Correct-by-Construction Behavior Tree Synthesis from Signal Temporal Logic Specifications with Application to Robotic Missions

As robots move from controlled environments into real-world settings, it becomes increasingly crucial to ensure that they perform as expected. A key step toward that goal is a rigorous specification of the desired robot behavior, capturing intricate temporal, spatial, and logical requirements. Complementing this, plan and control synthesis methods are needed to fulfill these specifications with provable guarantees. This manuscript presents temporal logics - particularly linear and signal temporal logic - as expressive specification languages for robot behavior over time. We then discuss principles of formal synthesis, from discrete graph- and game-based approaches to sampling-based motion planning, trajectory optimization, and control-certificate-based synthesis. Finally, we outline challenges in deploying formal synthesis in real-world robotics, emphasizing the interplay between modeling fidelity, computational tractability, and the types of rigorous guarantees that can be achieved.

Synthesizing deployable robot behavior trees (BTs) from natural language (NL) requires grounding to ensure every generated BT references only skills a robot can actually execute. Existing LLM-based BT synthesis approaches often place this grounding responsibility on the prompt author. This makes deployment brittle when the author does not know which skills the robot can execute, how those skills are parameterized, or how the robot runtime software constrains valid BT structure. This paper proposes a contract-grounded BT synthesis architecture in which a coding agent queries a robot-side Model Context Protocol (MCP) server to retrieve an explicit contract consisting of a skill library, permitted BT operators, and optional BT composition templates, before synthesizing a BT for validation and execution. In our framework, non-expert operators issue NL commands without knowledge of robot implementation details, while a robot runtime validation gate enforces correctness before execution. We evaluate two LLMs, a closed model (Sonnet 4.6) and a smaller open-source model (Gemma4:31b), across 110 simulated tasks in PyRoboSim and 14 tasks on a physical Husarion Panther robot. Results show that contract grounding enables near-perfect BT validation and high task success, that BT composition templates substantially recover success on reactive control-flow tasks for the smaller model, and that the architecture transfers to physical hardware running a Nav2 stack opaque to both operator and agent.

This paper investigates continuous-time motion planning under Signal Temporal Logic (STL) specifications. The goal is to generate smooth robot trajectories that satisfy high-level logical and timing requirements while respecting low-level motion constraints. To this end, we propose an efficient framework that combines timed-automata reasoning with graphs of convex sets (GCS). An STL specification is first represented by a timed automaton, which is then coupled with a convex decomposition of the configuration space to form a joint transition system encoding both task progress and region occupancy. Based on this joint transition system, the STL motion-planning problem is reformulated as a shortest-path problem over a GCS, whose solution induces a smooth Bézier-spline trajectory satisfying the STL specification, smoothness requirements, and velocity bounds. We establish the soundness of the proposed formulation and analyze its computational complexity, showing that, once the timed automaton and convex decomposition are fixed, the convex relaxation scales polynomially with the configuration-space dimension and the Bézier degree. We further develop a compact timed-automaton construction for an expressive STL fragment using dedicated templates and Boolean composition. Numerical experiments on low-dimensional benchmarks, a $3$-D quadrotor, a $30$-DoF humanoid, and a hardware experiment on a UR-3 robot arm demonstrate that the proposed method efficiently solves complex STL motion-planning problems and produces smooth executable trajectories.