Konstantin Slutsky

This article presents a formal specification framework for planning and control of autonomous robots, focusing on the challenge of managing complex tradeoffs among multiple potentially conflicting objectives. These include hierarchical relationships and noncomparable objectives, some of which may be too complex to be captured by standard additive cost functions. We leverage the rulebook formalism to represent such objectives and their relationships and formulate two control synthesis problems: single-strategy synthesis, which seeks one optimal strategy, and complete synthesis, which computes the full set of optimal strategies with respect to a rulebook, analogous to the Pareto front in multiobjective planning. We show that our formulation generalizes existing temporal logic-based and optimization-based planning and control, providing a unifying framework across robotics, formal methods, control theory, and operation research. For single-strategy synthesis, we identify tractable subclasses and present a polynomial-time algorithm that accommodates richer combinations of objectives than prior work. For complete synthesis, we introduce an algorithm to compute all optimal solutions and analyze its computational complexity. In both cases, we present case studies that include complex multiobjective planning problems and demonstrate the practical effectiveness of our approach compared to existing methods.

Free Borel $\mathbb{R}^d$Rd-flows are smoothly equivalent if there is a Borel bijection between the phase spaces that maps orbits onto orbits and is a $C^\infty$C∞-smooth orientation preserving diffeomorphism between orbits. We show that all free non-tame Borel $\mathbb{R}^d$Rd-flows are smoothly equivalent in every dimension $d \ge 2$d≥2. This answers a question of B. Miller and C. Rosendal.

We consider the shortest path problem on graphs with weights taking values in Cartesian products of cost monoids. Such cost structures appear in multiobjective planning including, for instance, the minimum-violation planning framework. It is known that these products often do not satisfy the conditions of a cost monoid. Classical dynamic programming graph search algorithms may therefore fail to find an optimal solution. We isolate the concept of a regular cost monoid and propose an iterative search algorithm that finds an optimal path in graphs weighted by products of such costs. Our algorithm allows this class of multiobjective planning problems to be solved in polynomial time.

The behavior of self-driving cars must be compatible with an enormous set of conflicting and ambiguous objectives, from law, from ethics, from the local culture, and so on. This paper describes a new way to conveniently define the desired behavior for autonomous agents, which we use on the self-driving cars developed at nuTonomy. We define a "rulebook" as a pre-ordered set of "rules", each akin to a violation metric on the possible outcomes ("realizations"). The rules are partially ordered by priority. The semantics of a rulebook imposes a pre-order on the set of realizations. We study the compositional properties of the rulebooks, and we derive which operations we can allow on the rulebooks to preserve previously-introduced constraints. While we demonstrate the application of these techniques in the self-driving domain, the methods are domain-independent.

Any free Borel flow is shown to admit a cross section with only two possible distances between adjacent points. Non smooth flows are proved to be Lebesgue orbit equivalent if and only if they admit the same number of invariant ergodic probability measures.

The main result of the paper is classification of free multidimensional Borel flows up to Lebesgue Orbit Equivalence, by which we understand an orbit equivalence that preserves the Lebesgue measure on each orbit. Two non smooth Euclidean flows are shown to be Lebesgue Orbit Equivalence if and only if they admit the same number of invariant ergodic probability measures.