This paper presents a formal specification framework for planning and control of autonomous robots, focusing on the challenge of managing complex trade-offs among multiple, potentially conflicting objectives. These include hierarchical relationships and non-comparable objectives, some of which may be too complex to be captured by standard additive cost functions. We leverage therulebookformalism 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 multi-objective 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 operations research. For single-strategy, 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 multi-objective planning problems and demonstrate the practical effectiveness of our approach compared to existing methods.

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, an Aptiv company. 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.

Abstract A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In particular, any completely metrizable group topology on a free product is discrete.

Abstract We show that every two-dimensional class of topological similarity, and hence every diagonal conjugacy class of pairs, is meager in the group of order preserving bijections of the rationale and in the group of automorphisms of the ordered rational Urysohn space.