Safe Passage: Ensuring Collision-Free Navigation

• Safe Passage is a cross-domain safety concept that defines collision-free navigation through constrained and dynamic environments using specific forbidden states.
• Research demonstrates formal representations through safe sets, traversability maps, and dynamic metrics to address diverse operational risks.
• Adaptive planning and control architectures, including MPC and barrier functions, underpin robust safe passage in robotic, aerial, maritime, and human-centered applications.

Safe passage is a cross-domain safety concept for moving an agent, vehicle, or person through constrained space without entering states that are collision-prone, dynamically unrecoverable, socially unacceptable, or operationally unverified. In contemporary research, the term spans hierarchical visual navigation for mobile robots in cluttered indoor spaces, provably safe multi-UAV routing in dense airspace, route choice for autonomous ships in restricted waterways, socially acceptable robot motion in crowded hallways, and multimodal or forensic support for vulnerable users during mobility handoffs such as exiting a vehicle or after a ride has officially ended (Zhang et al., 2 Mar 2026, Chen et al., 2017, Xu et al., 11 Jan 2025, Meinhardt et al., 21 Jan 2025).

1. Scope and operational meanings

Across the literature, safe passage is not a single formalism but a family of task-specific safety objectives. In robotics, it commonly denotes collision-free traversal of cluttered, narrow, or previously unseen environments under explicit geometric and dynamic constraints. In transportation systems, it extends to space-time deconfliction, legally compliant routing, waiting-time reduction as a proxy for exposure to crime, or post-trip traceability after anomalous events (Zhang et al., 2 Mar 2026, Chen et al., 2017, Valencia et al., 2023, Minja et al., 8 Jul 2026).

Domain	Operational meaning of safe passage	Representative work
Cluttered mobile robot navigation	Safe traversal through cluttered, narrow, and unseen environments using explicit safety-aware planning and control	(Zhang et al., 2 Mar 2026)
Human-occupied and crowded spaces	Collision avoidance with moving people while reducing freezing, disturbance, or social disruption	(Majd et al., 2021, &&&10&&&, Zhou et al., 2023)
Airspace and multi-UAV routing	Guaranteed arrival with collision-free space-time separation under bounded disturbances	(Chen et al., 2017, Chen et al., 2016)
Restricted waterways	Route choice favoring larger and more consistent maneuvering space and avoiding bottlenecks	(Xu et al., 11 Jan 2025)
Controlled-airspace entry	Flight-specific safety cases for safe authorization into managed airspace	(Hunter et al., 4 Feb 2025)
Human-centered transitions	Safe exit from highly automated vehicles and safe post-trip continuity in ride-hailing	(Meinhardt et al., 21 Jan 2025, Minja et al., 8 Jul 2026)

This breadth reflects a common structure. Safe passage is usually defined relative to a destination, a set of forbidden states, and an admissible action model. What changes from domain to domain is the representation of danger: obstacle occupancy, human motion uncertainty, regulatory altitude bands, dense-crowd disturbance, narrow-waterway geometry, unsafe curbside conditions, or the forensic blind spot after trip cancellation. A plausible implication is that safe passage is best treated as a systems property rather than a purely geometric one.

2. Formal representations of safety

Several papers formulate safe passage through explicit safe sets. In human-occupied indoor navigation, the robot must reach a goal set while remaining inside a time-varying safe region

$$\mathcal{X}_s(t) = \{\mathbf{x}\in \mathcal{X}\mid h(\mathbf{x}(t))\ge 0 \},$$

with trajectories required to satisfy $\sigma(t)\in\mathcal{X}_s(t)$ for all $t$ (Majd et al., 2021). This is a standard control-theoretic view: safety is forward invariance of a set.

A stricter state-based notion appears in fixed-wing low-altitude flight, where the key object is the inevitable collision state set

$$\mathcal{X}_{ICS} = \left\{ \mathbf{x}\in\mathcal{X}^+ \;\middle|\; \forall \bm{\eta}\in \Gamma(\mathbf{x},\infty),\; \exists s\in[0,\infty)\ \text{s.t.}\ \bm{\eta}(s)\in\mathcal{X}^- \right\}.$$

Here, safe passage means never entering a state from which all future feasible paths eventually collide with terrain or violate altitude constraints (Lim et al., 2024).

Perception-driven mobile robot work often encodes safety as a continuous traversability or clearance field rather than a binary occupancy set. SaferPath uses an image-plane traversability score map $\mathcal{S}(u,v)\in[-1,1]$, where negative values indicate traversable/free space, positive values indicate obstacles/unsafe regions, and values near zero mark boundaries. Safety is enforced over a tube representing the robot body, with constraints of the form

$$\mathcal{S}\!\left(\mathcal{X}_{\text{tube}}^{(k)}\right)\le \delta,$$

so the path is judged not as a point trace but as a swept-width corridor (Zhang et al., 2 Mar 2026).

Maritime route safety is expressed at route level through a dynamic width characterization function $W(s)$ and the Safety Performance Index

$\kappa_{sp} = \frac{\bar{\omega}_{\scriptscriptstyle dwc}}{\displaystyle\sum_{i=1}^{n} -\log_{10}\left(\frac{W(s_i)}{\xi}\right)\,\mathbbm{1}_{\{W(s_i) < \xi\}}},$

which balances global average width against penalties for locally narrow sections (Xu et al., 11 Jan 2025). Passage-oriented planning adopts yet another abstraction: if $P_\sigma(1)$ is the set of passages traversed by a path $\sigma$, then its accessible free space is summarized by

$\sigma(t)\in\mathcal{X}_s(t)$0

the narrowest passage crossed along the entire path (Huang et al., 30 Jun 2025).

In multi-vehicle airspace, safety is represented as space-time reservations. Sequential path planning constructs reachable tubes such as

$\sigma(t)\in\mathcal{X}_s(t)$1

with lower-priority vehicles treating these reservations as moving obstacles. Safe passage is therefore not only spatial separation but non-overlap of reachable tubes in space-time under worst-case disturbances (Chen et al., 2016).

Taken together, these formulations show that safe passage is rarely reducible to Euclidean clearance alone. The common technical move is to replace raw geometry with a safety representation that is invariant under the relevant failure mode: body width, uncertainty, disturbance, dynamics, or regulation.

3. Planning and control architectures for cluttered autonomy

A large part of the recent literature treats safe passage as a layered planning-and-control problem rather than an end-to-end prediction problem. SaferPath is explicit on this point: it uses learned visual navigation only as guidance, then wraps it with a traversability mapper, a safety-constrained optimizer, and MPC tracking. The core optimization scales a reference trajectory anisotropically through a low-dimensional parameter matrix $\sigma(t)\in\mathcal{X}_s(t)$2 and refines it with Model Predictive Stein Variational Evolution Strategy. In narrow passageways, the baseline end-to-end models GNM, ViNT, and NoMaD all have $\sigma(t)\in\mathcal{X}_s(t)$3 success with more than $\sigma(t)\in\mathcal{X}_s(t)$4 collisions on average, whereas SaferPath variants achieve success rates of $\sigma(t)\in\mathcal{X}_s(t)$5, $\sigma(t)\in\mathcal{X}_s(t)$6, and $\sigma(t)\in\mathcal{X}_s(t)$7 with collision averages of $\sigma(t)\in\mathcal{X}_s(t)$8, $\sigma(t)\in\mathcal{X}_s(t)$9, and $t$0, respectively (Zhang et al., 2 Mar 2026).

EAST approaches the same problem from planning-and-control co-design. It combines a costmap-based A* planner, a convex cone-shaped reachable set for the closed-loop unicycle, a reference governor, and CBF constraints for moving obstacles. In static environments, the Dynamic Safety Margin

$t$1

defines a local safe zone around the governor state, and Theorem 1 establishes collision-free motion with static obstacles if $t$2 initially (Li et al., 2023). This architecture makes safe passage adaptive: fast in open areas, cautious in narrow passages, and temporarily off-path around moving obstacles.

Sampling-based planners have also been augmented with formal safety filters. In human-occupied corridors, CBF-TB-RRT grows a time-stamped tree in configuration-time space while steering each segment through a QP constrained by barrier functions against static and predicted dynamic obstacles. Human motion is predicted by JS-MDP, then converted into probabilistic occupancy discs; the resulting control law keeps the trajectory inside the predicted safe set at each step (Majd et al., 2021). The method yields behaviors characteristic of safe passage rather than shortest-path motion: waiting at corridor entrances, delaying turns until gaps appear, and moving close to a wall to let people pass.

Other work makes the passage structure itself the planning primitive. Spline-based harmonic-potential planning first decomposes free space into polygonal cells, then assigns each cell a harmonic potential whose Dirichlet boundary condition is a cardinal B-spline curve engineered to have a unique minimum on the chosen exit facet. The resulting control law

$t$3

funnels the agent cell-by-cell along a prescribed chain, with no spurious interior minima because the potential is harmonic (Nicu et al., 19 Jan 2026). PTOPP, by contrast, leaves the ambient planner sampling-based but changes the objective: instead of length or local clearance, it optimizes which passages the path traverses, typically maximizing the minimum or lexicographically weighted passage widths along the entire path (Huang et al., 30 Jun 2025).

A broad pattern emerges. Safe passage is most robust when high-level intent, local geometry, and low-level dynamic feasibility are separated but coupled: perception or learning proposes, geometry filters, optimization refines, and feedback control enforces.

4. Safe passage in shared human spaces

In dense human environments, collision freedom is necessary but not sufficient. The passage must also be socially acceptable, legible, and minimally disruptive. “Look Before You Leap” addresses narrow hallways where robots otherwise freeze behind slow humans. Its planner uses motion primitives plus a CVaR-based risk term over hypothetical humans emerging from occluded space, so the robot first performs a “peek” into the passing lane and only commits to a pass if tail risk drops below a threshold. The resulting behavior improves time to goal in longer hallways while producing significantly fewer human path changes than CADRL and PSMM, and only slightly more personal-space violations than HATEB, mostly during overtaking (Sharma et al., 2024).

A more explicit disturbance model appears in dense-crowd navigation with integrated macro and micro dynamics. This framework defines a Flow Disturbance Penalty from local density–velocity flux and an Individual Disturbance Penalty from Wasserstein distance between pedestrian trajectory distributions with and without the robot. It also conditions pedestrian reaction on awareness inferred from body orientation and gaze, and enforces temporal consistency so the robot’s intent remains legible over time (Zhou et al., 2023). In real-world downstream experiments it reports $t$4 success, $t$5 collisions, $t$6 freezing, and $t$7 frontal interactions; upstream experiments remain collision-free but become harder, with $t$8 success and $t$9 freezing events.

Sampling-plus-CBF work in human corridors reinforces the same point from a different angle. There, safe passage is achieved not by forcing priority but by choosing when to wait, when to advance, and when to re-route around predicted human occupancy. In the reported scenarios, the robot safely yields to moving groups, postpones entry into crowded corridors, and exploits openings only when barrier constraints remain feasible (Majd et al., 2021).

These papers collectively argue that shared-space safe passage requires at least three layers of reasoning: predictive safety with respect to uncertain human motion, behavioral moderation to avoid freezing or aggressive squeezing, and explicit disturbance metrics that quantify what the robot does to surrounding people rather than only what surrounding people might do to the robot.

5. Space-time reservations, route safety, and admission control

At infrastructure scale, safe passage becomes a problem of deconfliction, authorization, and route selection over large state spaces. In dense urban airspace, Hamilton–Jacobi reachability and Sequential Path Planning decompose the multi-UAV problem by priority order. Each higher-priority vehicle reserves a reachable tube in space-time; lower-priority vehicles treat these tubes as moving obstacles and compute backward reachable sets guaranteeing arrival before scheduled time while avoiding all reservations and static obstacles. In simulations over San Francisco and the Bay Area, all $$\mathcal{X}_{ICS} = \left\{ \mathbf{x}\in\mathcal{X}^+ \;\middle|\; \forall \bm{\eta}\in \Gamma(\mathbf{x},\infty),\; \exists s\in[0,\infty)\ \text{s.t.}\ \bm{\eta}(s)\in\mathcal{X}^- \right\}.$$0 vehicles in the city case and all $$\mathcal{X}_{ICS} = \left\{ \mathbf{x}\in\mathcal{X}^+ \;\middle|\; \forall \bm{\eta}\in \Gamma(\mathbf{x},\infty),\; \exists s\in[0,\infty)\ \text{s.t.}\ \bm{\eta}(s)\in\mathcal{X}^- \right\}.$$1 vehicles in the multi-city case reach their destinations without collisions for the tested disturbance levels and arrival schedules (Chen et al., 2017).

The disturbance-and-intruder extension preserves the same idea but enlarges the reservation logic. Robust trajectory tracking produces invariant error sets, and intruder-aware augmented obstacle sets ensure that when an adversarial intruder appears, a vehicle can switch to avoidance without being forced into collision with other reserved tubes. The paper emphasizes that this preserves tractability: complexity scales linearly in the number of vehicles with disturbances only, and quadratically when a single intruder is included (Chen et al., 2016).

For controlled-airspace entry of small uncrewed aircraft, SafeSPLE shifts safe passage from trajectory synthesis to assurance synthesis. It constructs a safety-case product line with a 51-feature model and parameterized GSN fragments. The case study shows how one flight with a DJI Mini 4 Pro is accepted because checks such as $$\mathcal{X}_{ICS} = \left\{ \mathbf{x}\in\mathcal{X}^+ \;\middle|\; \forall \bm{\eta}\in \Gamma(\mathbf{x},\infty),\; \exists s\in[0,\infty)\ \text{s.t.}\ \bm{\eta}(s)\in\mathcal{X}^- \right\}.$$2 and $$\mathcal{X}_{ICS} = \left\{ \mathbf{x}\in\mathcal{X}^+ \;\middle|\; \forall \bm{\eta}\in \Gamma(\mathbf{x},\infty),\; \exists s\in[0,\infty)\ \text{s.t.}\ \bm{\eta}(s)\in\mathcal{X}^- \right\}.$$3 are satisfied, while a DEERC D20 case fails because

$$\mathcal{X}_{ICS} = \left\{ \mathbf{x}\in\mathcal{X}^+ \;\middle|\; \forall \bm{\eta}\in \Gamma(\mathbf{x},\infty),\; \exists s\in[0,\infty)\ \text{s.t.}\ \bm{\eta}(s)\in\mathcal{X}^- \right\}.$$4

is false, so the wind-gust subgoal is not supported (Hunter et al., 4 Feb 2025). Here, safe passage means justified entry into controlled airspace rather than merely local collision avoidance.

Maritime routing in restricted waters defines safe passage geometrically. GARSA computes a dynamic width characterization function from line and point boundary elements, then ranks routes by the Safety Performance Index. In the Port of Hamburg case study, Route 5 has mean dynamic width $$\mathcal{X}_{ICS} = \left\{ \mathbf{x}\in\mathcal{X}^+ \;\middle|\; \forall \bm{\eta}\in \Gamma(\mathbf{x},\infty),\; \exists s\in[0,\infty)\ \text{s.t.}\ \bm{\eta}(s)\in\mathcal{X}^- \right\}.$$5 m, minimum width $$\mathcal{X}_{ICS} = \left\{ \mathbf{x}\in\mathcal{X}^+ \;\middle|\; \forall \bm{\eta}\in \Gamma(\mathbf{x},\infty),\; \exists s\in[0,\infty)\ \text{s.t.}\ \bm{\eta}(s)\in\mathcal{X}^- \right\}.$$6 m, and SPI $$\mathcal{X}_{ICS} = \left\{ \mathbf{x}\in\mathcal{X}^+ \;\middle|\; \forall \bm{\eta}\in \Gamma(\mathbf{x},\infty),\; \exists s\in[0,\infty)\ \text{s.t.}\ \bm{\eta}(s)\in\mathcal{X}^- \right\}.$$7, while shorter alternatives contain severe bottlenecks such as Route 3 with widths of $$\mathcal{X}_{ICS} = \left\{ \mathbf{x}\in\mathcal{X}^+ \;\middle|\; \forall \bm{\eta}\in \Gamma(\mathbf{x},\infty),\; \exists s\in[0,\infty)\ \text{s.t.}\ \bm{\eta}(s)\in\mathcal{X}^- \right\}.$$8, $$\mathcal{X}_{ICS} = \left\{ \mathbf{x}\in\mathcal{X}^+ \;\middle|\; \forall \bm{\eta}\in \Gamma(\mathbf{x},\infty),\; \exists s\in[0,\infty)\ \text{s.t.}\ \bm{\eta}(s)\in\mathcal{X}^- \right\}.$$9, and $\mathcal{S}(u,v)\in[-1,1]$0 m at different arc-length positions. A comparison with A* further shows that the shortest path can contain a narrow section about $\mathcal{S}(u,v)\in[-1,1]$1 m wide and $\mathcal{S}(u,v)\in[-1,1]$2 m long that GARSA deliberately avoids (Xu et al., 11 Jan 2025).

Transit scheduling literature reaches a similar conclusion through a different mechanism. In bus rapid transit, the paper on passenger safety at scheduled stops treats waiting time as exposure to unsafe environments such as crime and harassment. Dynamic programming then minimizes passenger waiting and timetable deviation; the reported waiting-time area at stop 1 drops from $\mathcal{S}(u,v)\in[-1,1]$3 in the baseline to $\mathcal{S}(u,v)\in[-1,1]$4 under the optimized policy, with analogous reductions at the other stops (Valencia et al., 2023). This suggests that safe passage can also mean shortening the unsafe dwell before boarding, not only regulating the vehicle once it is moving.

6. Human-centered continuity, post-trip safety, and emerging directions

Some recent work extends safe passage beyond vehicle motion to the safety of transitions around vehicles. PathFinder treats the exit from a highly automated vehicle as a distinct high-risk phase for blind and visually impaired people. Its multimodal interface combines tactile obstacle buttons, a vehicle-centered layout, a movable compass needle, and auditory announcements about destination direction, curb distance, surface type, and nearby hazards. In a three-factorial study with $\mathcal{S}(u,v)\in[-1,1]$5 BVIPs, PathFinder yields a significant main effect on mental demand,

$\mathcal{S}(u,v)\in[-1,1]$6

reducing mean mental demand from $\mathcal{S}(u,v)\in[-1,1]$7 to $\mathcal{S}(u,v)\in[-1,1]$8, while maintaining high perceived safety in both urban and rural scenarios (Meinhardt et al., 21 Jan 2025). Safe passage here is a safe transition from “the car has stopped” to “the passenger knows where and how to exit.”

Safe2Hail addresses another transition point: the period after a ride-hailing trip is cancelled or prematurely terminated. It introduces a time-bounded post-trip synchronization mechanism that logs driver–passenger proximity every $\mathcal{S}(u,v)\in[-1,1]$9 seconds for up to $$\mathcal{S}\!\left(\mathcal{X}_{\text{tube}}^{(k)}\right)\le \delta,$$0 seconds, using the Haversine formula and thresholds at $$\mathcal{S}\!\left(\mathcal{X}_{\text{tube}}^{(k)}\right)\le \delta,$$1 m, $$\mathcal{S}\!\left(\mathcal{X}_{\text{tube}}^{(k)}\right)\le \delta,$$2 m, and $$\mathcal{S}\!\left(\mathcal{X}_{\text{tube}}^{(k)}\right)\le \delta,$$3 m. In beta-tested simulations it reports accuracies of $$\mathcal{S}\!\left(\mathcal{X}_{\text{tube}}^{(k)}\right)\le \delta,$$4 for premature-end scenarios, $$\mathcal{S}\!\left(\mathcal{X}_{\text{tube}}^{(k)}\right)\le \delta,$$5 for cancellation, $$\mathcal{S}\!\left(\mathcal{X}_{\text{tube}}^{(k)}\right)\le \delta,$$6 for route deviation, and $$\mathcal{S}\!\left(\mathcal{X}_{\text{tube}}^{(k)}\right)\le \delta,$$7 when GPS is disabled (Minja et al., 8 Jul 2026). The framework is explicitly forensic: safe passage is extended from the official trip to verified physical separation after an anomaly.

Several recurring limitations remain. Perception coverage is a central weakness in monocular visual navigation and in post-trip mobile sensing; dynamic-obstacle guarantees are often local or conditional on QP feasibility; infrastructure-scale approaches rely on accurate disturbance bounds, map knowledge, or regulatory acceptance; and geometric route safety does not by itself model social norms, cyber threats, or adversarial agents in full generality (Zhang et al., 2 Mar 2026, Li et al., 2023, Chen et al., 2017, Xu et al., 11 Jan 2025). Taken together, the literature suggests that future safe-passage systems will combine richer sensing, predictive scene understanding, explicit uncertainty sets, and stronger assurance artifacts, while keeping the core principle unchanged: movement is authorized only when the relevant safety envelope—geometric, dynamic, social, or forensic—remains intact.