs or observations. Possible tasks include navigation, localization and mapping when a mobile robot is deployed in an unknown environment. These models allow direct comparisons to be made between traditional depth sensors, highlighting cases in which touch sensing may be interchangeable with time of flight or vision sensors, and characterizing unique advantages provided by touch sensing. The models include contact detection, compression, load bearing, and deflection. The results could serve as a basic building block for innovative touch sensor designs for mobile robot sensor fusion systems.

Aref Amiri, Basak Sakcak, Steven M. LaValle

This paper presents a framework for safe navigation of a unicycle point robot to a goal position in an environment populated with obstacles from almost any admissible state, considering input limits. We introduce a novel QP formulation to create a Cinfinity-smooth vector field with reduced total bending and total turning. Then we design an analytic, non-linear feedback controller that inherently satisfies the conditions of Nagumo's theorem, ensuring forward invariance of the safe set without requiring any online optimization. We have demonstrated that our controller, even under hard input limits, safely converges to the goal position. Simulations confirm the effectiveness of the proposed framework, resulting in a twice faster arrival time with over 50\% lower angular control effort compared to the baseline.

Markku Suomalainen, Basak Sakcak, Adhi Widagdo et al.

We propose unwinding the rotations experienced by the user of an immersive telepresence robot to improve comfort and reduce VR sickness of the user. By immersive telepresence we refer to a situation where a 360\textdegree~camera on top of a mobile robot is streaming video and audio into a head-mounted display worn by a remote user possibly far away. Thus, it enables the user to be present at the robot's location, look around by turning the head and communicate with people near the robot. By unwinding the rotations of the camera frame, the user's viewpoint is not changed when the robot rotates. The user can change her viewpoint only by physically rotating in her local setting; as visual rotation without the corresponding vestibular stimulation is a major source of VR sickness, physical rotation by the user is expected to reduce VR sickness. We implemented unwinding the rotations for a simulated robot traversing a virtual environment and ran a user study (N=34) comparing unwinding rotations to user's viewpoint turning when the robot turns. Our results show that the users found unwound rotations more preferable and comfortable and that it reduced their level of VR sickness. We also present further results about the users' path integration capabilities, viewing directions, and subjective observations of the robot's speed and distances to simulated people and objects.

Basak Sakcak, Luca Bascetta, Gianni Ferretti et al.

This paper proposes a novel sampling-based motion planner, which integrates in RRT* (Rapidly exploring Random Tree star) a database of pre-computed motion primitives to alleviate its computational load and allow for motion planning in a dynamic or partially known environment. The database is built by considering a set of initial and final state pairs in some grid space, and determining for each pair an optimal trajectory that is compatible with the system dynamics and constraints, while minimizing a cost. Nodes are progressively added to the tree of feasible trajectories in the RRT* algorithm by extracting at random a sample in the gridded state space and selecting the best obstacle-free motion primitive in the database that joins it to an existing node. The tree is rewired if some nodes can be reached from the new sampled state through an obstacle-free motion primitive with lower cost. The computationally more intensive part of motion planning is thus moved to the preliminary offline phase of the database construction {at the price of some performance degradation due to gridding. Grid resolution can be tuned so as to compromise between (sub)optimality and size of the database. The planner is shown to be }asymptotically optimal as the grid resolution goes to zero and the number of sampled states grows to infinity.