Composing Learned Robot Behaviors with Temporal Logic at Runtime

Moritz Zoellner; Anastasios Manganaris; Ahmed H. Qureshi; Rohan Paleja

cs.ROAug 13, 2026

Composing Learned Robot Behaviors with Temporal Logic at Runtime

Authors: Moritz Zoellner, Anastasios Manganaris, Ahmed H. Qureshi, Rohan Paleja

Organizations: Department of Computer Science, Purdue University

Abstract

Executing Linear Temporal Logic (LTL) instructions with learned robot policies faces two practical challenges: demonstrations may cover individual behaviors without containing the temporal compositions requested at deployment, and semantic success predicates often provide little useful motor guidance through quantitative robustness. We address these challenges by separating behavior learning from temporal composition. From the same offline demonstrations, we train an unconditioned multimodal diffusion policy and a semantic predictor that estimates which semantic outcomes are likely to follow a proposed action sequence. These predictions provide a learned guidance signal without requiring hand-designed robustness measures for semantic task objectives. At deployment, an LTL automaton tracks instruction progress and scores the policy's proposed actions according to their predicted semantic outcomes. Neither learned component receives the specification during training, allowing demonstrated behaviors to be reused in longer, previously unseen temporal compositions without retraining. For additional runtime safety constraints with informative continuous margins, an optional robustness-based controller locally refines the selected actions. Experiments in a navigation environment, CALVIN manipulation, and on a real robot demonstrate reliable execution of complex temporal instructions and additional safety constraints, with substantial improvements over temporal-logic baselines.

Figures & tables

Fig. 1: From demonstrations to runtime temporal composition. Our method learns motor behaviors and their semantic outcomes from offline demonstrations, then uses an LTL automaton at deployment to compose them into new instructions. Top: representative failures of baselines when executing semantic manipulation objectives. Bottom: representative executions of our method for LTL specifications that were not present in the data.

Fig. 2: Learning semantic outcome predictions from demonstrations. Left: an unconditioned multimodal action-chunking policy learns the motor behaviors present in the demonstration data. Middle: the same demonstrations supervise the semantic predictor by pairing each executed action chunk with the next distinct semantic label reached later in the trajectory. Right: at inference time, the predictor maps a proposed action chunk to a distribution over possible future semantic outcomes, allowing the controller to estimate what that behavior is likely to accomplish even before the corresponding proposition becomes true. Curves and probabilities are illustrative.

Fig. 3: Full overview of the runtime temporal-composition controller. The figure walks through one action-selection step for an example with atomic propositions

\mathrm{AP}=\{A,B,C\}

K=3

candidate action chunks, and an LTL automaton whose accepting state is indicated by a double circle. Left: the behavior policy proposes three candidate action chunks, and

g_{\psi}

maps each candidate to a semantic prediction

\hat{\ell}_{k}^{+}

, whose entries give the predicted probabilities that the individual atomic propositions hold in the next distinct semantic label. From each

\hat{\ell}_{k}^{+}

, we construct a factorized distribution over complete Boolean labels

\sigma\in\Sigma=2^{\mathrm{AP}}

. Center: each possible label

\sigma

induces a transition from the current automaton state, producing a distribution over next automaton states that is scored by progress toward acceptance using

U_{\phi}

. In the illustrated example, the second candidate receives the highest score. Right: the controller selects this candidate for execution and can optionally refine it using robustness for an additional runtime safety constraint. After the selected chunk is executed, the observed semantic label updates the automaton state

q_{t}

, the policy proposes new candidates, and the process repeats in closed loop.

Fig. 4: 2D navigation environment and semantic vocabulary. The point agent is trained from single-goal demonstrations to reach four colored regions. Each region induces one atomic proposition through the distance-based predicates shown on the right; the same predicates are used by all methods.

Fig. 5: Composition from primitive demonstrations. Top: executed LTL satisfaction for increasingly long prefixes of the sequence blue

\rightarrow

yellow

\rightarrow

green

\rightarrow

red

\rightarrow

blue, together with representative four-goal rollouts. Bottom: success on three structurally different specifications using the same trained models:

\phi_{1}=(\neg g\,\mathbf{U}\,r)\wedge(\neg g\,\mathbf{U}\,b)\wedge\mathbf{F}\bigl(g\wedge\mathbf{F}(y\wedge\mathbf{F}(r\wedge\mathbf{F}(b\wedge\mathbf{F}(y\wedge\mathbf{F}g))))\bigr)

\phi_{2}=\mathsf{S}(r,y,g,b,r,y,g,b)\vee\mathsf{S}(g,b,y,r,g,b,y,r)

\phi_{3}=\mathbf{G}\mathbf{F}r\wedge\mathbf{G}\mathbf{F}b\wedge\mathbf{G}\mathbf{F}g\wedge\mathbf{G}\mathbf{F}y

. Here,

r,b,g,y

denote contact with the corresponding colored regions, and

\mathsf{S}(p_{1},\ldots,p_{m})=\mathbf{F}(p_{1}\wedge\mathbf{X}\mathbf{F}(p_{2}\wedge\cdots\wedge\mathbf{X}\mathbf{F}p_{m}))

denotes strict ordered visitation. Recurrence is evaluated over two completed rounds.

Fig. 6: CALVIN manipulation environment and semantic vocabulary. The robot interacts with a switch, button, drawer, and sliding door. The right panel lists the atomic propositions and simulator-state predicates used to label these behaviors throughout the experiments.

Fig. 7: Semantic guidance and temporal composition in CALVIN. Top: success on seven individual semantic goals. Hatched background bars show the success rate of generated state trajectories for LTLDoG and TeLoGraF. Bottom: full LTL satisfaction (%) on six composite instructions and three runtime safety constraints. Parentheses report results without safety refinement; N/A denotes configurations not evaluated. The same trained behavior policy and semantic predictor are reused across all specifications; safety rows additionally activate the optional robustness refinement. Each tested method–task pair uses 50 executed rollouts.

Fig. 8: Effect of optional safety refinement. Example executions with and without refinement for region, orientation, and gripper constraints. Joint task-and-constraint success increases from 42%, 0%, and 0% without refinement to 98%, 82%, and 98%, respectively.

Fig. 9: Physical execution of runtime temporal instructions. For STL-GPC, the robustness predicates are $r_{\texttt{box\_grabbed}}=g$ , $r_{\texttt{pour\_left}}=-\theta-90^{\circ}$ , and $r_{\texttt{pour\_right}}=\theta-90^{\circ}$ , where $\theta$ is the wrist angle and $g=1$ for a closed gripper, $-1$ otherwise. Success rates for five runtime instructions: $\phi_{1}=\mathbf{F}(\texttt{box\_grabbed}\wedge\mathbf{F}\,\texttt{pour\_left})$ ; $\phi_{2}=\mathbf{F}(\texttt{box\_grabbed}\wedge\mathbf{F}\,\texttt{pour\_right})$ ; $\phi_{3}=\phi_{1}\wedge\mathbf{G}\neg\texttt{unsafe}$ ; $\phi_{4}=\phi_{1}\wedge(\texttt{upright}\,\mathbf{U}\,\texttt{near\_bowl})$ ; $\phi_{5}=\mathbf{F}\bigl(\texttt{box\_grabbed}\wedge\mathbf{G}\mathbf{F}(\texttt{pour\_left}\wedge\mathbf{F}\,\texttt{pour\_right})\bigr)$ . Each condition in $\phi_{1}$ – $\phi_{4}$ uses $N=20$ real-robot trials; our method achieves 100% success on $\phi_{5}$ over $N=5$ trials (evaluated for three full cycles).

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Many robotic tasks are temporally extended and demand precise specifications of subgoals, constraints, and their temporal ordering. Yet human operators typically communicate such tasks in natural language, which is inherently ambiguous, underspecified, and context dependent. Translating human instructions into formal task specifications, such as Linear Temporal Logic (LTL), is therefore essential for verifiable and safe robotic execution. Existing LLM-based translators attempt to bridge this gap through open-ended reasoning or post-hoc constraint enforcement, but the former may violate domain constraints, whereas the latter can disrupt the reasoning needed for novel instructions. This paper proposes Self-Constrained Reasoning (SCR), a framework that mitigates this trade-off by internalizing structural knowledge into the model's decision-making process rather than imposing it as an external filter. By combining a structural constraint representation with a hierarchical decision-making formulation, SCR guides reasoning within a formally grounded space while preserving adaptability to unseen instructions. Experiments show that SCR improves both domain-constraint satisfaction and generalization, providing an effective and interpretable approach for translating human intent into verifiable specifications for robotic execution.

Abstract

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