Kaier Liang

Licheng Luo, Kaier Liang, Cristian-Ioan Vasile et al.

Executing complex manipulation in cluttered environments requires satisfying coupled geometric and temporal constraints. Although Spatio-Temporal Logic (SpaTiaL) offers a principled specification framework, its use in gradient-based optimization is limited by non-differentiable geometric operations. Existing differentiable temporal logics focus on the robot's internal state and neglect interactive object-environment relations, while spatial logic approaches that capture such interactions rely on discrete geometry engines that break the computational graph and preclude exact gradient propagation. To overcome this limitation, we propose Differentiable SpaTiaL, a fully tensorized toolbox that constructs smooth, autograd-compatible geometric primitives directly over polygonal sets. To the best of our knowledge, this is the first end-to-end differentiable symbolic spatio-temporal logic toolbox. By analytically deriving differentiable relaxations of key spatial predicates--including signed distance, intersection, containment, and directional relations--we enable an end-to-end differentiable mapping from high-level semantic specifications to low-level geometric configurations, without invoking external discrete solvers. This fully differentiable formulation unlocks two core capabilities: (i) massively parallel trajectory optimization under rigorous spatio-temporal constraints, and (ii) direct learning of spatial logic parameters from demonstrations via backpropagation. Experimental results validate the effectiveness and scalability of the proposed framework.Code Available: https://github.com/plen1lune/DiffSpaTiaL

Kaier Liang, Gustavo A. Cardona, Disha Kamale et al.

This paper presents a novel framework for inferring timed temporal logic properties from data. The dataset comprises pairs of finite-time system traces and corresponding labels, denoting whether the traces demonstrate specific desired behaviors, e.g. whether the ship follows a safe route or not. Our proposed approach leverages decision-tree-based methods to infer Signal Temporal Logic classifiers using primitive formulae. We formulate the inference process as a mixed integer linear programming optimization problem, recursively generating constraints to determine both data classification and tree structure. Applying a max-flow algorithm on the resultant tree transforms the problem into a global optimization challenge, leading to improved classification rates compared to prior methodologies. Moreover, we introduce a technique to reduce the number of constraints by exploiting the symmetry inherent in STL primitives, which enhances the algorithm's time performance and interpretability. To assess our algorithm's effectiveness and classification performance, we conduct three case studies involving two-class, multi-class, and complex formula classification scenarios.

Licheng Luo, Kaier Liang, Yu Xia et al.

While Temporal Logic provides a rigorous verification framework for robotics, it typically operates on trajectory-level signals and does not natively represent the object-centric geometric relations that are central to manipulation. Spatio-Temporal Logic (SpaTiaL) overcomes this by explicitly capturing geometric spatial requirements, making it a natural formalism for manipulation-task verification. Consequently, translating natural language (NL) into verifiable SpaTiaL specifications is a critical objective. Yet, existing NL-to-Logic methods treat specifications as flat sequences, entangling nested temporal scopes with spatial relations and causing performance to degrade sharply under deep nesting. We propose NL2SpaTiaL, a framework modeling specifications as Hierarchical Logical Trees (HLT). By generating formulas as structured HLTs in a single shot, our approach decouples semantic parsing from syntactic rendering, aligning with human compositional spatial reasoning. To support this, we construct, to the best of our knowledge, the first NL-to-SpaTiaL dataset with explicit hierarchical supervision via a logic-first synthesis pipeline. Experiments with open-weight LLMs demonstrate that our HLT formulation significantly outperforms flat-generation baselines across various logical depths. These results show that explicit HLT structure is critical for scalable NL-to-SpaTiaL translation, ultimately enabling a rigorous ``generate-and-test'' paradigm for verifying candidate trajectories in language-conditioned robotics. Project website: https://sites.google.com/view/nl2spatial

Kaier Liang, Eric Sihite, Pravin Dangol et al.

Despite many accomplishments by legged robot designers, state-of-the-art bipedal robots are prone to falling over, cannot negotiate extremely rough terrains and cannot directly regulate unilateral contact forces. Our objective is to integrate merits of legged and aerial robots in a single platform. We will show that the thrusters in a bipedal legged robot called Harpy can be leveraged to stabilize the robot's frontal dynamics and permit jumping over large obstacles which is an unusual capability not reported before. In addition, we will capitalize on the thrusters action in Harpy and will show that one can avoid using costly optimization-based schemes by directly regulating contact forces using an Reference Governor (RGs). We will resolve gait parameters and re-plan them during gait cycles by only assuming well-tuned supervisory controllers. Then, we will focus on RG-based fine-tuning of the joints desired trajectories to satisfy unilateral contact force constraints.