[Paper Review] Active Perception and Control from PrSTL Specifications

Rafael Rodrigues da Silva, Vince Kurtz+1 more|arXiv (Cornell University)|Nov 3, 2021

Formal Methods in Verification19 references4 citations

TL;DR

This paper proposes a novel framework for active perception and control in partially observed, noisy hybrid systems using probabilistic signal temporal logic (PrSTL) specifications. By combining bounded model checking (BMC) with sampling-based trajectory synthesis and counterexample-guided inductive synthesis (CEGIS), the method generates controllers that satisfy complex temporal logic tasks under uncertainty, achieving a 92.07% average success rate in Monte Carlo simulations with 95% confidence bounds.

ABSTRACT

Next-generation intelligent systems must plan and execute complex tasks with imperfect information about their environment. As a result, plans must also include actions to learn about the environment. This is known as active perception. Most active perception algorithms rely on reward or cost functions, which are usually challenging to specify and offer few theoretical guarantees. On the other hand, symbolic control methods can account for complex tasks using temporal logic but often do not deal well with uncertainties. This work combines symbolic control with active perception to achieve complex tasks in a partially observed and noisy control system with hybrid dynamics. Our basic idea is to employ a counterexample-guided-inductive-synthesis approach for control from probabilistic signal temporal logic (PrSTL) specifications. Our proposed algorithm combines bounded model checking (BMC) with sampling-based trajectory synthesis for uncertain hybrid systems. Active perception is inherently built into the framework because PrSTL formulas are defined in the chance domain.

Motivation & Objective

• To address the challenge of planning complex tasks in partially observed, noisy environments where uncertainty in initial states and dynamics must be actively reduced through perception.
• To overcome the limitations of reward-based active perception and symbolic control by integrating probabilistic signal temporal logic (PrSTL) with belief space control for hybrid systems.
• To enable scalable controller synthesis for complex PrSTL specifications by decoupling logical and dynamical constraints through a hierarchical architecture.
• To incorporate active perception into controller synthesis by modeling observation effects on belief updates during planning, even when measurements are unavailable during design.
• To validate the approach on motion planning and robot manipulation tasks under uncertainty, demonstrating robustness and high success rates.

Proposed method

• Employ a switched linear system with Gaussian noise to model system dynamics, enabling efficient belief propagation via Kalman filtering.
• Use probabilistic signal temporal logic (PrSTL) to specify high-level tasks with chance constraints, capturing uncertainty in real-time temporal requirements.
• Apply a custom bounded model checking (BMC) solver to extract sequences of convex chance constraints from PrSTL formulas, decoupling logical from dynamical constraints.
• Integrate a sampling-based motion planner to synthesize belief trajectories that satisfy the BMC-generated constraints, ensuring feasibility under uncertainty.
• Use counterexample-guided inductive synthesis (CEGIS) to iteratively refine the BMC constraints when no valid trajectory is found, improving convergence and correctness.
• Approximate unknown observations during planning using the Maximum Likelihood Observation (MLO) method, enabling tractable belief state updates while preserving plan robustness.

Experimental results

Research questions

• RQ1 How can active perception be systematically integrated into controller synthesis for hybrid systems with partial observability and process noise?
• RQ2 Can a hierarchical controller synthesis framework combining BMC and sampling-based planning achieve scalability for complex PrSTL specifications under uncertainty?
• RQ3 To what extent does approximating observations via MLO during planning preserve the correctness and robustness of the final execution?
• RQ4 How can belief dynamics under uncertain initial states and noisy measurements be effectively captured and controlled using PrSTL specifications?
• RQ5 What is the empirical success rate of the proposed method in satisfying high-level task specifications under probabilistic constraints?

Key findings

• The proposed method achieved an average success probability of 92.07% ± 9.21 across 30 Monte Carlo simulations, demonstrating robustness under uncertainty.
• In the light-dark domain example, 96% of simulated executions satisfied the PrSTL specification, closely matching the required 95% confidence level.
• The algorithm successfully enabled task completion even when the initial state was outside the 95% confidence region, due to effective active perception and belief tracking.
• The robot manipulation task required active perception to correct for initial belief errors in puck and target positions; the system autonomously planned perception actions before grasping.
• The use of MLO approximation during planning enabled feasible trajectory generation despite unobserved measurements, and simulations confirmed that the approximation captured essential plan behaviors.
• The framework successfully handled non-convex PrSTL specifications and hybrid dynamics, extending beyond prior work restricted to convex fragments or deterministic systems.