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Reactive Temporal Logic-based Planning and Control for Interactive Robotic Tasks

Farhad Nawaz, Shaoting Peng, Lars Lindemann, Nadia Figueroa, Nikolai Matni

TL;DR

This work tackles real-time, safe, and reactive human–robot interaction by coupling a discrete reactive temporal logic (RTL) task planner with a continuous DS-based motion planner. The RTL layer uses controllable and uncontrollable propositions to form a reactive specification $oldsymbol{Ψ}$, verified by Büchi automata, while the motion layer enforces safety and stability through time-varying control barrier functions and control Lyapunov functions within a CLF-CBF-QP framework. A 200 Hz task planner, driven by Spot-generated automata, selects high-level behaviors, and a 1 kHz motion planner executes safe nominal motions and time-critical STL tasks, with smooth switching between behaviors. Demonstrations on a Franka arm wiping tasks (whiteboard and mannequin) show real-time adaptation to environmental changes (stains, dropped erasers) and compliant human interaction, validating the method’s safety guarantees and reactivity. The framework advances interactive robotics by providing formal guarantees of task satisfaction and disturbance rejection in dynamic, human-centered settings, with potential extensions to higher-dimensional manifolds and supervisory LLM-based control.

Abstract

Robots interacting with humans must be safe, reactive and adapt online to unforeseen environmental and task changes. Achieving these requirements concurrently is a challenge as interactive planners lack formal safety guarantees, while safe motion planners lack flexibility to adapt. To tackle this, we propose a modular control architecture that generates both safe and reactive motion plans for human-robot interaction by integrating temporal logic-based discrete task level plans with continuous Dynamical System (DS)-based motion plans. We formulate a reactive temporal logic formula that enables users to define task specifications through structured language, and propose a planning algorithm at the task level that generates a sequence of desired robot behaviors while being adaptive to environmental changes. At the motion level, we incorporate control Lyapunov functions and control barrier functions to compute stable and safe continuous motion plans for two types of robot behaviors: (i) complex, possibly periodic motions given by autonomous DS and (ii) time-critical tasks specified by Signal Temporal Logic~(STL). Our methodology is demonstrated on the Franka robot arm performing wiping tasks on a whiteboard and a mannequin that is compliant to human interactions and adaptive to environmental changes.

Reactive Temporal Logic-based Planning and Control for Interactive Robotic Tasks

TL;DR

This work tackles real-time, safe, and reactive human–robot interaction by coupling a discrete reactive temporal logic (RTL) task planner with a continuous DS-based motion planner. The RTL layer uses controllable and uncontrollable propositions to form a reactive specification , verified by Büchi automata, while the motion layer enforces safety and stability through time-varying control barrier functions and control Lyapunov functions within a CLF-CBF-QP framework. A 200 Hz task planner, driven by Spot-generated automata, selects high-level behaviors, and a 1 kHz motion planner executes safe nominal motions and time-critical STL tasks, with smooth switching between behaviors. Demonstrations on a Franka arm wiping tasks (whiteboard and mannequin) show real-time adaptation to environmental changes (stains, dropped erasers) and compliant human interaction, validating the method’s safety guarantees and reactivity. The framework advances interactive robotics by providing formal guarantees of task satisfaction and disturbance rejection in dynamic, human-centered settings, with potential extensions to higher-dimensional manifolds and supervisory LLM-based control.

Abstract

Robots interacting with humans must be safe, reactive and adapt online to unforeseen environmental and task changes. Achieving these requirements concurrently is a challenge as interactive planners lack formal safety guarantees, while safe motion planners lack flexibility to adapt. To tackle this, we propose a modular control architecture that generates both safe and reactive motion plans for human-robot interaction by integrating temporal logic-based discrete task level plans with continuous Dynamical System (DS)-based motion plans. We formulate a reactive temporal logic formula that enables users to define task specifications through structured language, and propose a planning algorithm at the task level that generates a sequence of desired robot behaviors while being adaptive to environmental changes. At the motion level, we incorporate control Lyapunov functions and control barrier functions to compute stable and safe continuous motion plans for two types of robot behaviors: (i) complex, possibly periodic motions given by autonomous DS and (ii) time-critical tasks specified by Signal Temporal Logic~(STL). Our methodology is demonstrated on the Franka robot arm performing wiping tasks on a whiteboard and a mannequin that is compliant to human interactions and adaptive to environmental changes.
Paper Structure (18 sections, 1 theorem, 12 equations, 7 figures, 2 tables, 1 algorithm)

This paper contains 18 sections, 1 theorem, 12 equations, 7 figures, 2 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Preliminaries
  3. Linear Temporal Logic and Büchi Automaton
  4. Signal Temporal Logic and Control Barrier Functions
  5. Problem formulation
  6. Controllable Propositions
  7. Reactive temporal logic
  8. Task and Motion Plan
  9. Proposed Methodology
  10. Task Planner
  11. Motion Planner
  12. Nominal motion plans
  13. STL tasks
  14. Switching between behaviors
  15. Experimental Results
  16. ...and 3 more sections

Key Result

Theorem 1

Let $u(x, t) \in K(x, t)$ be a feedback control law that is Lipschitz in $x$ and piecewise continuous in $t$. Then, the set $\mathcal{C}(t)$ is forward invariant for the control law $u(x, t)$ if $B(x, t)$ is a time-varying control barrier function.

Figures (7)

  • Figure 1: Periodic wiping motion on the (a) right side and (b) left side of the board, (c) wiping the blue stain detected by a camera, (d) eraser dropped because of human perturbation and (e) robot picks up the dropped eraser.
  • Figure 2: The control flow of our proposed pipeline. The state of the robot is $x$, the low level control input are the joint torques $\tau$, and the desired velocity in state space is $\dot{x}_\mathrm{ref}$.
  • Figure 3: Automaton $\mathcal{B}_{\Psi}$ for ${\Psi := G (\textit{h} \Rightarrow \textit{s}) \land G (\neg \textit{h} \Rightarrow F \textit{(p)})}$, where $\textnormal{!p} \equiv \neg \textnormal{p}$.
  • Figure 4: Whiteboard wiping: (a) switching between nominal motions (b) going to the stain position (c) wiping off stain (d) human perturbation and eraser pick up.
  • Figure 5: Mannequin wiping: (a) switching between nominal motions (b) going to the back (c) wiping the back (d) dipping the towel in water (e) human squeezing the wet towel and (f) continuing wiping.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Definition 1