[Paper Review] Safe Interval Path Planning With Kinodynamic Constraints

Zain Alabedeen Ali, Konstantin Yakovlev|arXiv (Cornell University)|Feb 1, 2023

Robotic Path Planning Algorithms4 citations

TL;DR

This paper proposes SIPP-IP, a provably complete and optimal extension of Safe Interval Path Planning (SIPP) that handles kinodynamic constraints—specifically, non-instantaneous acceleration and deceleration—by introducing interval projection to reason about time-to-stop and time-to-accelerate. Unlike original SIPP or naive variants, SIPP-IP avoids incompleteness by modeling safe intervals with dynamic feasibility, achieving two orders of magnitude speedup over A* and outperforming incomplete SIPP variants in both completeness and solution quality.

ABSTRACT

Safe Interval Path Planning (SIPP) is a powerful algorithm for solving single-agent pathfinding problem when the agent is confined to a graph and certain vertices/edges of this graph are blocked at certain time intervals due to dynamic obstacles that populate the environment. Original SIPP algorithm relies on the assumption that the agent is able to stop instantaneously. However, this assumption often does not hold in practice, e.g. a mobile robot moving with a cruising speed is not able to stop immediately but rather requires gradual deceleration to a full stop that takes time. In other words, the robot is subject to kinodynamic constraints. Unfortunately, as we show in this work, in such a case original SIPP is incomplete. To this end, we introduce a novel variant of SIPP that is provably complete and optimal for planning with acceleration/deceleration. In the experimental evaluation we show that the key property of the original SIPP still holds for the modified version -- it performs much less expansions compared to A* and, as a result, is notably faster.

Motivation & Objective

• To address the incompleteness of original SIPP when applied to agents with non-instantaneous acceleration and deceleration.
• To develop a provably complete and optimal path planning algorithm that accounts for kinodynamic constraints in dynamic environments with time-varying obstacles.
• To preserve the efficiency of SIPP by minimizing node expansions while ensuring correctness under realistic motion dynamics.
• To empirically validate that SIPP-IP outperforms A* and incomplete SIPP variants in success rate, solution cost, and runtime.

Proposed method

• Introduce interval projection to model time intervals during which an agent can safely stop or accelerate, based on kinodynamic constraints.
• Modify SIPP’s safe interval propagation to account for time-to-stop and time-to-accelerate, ensuring only dynamically feasible transitions are considered.
• Use conservative collision checking that reserves blocked intervals for moving obstacles even if partially overlapping, and extend non-integer time limits to nearest integers for safety.
• Introduce a novel node expansion strategy that allows reasoning about waiting actions at different points in the search tree, avoiding premature commitment to non-feasible paths.
• Implement SIPP-IP using techniques from SIPPwRT to support efficient re-expansion and pruning of infeasible paths.
• Conduct experiments on a range of maps with dynamic obstacles, comparing SIPP-IP to A*, SIPP1 (kinodynamically constrained SIPP), and SIPP2 (re-expansion-enhanced SIPP).

Experimental results

Research questions

• RQ1 Can SIPP be extended to handle kinodynamic constraints such as non-instantaneous acceleration and deceleration while preserving completeness and optimality?
• RQ2 Why do standard extensions of SIPP fail when kinodynamic constraints are introduced, and what structural changes are needed to restore completeness?
• RQ3 Does the proposed SIPP-IP maintain the efficiency of SIPP in terms of node expansions and runtime, despite the added complexity of kinodynamic feasibility?
• RQ4 How does SIPP-IP compare to A* and incomplete SIPP variants in success rate, solution cost, and computational efficiency across diverse environments?

Key findings

• SIPP-IP achieves a 100% success rate on all test maps, while A* exceeded the node limit in many runs, and SIPP1/SIPP2 showed lower success rates due to incompleteness.
• On average, SIPP-IP solved all instances that were unsolvable by SIPP1 and SIPP2, demonstrating its completeness under kinodynamic constraints.
• In cost comparison, SIPP1 and SIPP2 produced solutions with higher costs than SIPP-IP: 42% of SIPP1 solutions and 22% of SIPP2 solutions exceeded SIPP-IP’s cost by more than 50% on the 'room' map.
• SIPP-IP reduced runtime by two orders of magnitude compared to A*, with average runtimes under 0.1 seconds on all maps except the largest one.
• SIPP-IP outperformed SIPP2 in runtime despite being more conservative, indicating that its interval projection strategy reduces unnecessary expansions.
• The algorithm is suitable for real-time robotic applications, as its average runtime is below 0.1 seconds on all but the largest maps.