Autonomous vehicles must often contend with conflicting planning requirements, e.g., safety and comfort could be at odds with each other if avoiding a collision calls for slamming the brakes. To resolve such conflicts, assigning importance ranking to rules (i.e., imposing a rule hierarchy) has been proposed, which, in turn, induces rankings on trajectories based on the importance of the rules they satisfy. On one hand, imposing rule hierarchies can enhance interpretability, but introduce combinatorial complexity to planning; while on the other hand, differentiable reward structures can be leveraged by modern gradient-based optimization tools, but are less interpretable and unintuitive to tune. In this paper, we present an approach to equivalently express rule hierarchies as differentiable reward structures amenable to modern gradient-based optimizers, thereby, achieving the best of both worlds. We achieve this by formulating rank-preserving reward functions that are monotonic in the rank of the trajectories induced by the rule hierarchy; i.e., higher ranked trajectories receive higher reward. Equipped with a rule hierarchy and its corresponding rank-preserving reward function, we develop a two-stage planner that can efficiently resolve conflicting planning requirements. We demonstrate that our approach can generate motion plans in ~7-10 Hz for various challenging road navigation and intersection negotiation scenarios.

This paper addresses the multi-faceted problem of robot grasping, where multiple criteria may conflict and differ in importance. We introduce Grasp Ranking and Criteria Evaluation (GRaCE), a novel approach that employs hierarchical rule-based logic and a rank-preserving utility function to optimize grasps based on various criteria such as stability, kinematic constraints, and goal-oriented functionalities. Additionally, we propose GRaCE-OPT, a hybrid optimization strategy that combines gradient-based and gradient-free methods to effectively navigate the complex, non-convex utility function. Experimental results in both simulated and real-world scenarios show that GRaCE requires fewer samples to achieve comparable or superior performance relative to existing methods. The modular architecture of GRaCE allows for easy customization and adaptation to specific application needs.

Trajectory prediction modules are key enablers for safe and efficient planning of autonomous vehicles (AVs), particularly in highly interactive traffic scenarios. Recently, learning-based trajectory predictors have experienced considerable success in providing state-of-the-art performance due to their ability to learn multimodal behaviors of other agents from data. In this paper, we present an algorithm called multi-predictor fusion (MPF) that augments the performance of learning-based predictors by imbuing them with motion planners that are tasked with satisfying logic-based rules. MPF probabilistically combines learning- and rule-based predictors by mixing trajectories from both standalone predictors in accordance with a belief distribution that reflects the online performance of each predictor. In our results, we show that MPF outperforms the two standalone predictors on various metrics and delivers the most consistent performance.

In this paper, we study how graph transformations based on sesqui-pushout rewriting can be reversed and how the composition of rewrites can be constructed. We illustrate how such reversibility and composition can be used to design an audit trail system for individual graphs and graph hierarchies. This provides us with a compact way to maintain the history of updates of an object, including its multiple versions. The main application of the designed framework is an audit trail of updates to knowledge represented by hierarchies of graphs. Therefore, we introduce the notion of rule hierarchy that represents a transformation of the entire hierarchy, study how rule hierarchies can be applied to hierarchies and analyse the conditions under which this application is reversible. We then present a theory for constructing the composition of consecutive hierarchy rewrites. The prototype audit trail system for transformations in hierarchies of simple graphs with attributes is implemented as part of the ReGraph Python library.

Many systems have been developed in recent years to mine logical rules from large-scale Knowledge Graphs (KGs), on the grounds that representing regularities as rules enables both the interpretable inference of new facts, and the explanation of known facts. Among these systems, the walk-based methods that generate the instantiated rules containing constants by abstracting sampled paths in KGs demonstrate strong predictive performance and expressivity. However, due to the large volume of possible rules, these systems do not scale well where computational resources are often wasted on generating and evaluating unpromising rules. In this work, we address such scalability issues by proposing new methods for pruning unpromising rules using rule hierarchies. The approach consists of two phases. Firstly, since rule hierarchies are not readily available in walk-based methods, we have built a Rule Hierarchy Framework (RHF), which leverages a collection of subsumption frameworks to build a proper rule hierarchy from a set of learned rules. And secondly, we adapt RHF to an existing rule learner where we design and implement two methods for Hierarchical Pruning (HPMs), which utilize the generated hierarchies to remove irrelevant and redundant rules. Through experiments over four public benchmark datasets, we show that the application of HPMs is effective in removing unpromising rules, which leads to significant reductions in the runtime as well as in the number of learned rules, without compromising the predictive performance.