Real-Time Safety-Aware Trajectory Generation

Updated 6 September 2025

Real-Time Safety-Aware Trajectory Generation is defined as the development of motion plans that ensure collision avoidance and constraint satisfaction under real-time conditions.
It employs rigorous methods such as offline reachability analysis, control barrier functions, and optimization-based approaches to balance speed and safety in dynamic environments.
Key techniques include adaptive meta-planning, motion primitive integration, and parallel trajectory optimization to maintain robust safety despite uncertainties and disturbances.

Real-time safety-aware trajectory generation refers to the design and execution of motion plans for robots and autonomous systems that guarantee strict safety properties—primarily collision avoidance and constraint satisfaction—under real-time computational constraints and in the presence of uncertainties or disturbances. This domain has seen a convergence of formal methods (e.g., reachability analysis, control barrier functions), optimization (both offline and online), and algorithmic adaptations (meta-planning, parallel computing, motion primitive search) to address the fundamental speed-safety trade-off. The following sections synthesize the most technically advanced techniques in the literature and illustrate their mathematical underpinnings, safety guarantees, practical realization, and scaling properties.

1. Offline Reachability and Safety Bounds

A dominant paradigm in safety-aware planning separates the computation of worst-case system behaviors from real-time trajectory synthesis. This is epitomized in frameworks such as FaSTrack (Fridovich-Keil et al., 2017) and Reachability-based Trajectory Design (RTD) (Kousik et al., 2018, Vaskov et al., 2019, Holmes et al., 2020), where Hamilton–Jacobi (HJ) reachability is used to compute a robust Tracking Error Bound (TEB) or Forward Reachable Set (FRS) offline.

For a tracking system

$\frac{ds}{dt} = f(s, u_s, d),\quad s \in \mathcal{S},\quad u_s \in \mathcal{U}_s,\quad d \in \mathcal{D},$

and a simpler nominal/planning system

$\frac{dp}{dt} = h(p, u_p),\quad p \in \mathcal{P},\quad u_p \in \mathcal{U}_p,$

the TEB is determined as the invariant set for the relative dynamics $r = s - Qp$ , via HJ analysis: $\frac{dr}{dt} = g(r, u_s, u_p, d).$ The controlled invariant set—the TEB—is computed as the sublevel set $V(r) \leq c$ of the value function $V$ derived from solving the associated HJ–Isaacs PDE, ensuring that for any online planned trajectory, as long as the system’s state remains within this tube, the tracking system will not violate safety constraints, even under worst-case disturbances.

These precomputed sets (TEBs, SSBs, and FRSs) are then used online to augment sensed obstacles, ensuring collision avoidance even in unstructured environments. The RTD framework further encodes this via parameter projection maps and SOS-polynomial-based overapproximations. Notably, ARMTD (Holmes et al., 2020) leverages zonotopic reachable sets per manipulator joint to enable scalable synthesis for articulated robots.

2. Meta-Planning and Real-Time Replanning

Real-time adaptive motion planning in complex and unknown environments is typically achieved by integrating multiple planning models with explicitly characterized safety margins. FaSTrack’s meta-planning (Fridovich-Keil et al., 2017) is a key construct, deploying a portfolio of planners $\{\pi_1, \pi_2, \ldots, \pi_N\}$ with varying speed/TEB trade-offs. The meta-planner builds a search tree (analogous to RRT) and attempts to graft new waypoints using the fastest viable planner (largest TEB). Upon failure (due to proximity to obstacles), it switches to a slower planner (smaller TEB), verifying safe transitions through precomputed Switching Safety Bounds (SSBs).

Online replanning is triggered by sensor updates, leveraging minimum sensing horizon constraints (TEB plus planning model travel during the replanning interval) to preserve safety. The meta-planner maintains safety by ensuring the TEB never intersects augmented obstacles, dynamically switching planners based on local configuration. For time-varying systems, recent advances (Siriya et al., 5 Dec 2024) extend this construct: offline HJ-based value functions and optimal safe controllers support an online planning layer that can perform "teleportation," i.e., immediate reset of planning state within the invariant TEB tube, thus maximizing both flexibility and safety.

3. Optimization-based Safety and Scalability

Model predictive control (MPC) and related optimization approaches have traditionally faced challenges in real-time enforcement of safety, especially under nonconvex, high-dimensional constraints. Recent work integrates formal safety directly into real-time optimization:

Risk-Averse MPC (Ploeg et al., 2022) incorporates artificial potential-based risk fields for static/dynamic hazards, using multivariate Gaussian penalty terms on predicted proximity to objects or infrastructural features. The resulting nonlinear MPC problem remains tractable, achieving real-time execution (<50 ms per cycle) while supporting anticipatory maneuvers.
Spatiotemporal Safety Constraints (Zheng et al., 2023) extend this further by encoding barrier-type separation requirements (e.g., $h(x, O_i(t)) \geq 0$ for all $i,t$ ) within the parallelized trajectory optimization using direct multiple shooting. Time-discounted soft costs are used for robustness to multimodal behavior in surrounding vehicles, and a multi-objective decision module balances safety, efficiency, and passenger comfort.
Geometry-Aware Predictive Safety Filters (Bena et al., 15 Aug 2025) synthesize control barrier functions (CBFs) via the numerical solution of Poisson's equation over a configuration-space domain "buffered" with the robot's full geometry. These CBF constraints, enforced in nonlinear MPC, guarantee traversal within the evolving safe set, encoding both position and orientation, and adapt online using perception data (e.g., level-set boundary evolution via optical flow).

Optimization-based approaches are also prominent for manipulation and highway scenarios. Hybrid frameworks (Lu et al., 6 Aug 2025) combine learning-based GNN predictors for velocity profiles with MIQP-based path optimizers, which use linearized vehicle OBB approximations to reduce binary variable count while maintaining strict spatiotemporal safety constraints.

4. Algorithmic Innovation: Motion Primitives, Parallelism, and Funnel Generators

Optimization-free and parallelized approaches have emerged as alternatives for scaling trajectory generation:

Motion primitive-based planning (e.g., STITCHER (Levy et al., 30 Dec 2024)) decomposes the planning problem into graph search over closed-form primitives (double/triple integrator models), using geometric pathfinding and BeLLMan-based cost-to-go as a heuristic for A* search. Collision avoidance is handled via conservative spatial checking and selection of state/control-constrained primitives.
Funnel Generators (Ravanbakhsh et al., 2019) utilize SOS programming to compute reference-restricted funnels—a family of invariant tubes—by considering only a semi-algebraically defined set of admissible reference trajectories. This reduces conservatism relative to traditional, worst-case tube computation and enables "plug-in" integration with existing motion planners by funnel concatenation.
Parallel trajectory optimization (Zheng et al., 2023) and consensus ADMM (Zheng et al., 10 Feb 2025) are deployed to decompose high-dimensional, multi-agent or contingency-aware planning problems. For occlusion-aware planning, real-time solution of biconvex NLPs (for exploration versus fallback policies) leverages the ADMM’s decomposition into convex subproblems, with reachability analysis informing dynamic velocity constraints.

5. Safety Certification, Online Assessment, and System Integration

Practical deployment of real-time safety-aware trajectory generation necessitates embedded safety certification, runtime verification, and modular integration with low-level actuation and perception stacks:

Embedded trajectory checkers (Dinh et al., 2021) evaluate planned trajectories against formalized, first-order safety rules, including worst-case assessments (e.g., for cut-in vehicles or sudden obstacles), implemented in real time on automotive-grade platforms (AURIX TC397B), achieving bounded linear scaling with obstacle count and trajectory length.
Time safeguard concepts (Moller et al., 10 Jul 2025) complement geometric/dynamic feasibility by monitoring temporal consistency of planning module outputs. The safeguarding module detects violation of maximum reaction time $T_{\text{max}}$ between trajectories and triggers fallback as necessary, working on RTOS-enabled real-time units with strict temporal isolation.
Cost-based plausibility metrics assist in ranking and selecting among feasible trajectories, integrating lateral/longitudinal comfort, deviation penalties, and velocity reference offsets into a unified cost for automated safety-verification at runtime, ensuring both functional safety and user-comfort criteria are met.

Integration challenges addressed in these works include efficient middleware communication (e.g., ROS 2 to DDS translation for hard RTOS), modularity for HIL and field testing, and scalable deployment for both low-latency and determinism.

6. Domain-Specific Extensions and Robustness

Safety-aware trajectory generation methods are adapted to various operational domains:

Manipulator arms (Holmes et al., 2020, Michaux et al., 2023) employ reachability-based signed distance functions (RDFs): neural network surrogates trained to represent the minimum swept-volume distance to obstacles across all links, supporting differentiable, real-time collision constraint integration in high-DOF arms.
Multi-robot teams (Şenbaşlar et al., 2021) use distributed replanning via Bézier curves and convex polytope constraints, ensuring safety without inter-robot communication and maintaining robustness to robot failure or tracking error.
Occlusion-aware AV planning (Zheng et al., 10 Feb 2025) leverages reachability analysis to model phantom vehicles' dynamic velocity boundaries and employs contingency planning (joint optimization of exploration and fallback policies), maintaining safety and efficiency in occluded intersection scenarios.
Scenario generation and validation (Zhou et al., 23 May 2025, Stoler et al., 14 Jul 2025) integrate real-time trajectory generation with adversarial and crash-grounded data-driven scenario design for stress-testing and safety-validation in simulated environments, employing contrastive pretraining and vision-LLMs to enhance semantic realism of generated trajectories.

7. Scaling, Computational Trade-offs, and Comparative Analysis

These frameworks consistently decouple heavy offline computations (HJ reachability, funnel/TEB calculation, neural network training) from lightweight online planning. The primary trade-offs center on:

Optimality versus computational time: Optimization-free and parallelized approaches (e.g., STITCHER, parallel trajectory optimization) can produce near-optimal, dynamically feasible, and safe trajectories in milliseconds, outperforming conventional optimization-based methods under strict real-time constraints (Levy et al., 30 Dec 2024, Zheng et al., 2023).
Conservatism versus reactivity: Reference-restricted funnels and adaptive TEBs yield less conservative safety margins compared to global worst-case tubes, enabling more agile behavior without sacrificing provable safety (Ravanbakhsh et al., 2019, Siriya et al., 5 Dec 2024).
Empirical validation: Reported system-level success rates up to 97% (e.g., hybrid MIQP + GNN frameworks (Lu et al., 6 Aug 2025)), real-time per-cycle compute times ( $\ll$ 100 ms), and experimental demonstrations on both AV and manipulation platforms substantiate the practical deployability of these strategies.

In summary, real-time safety-aware trajectory generation is characterized by an overview of rigorous offline safety certification, fast and adaptive online planning, formal runtime verification, and modular system integration tailored to the domain's operational realities. The field is marked by continued advances in reachability analysis, optimization theory, learning-based prediction, and scalable system architecture, supporting deployment of safety-critical autonomous systems in uncertain and dynamic environments.