Scalable Integrated Task and Motion Planning from Signal Temporal Logic Specifications (1803.11247v2)

Abstract: Many safety-critical systems must achieve high-level task specifications with guaranteed safety and correctness. Much recent progress towards this goal has been made through controller synthesis from signal temporal logic (STL) specifications. Existing approaches, however, either consider some a priori discretization of the state-space, deal only with a convex fragment of STL, or are not provably complete. We propose a scalable, provably complete algorithm that directly synthesizes continuous trajectories to satisfy non-convex STL specifications. We separate discrete task planning and continuous motion planning on the fly and harness highly efficient satisfiability modulo theories (SMT) and linear programming (LP) solvers to find dynamically feasible trajectories for high dimensional systems that satisfies non-convex STL specifications. The proposed design algorithms are proved sound and complete, and simulation results demonstrate the scalability of our approach.

Scalable Symbolic Control from Signal Temporal Logic Specifications

This paper addresses the synthesis of symbolic control strategies from Signal Temporal Logic (STL) specifications, focusing on autonomous intelligent physical systems (IPS). The authors present a methodology that overcomes several limitations of existing approaches, such as reliance on discretization and handling only convex fragments of STL. The paper introduces a scalable, provably complete algorithm that directly generates dynamically feasible trajectories satisfying non-convex STL specifications using state-of-the-art Satisfiability Modulo Theories (SMT) and Linear Programming (LP) solvers.

Main Contributions

The contribution of this research lies in developing a two-layer control architecture combining discrete and continuous planning derived from a counterexample-guided inductive synthesis (CEGIS) approach. It separates discrete task planning and continuous motion planning in real-time using a feedback loop.

1. Verification Process: The approach includes an encoding mechanism that interprets STL formulas as constraint satisfiability problems (CSPs) within an SMT framework. SMT solvers leverage the logical structure of STL to explore the state space efficiently.
2. Scalability and Completeness: The algorithm guarantees completeness by demonstrating that if a feasible solution exists within a finite search space, it will be found. Previous symbolic control techniques have struggled with scalability issues, particularly in high-dimensional state spaces. This framework mitigates these limitations through an efficient search strategy and computationally optimized discrete plan generation.
3. Handling Non-Convexities: The paper emphasizes addressing non-convex STL formulas, which allows for more expressive task descriptions that include complex logical constraints, such as disjunctions and nested temporal operators.

Detailed Methodology

• Discrete Planning: The discrete planning layer generates candidate state sequences (runs) based on STL predicates using a CSP encoding. This is achieved by incrementally finding plans of increasing length until a feasible trajectory is found or all possibilities are exhausted.
• Continuous Planning: This layer refines the candidate discrete sequences into dynamically feasible trajectories through robust control techniques, ensuring satisfaction of the continuous dynamics described by the system's linear equations.
• Robust Control Synthesis: The controller design includes a search for trajectories with maximal robust satisfaction of STL specifications. This involves quadratic optimization to ensure the stable tracking of target behaviors in the presence of disturbances.

Implications and Future Work

The implications of this work extend significantly to the control of complex systems involving safety-critical tasks, where guaranteed satisfaction of task specifications is paramount. Practically, this can improve autonomous vehicles, robotic inspections, and automated infrastructure maintenance.

Theoretically, the paper contributes to the field of formal methods in control by advancing the intersection of logic synthesis and optimal control. Future work might explore extending this methodology to hybrid systems involving both discrete and continuous state changes, as well as non-linear system dynamics. Another potential area is the integration of learning mechanisms that could adaptively refine STL specifications based on observed system performance and environmental interactions.

Results

The approach was validated through a simulation of a power line inspection task using a quadrotor model. The scenario demonstrated the methodology's capability to handle non-convex task specifications requiring avoidance constraints and goal reachability within a specified time frame.

In conclusion, this work presents a significant advancement in solving the STL symbolic control problem for high-dimensional systems, offering both theoretical guarantees and practical applicability. It opens new avenues for research into more adaptive, responsive control systems guided by advanced temporal logic specifications.