Automatic Robot Failure Synthesis

• Automatic robot failure synthesis is a set of algorithmic methods that generate, detect, and repair failures in autonomous systems using formal and Bayesian approaches.
• Key methodologies include adversarial test generation, rare-event sampling, and property-based scenario generation to systematically uncover and classify failure modes.
• These techniques enhance system reliability by enabling counterfactual corrections and synthesis-based recovery, paving the way for robust autonomous performance.

Automatic robot failure synthesis is a set of algorithmic methodologies for generating, detecting, and leveraging robot failures via programmatic means, with objectives spanning verification, counterexample-guided repair, robustness improvement, and systematic exploration of adversarial scenarios. Central themes include adversarial test generation, Bayesian sampling for failure mode discovery, synthesis of robustness-optimal parameters, and recovery mechanisms grounded in formal specification. Cutting-edge frameworks utilize formal methods, differentiable simulation, property-based scenario generation, and synthesis-based repair to enhance both the empirical reliability and the formal correctness of autonomous robots under diverse uncertainty models.

1. Formal Adversarial Test Synthesis for Safety-Critical Robots

Formal test synthesis reframes robot failure generation as an adversarial optimization over parameterized specifications. In the approach of “Formal Test Synthesis for Safety-Critical Autonomous Systems based on Control Barrier Functions” (Akella et al., 2020), a black-box robot system, modeled as $\dot{x} = f(x) + g(x)u$, is paired with a temporal-logic operational specification of the form $$(\vee_{i\in I} F\phi_i)\wedge(\wedge_{j\in J} G\omega_j)$$. Demonstration data and a candidate library of smooth functions are used to learn approximate control barrier functions (CBFs) for both reachability (F$\phi_i$) and safety (G$\omega_j$) objectives.

Test synthesis is operationalized as a minimax saddle-point problem:

$$d^*(x) = \arg\min_{d\in\mathbb{R}^p} \left\{\max_{u\in\mathcal{U}(x,d)} \sum_{i\in I} [L_f h^F_i(x) + L_g h^F_i(x)u]\right\}$$

where $\mathcal{U}(x,d)$ is the set of controls that guarantee safety-barrier constraints via extended class-K functions. The outer minimization chooses parameterizations $d$ (e.g., obstacle layouts, agent timings) that make mission objectives maximally hard or outright unsatisfiable—even for the best possible controller.

Applied to multi-robot waypoint navigation and obstacle avoidance (Robotarium), this methodology discovered nontrivial adversarial failure scenarios: in 20 synthesized tests, 7 resulted in collisions, demonstrating its utility for uncovering latent failure modes unobservable in nominal demonstrations. Quantitative metrics (goal progress, safety margin) and trajectory visualizations further evidence the systematic identification of worst-case system behaviors.

2. Bayesian Failure Mode Prediction and Design Repair

Bayesian approaches to robot failure synthesis model failure-inducing perturbations or scenario parameters as random variables, conditioning on the high-cost (failure) event to generate a posterior over environment or fault parameters (Dawson et al., 2023, Dawson et al., 4 Apr 2024). The posterior is approximated via differentiable simulation coupled with gradient-based Markov chain Monte Carlo (MCMC), especially the Metropolis-Adjusted Langevin Algorithm (MALA).

Given a simulator $S(\theta, x)$ with design $\theta$ and perturbation $x$, and a failure indicator $FAILURE(x)$, the key posterior is:

$$p(x|FAILURE=1) \propto p(x)\, p(FAILURE=1|x) \approx \exp(J_r(x))$$

with $J_r(x) = J(S(\theta, x)) + \log p(x)$ as risk-adjusted cost. MALA proposals exploit auto-differentiation:

$$x' = x_k + \tau \nabla_x \ell(x_k) + \sqrt{2\tau}\,\eta,\quad \eta \sim \mathcal{N}(0,I)$$

Sampling from this posterior uncovers a diverse, representative set of high-risk failure scenarios.

A subsequent repair phase updates $\theta$ to minimize expected cost under sampled failures:

$$\theta_{k} \leftarrow \theta_{k-1} - \eta \nabla_\theta\, \mathbb{E}_{x\sim p(x|FAILURE=1)} [J(S(\theta, x))]$$

This adversarial inference-and-repair loop accelerates both discovery of novel failure modes and systematic robustness improvement. Results across domains—including robot swarm search, formation control under wind, and hardware push tasks—demonstrate up to $10\times$ lower worst-case cost, $2\times$ faster convergence, and large robustness gains post-repair (Dawson et al., 2023, Dawson et al., 4 Apr 2024).

3. Property-Based Scenario Generation and Failure Classification

Property-based testing frameworks for robots parameterize action correctness in terms of logical predicates linked to action ontologies (Sohail et al., 2021). Each action $a$ is associated with preconditions ($Pre_a$), invariants ($Inv_a$), and postconditions ($Post_a$). Scenario generation consists of randomized sampling over environment layouts, object models, and navigation obstacles, linked to a TOML configuration and instantiated OWL ontology.

Execution in simulation (e.g., Gazebo/ROS) is monitored by evaluating the predicates, automatically detecting and categorizing action failures. Classification granularity includes:

• invariant violation (“collision_during_approach”)
• postcondition violation (“object_not_elevated”, “object_slipped_off”)
• system breakdown (“ros_message_timeout”)

Comprehensive aggregation yields per-property failure rates, stage clustering, and diagnostic timelines. In tabletop manipulation, such frameworks have exposed rich modes of failure (60% from collisions, 30% from communication) and quantitatively differentiate nominal success rates (e.g., $T \approx 0.35$ for pick, $T \approx 0.37$ for pick-and-place). All scenario generation, execution, and reporting steps are fully automatic, supporting scalable failure synthesis without hand-tuning.

4. Rare-Event Sampling for Failure Verification and Synthesis

Rare-event methodologies address the inefficiency of sampling-based verification for low-probability failures in robots (Scher et al., 2023). The workflow consists of applying multilevel splitting (HDR) and Elliptical Slice Sampling (ESS) to efficiently sample from the failure region specified by temporal logic constraints (STL), under stochastic uncertainty models.

Given STL specifications $\varphi$ (with robust satisfaction function $\rho$), the region $\mathcal{L}(\varphi,0)^c$ denotes failure. The combined HDR+ESS sampler computes unbiased estimates of failure probability $P_{fail}$ with superior sample efficiency for $P_{fail}<10^{-2}$ compared to Monte Carlo. For parametric synthesis (e.g., LQR gains, trajectory means), score-function estimators and MCMC sampling from the failure region drive parameter updates to minimize $P_{fail}$.

Benchmark studies—including fixed-wing perching under actuation noise and RL-based AV control with sensor disturbances—confirm the method's ability to uncover multiple independent modes of failure and to guide synthesis towards safer parameterizations via gradient descent on the MCMC-estimated statistics.

5. Diagnosis, Counterfactual Correction, and Experience Enrichment

Failure synthesis also concerns automatic diagnosis of failed executions and generation of corrective counterfactual experiences (Mitrevski et al., 2021). Given parameterized execution models with relational preconditions and continuous success predictors (Gaussian processes), diagnosis is performed by sampling parameter perturbations around a failed action to identify the minimal set of near-violated predicates. This search formalizes as:

$$\min_{x'} \|x' - x^{fail}\|^2\,\,\,\, \text{s.t.}\,\,\,\, \exists p_j \in R_q\,:\, p_j(x') = 0$$

Corrective updates are synthesized by sampling offset directions opposite to the falsifying perturbations from a Gamma distribution, yielding candidate corrections $x^*$. The robot stores both synthetic failures and corrected successes, retraining the success predictor and refining the predicate definitions. Demonstrated on handle grasping with Toyota HSR, the method boosted success rates from $16\%$ to over $60\%$ with only a few dozen counterfactual corrections.

6. Specification-Level Recovery via Synthesis-Based Skill Repair

Automated recovery from failed high-level specifications leverages synthesis-based methods to generate new robot skills and relax violated environment assumptions (Meng et al., 30 Jun 2024). Task models represent robot-environment interaction as a two-player transition system, with GR(1) temporal logic tasks mapping to liveness and safety guarantees.

On specification violation (detected by SMT-checking Boolean formulas over observed transitions), the repair pipeline proceeds by relaxing safety assumptions:

$\Box\psi \longrightarrow \Box(\psi \vee \chi)$

where $\chi$ admits the observed violating transition. If realizability is lost, a skill-repair loop synthesizes new skills—symbolically encoded as precondition/postcondition transitions—by augmenting the controller's output set and re-synthesizing the strategy. Empirical results on Hello Robot Stretch demonstrate autonomous detection, automatic skill suggestion (e.g., detour moves), and controller update: recovery latency per violation is $16$–$100$s, with low monitoring and synthesis overhead per step.

7. Limitations, Extensions, and Future Directions

Current failure synthesis techniques depend on simulator fidelity, differentiability of components (for gradient-based sampling), and realizability of repairs within the abstraction's scope. Rare-event sampling may struggle with ultra-low-probability events, motivating extensions such as Sequential Monte Carlo and block samplers for mixed discrete/continuous domains. Symbolic skill repair does not recover from violations originating in low-level dynamics, and search-complexity may become prohibitive in combinatorially large task spaces.

Ongoing research explores local incremental repair, multi-agent generalizations, integration of robustness margins, and distributionally robust optimization of policies under the extended posterior over failure cases (Dawson et al., 4 Apr 2024, Meng et al., 30 Jun 2024, Scher et al., 2023). The synthesis loop between formal specification, adversarial test generation, diagnosis, and repair remains central for end-to-end verification and improvement of autonomous robot reliability.