Navigation · Theory · M9
M9-T5 — Other Platforms: Legged, Aerial, Marine and Off-Road
The vocabulary of navigation (map, plan, follow, recover) travels. The assumptions underneath it do not.
A grid, a path and a controller carry a wheeled robot through a hospital. Put the same stack on a quadruped, a drone, a boat or a tractor and parts of it silently stop being true. This lesson lists what each platform changes, so you can tell which pieces of what you have learned transfer and which need replacing.
Learning objectives
After this lesson, you should be able to:
- Name the assumptions of the 2D costmap and unicycle stack: flat ground, stopping and turning in place, position-only state, lethal-or-free obstacles.
- Say what legged, aerial, marine and off-road platforms change, and which of those assumptions fail for each.
- Compute basic platform constraints, such as a minimum turning radius or a wind correction angle.
- Decide when a grid-based planner is still adequate and when the representation itself has to change.
The intuition
Scout can do two things most platforms cannot: it can stop, and it can sit on the floor. Stopping gives it safety (the safest state is zero velocity), and a flat floor reduces the world to two dimensions. A fixed-wing aircraft cannot stop; a boat takes long to stop and drifts with the current; a legged robot can stop but must put each foot somewhere that will hold; a tractor must care what the ground is made of. Each difference attacks a simple assumption of the wheeled stack.
The useful way to approach a new platform is to keep the layering (sense, localize, map, plan, control, recover) and ask of each layer: what does this platform need that the wheeled version assumed away?
The mathematics
Assumptions of the wheeled stack
- Flat ground: a 2D occupancy grid with cost is enough.
- Stop and turn: a differential-drive robot can rotate on the spot, so recoveries (spin, back up, wait) exist and are safe.
- Position state: a pose (x, y, θ) describes the robot; velocity is a command.
- Kinematics, not dynamics: the robot goes where it is told within a controller delay.
- Obstacle = lethal, free = fine: terrain has no grade of passability.
What each platform changes
| Platform | Assumption that fails | What replaces it | What survives |
|---|---|---|---|
| Legged | Any free cell is standable; speed is limited by wheels | Terrain maps with height and slope; footstep or gait planning; stability and reachability limits; perception of what is under the foot | Global topology, goals, behaviour trees, recoveries (a stand-up is a recovery) |
| Aerial (multirotor) | Planar, kinematic, can stop on the ground | 3D maps (voxels, ESDFs), smooth trajectories in position and higher derivatives, thrust and attitude limits, wind | Layered maps, replanning, the planner/controller split |
| Aerial (fixed wing) | Can stop and turn in place | Minimum airspeed and turn radius: curves of bounded curvature (Dubins-like), altitude | Graph search over a state lattice |
| Marine | Zero speed means zero motion; commands act at once | Dynamics with inertia and drag, currents and waves, rules of the road, limited braking | Global routing on a chart, waypoint following |
| Off-road / agricultural | Cost depends on distance to obstacles only | Traversability from slope, roughness, soil and slip; slip-aware kinematics; vegetation that can be driven through | Costmap layering, path following |
Constraints you can compute
A fixed-wing aircraft in a coordinated turn with bank angle φ at airspeed v has a turn radius:
A vehicle moving through a moving medium (air or water) with speed v relative to the medium and a cross-current w must point upstream of its track, by the wind correction (crab) angle:
A legged robot adds a reachability constraint: each foothold must be within the leg’s reach of the body and on a surface whose slope and roughness are within limits. That is a constraint on the sequence of cells, not on a single cell.
A worked example
A fixed-wing survey drone. Airspeed 15 m/s, maximum bank 30°:
The drone cannot turn in a circle smaller than about 40 m, so a survey leg change needs a turn of that radius and waypoints closer than twice that cannot all be hit. A planner designed for a unicycle that can rotate on the spot would produce paths that the aircraft cannot fly. The planning layer must use curves of bounded curvature (Dubins paths for a forward-only vehicle), and the state is not (x, y) but (x, y, heading, altitude, airspeed).
The same drone in wind. With a 5 m/s crosswind:
A path planned as if the air were still is flown 19.5° off if the heading points along the track, so the drone drifts sideways. The controller must handle the wind, and a planner that estimates time to goal must use ground speed (10 to 20 m/s here, a factor of two).
A boat that cannot stop. A small vessel at 4 m/s that takes 30 s to stop travels about 60 m even with full reverse (if braking were uniform). “Stop and wait for the path to clear” is not available in a channel; the recovery has to be a manoeuvre planned in advance, the safety envelope must be much larger than the footprint, and the speed must match the distance at which obstacles are detected.
A legged robot on stairs. A step height of 0.18 m exceeds the 0.05 m a wheeled robot treats as a threshold. The costmap layer must come from height and slope (traversability, lesson M2-T6), and the planner must choose where each foot goes. Scout’s global graph of corridors and doors still applies; only the local motion changes.
Engineering implications and limitations
Start from the interface
What does the platform’s controller accept (velocity, attitude, footsteps)? What does it guarantee (stability, limits)? Plan at the level of that interface and let the platform’s own controller handle what it is best at, such as balance and attitude. Many commercial platforms ship a velocity interface with an inner stability controller, which makes the wheeled-style stack usable at a coarse level.
Change the representation before the algorithm
Often the first step is not a new planner but a new map: height, slope and roughness for legs and wheels off road; voxel or ESDF maps for 3D; charts and currents for boats. The planner then searches a richer cost.
Recovery is platform-specific
Spin and back up make sense for Scout. For a drone, recovery means holding position or landing; for a boat, slowing and keeping steerage; for a legged robot, stopping and re-standing. The behaviour tree structure carries over; the leaves change.
Where Nav2 fits
Nav2 is designed for ground robots with a 2D costmap and wheeled kinematics (differential, omnidirectional, Ackermann-like models are supported by some plugins). Other platforms use its ideas, behaviour trees, plugins and lifecycle, or other stacks, with planners suited to the platform. Check the documentation for the platform you use rather than assuming a Nav2 plugin fits.
Common misconceptions
“A different robot just needs a different controller.”
Often the map and the planner also change: terrain, 3D space and dynamics enter earlier than control.
“A drone is a robot that moves in 3D; use a 3D grid and A*.”
A grid path is not flyable: the trajectory must respect thrust, attitude and smoothness, and wind changes the true cost.
“Legged robots avoid the need for traversability maps because they can step over things.”
They need richer maps, because stepping depends on where the foot lands and on the surface under it.
“Recoveries are the same everywhere.”
Spin and back up are a luxury of ground robots that can stop. The recovery must suit the platform.
Engineering takeaways
- The wheeled stack assumes flat ground, stop-and-turn, position-only state, kinematics and lethal-or-free obstacles.
- Legged robots add footholds and stability; aerial robots add 3D, dynamics and wind; marine robots add inertia and currents; off-road robots add terrain.
- Fixed-wing turn radius v²/(g tan φ) and the crab angle asin(w/v) show how constraints enter the plan.
- Change the map representation first, then the planner, then the controller; keep the layering.
- Recovery behaviours and safety envelopes are platform-specific.
References and further reading
Primary sources for the platform-specific planning problems mentioned here.
- L. E. Dubins, “On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents”, American Journal of Mathematics 79(3), 1957.
- D. Mellinger and V. Kumar, “Minimum Snap Trajectory Generation and Control for Quadrotors”, IEEE International Conference on Robotics and Automation (ICRA), 2011.
- P. Fankhauser, M. Bloesch and M. Hutter, “Probabilistic Terrain Mapping for Mobile Robots with Uncertain Localization”, IEEE Robotics and Automation Letters 3(4), 2018.
- P. Krüsi, P. Furgale, M. Bosse and R. Siegwart, “Driving on Point Clouds: Motion Planning, Trajectory Optimization, and Terrain Assessment in Generic Nonplanar Environments”, Journal of Field Robotics 34(5), 2017.
- T. I. Fossen, “Handbook of Marine Craft Hydrodynamics and Motion Control”, Wiley, 2011.
Knowledge check
Three conceptual questions. Write an answer, then reveal the explanation. Your answers stay in your browser.
Question 1
A fixed-wing drone flies at 20 m/s with a maximum bank of 25°. What is its minimum turn radius?
Explanation
R = v² / (g tan φ) = 400 / (9.81 × tan 25°) = 400 / (9.81 × 0.4663) = 87.4 m.
Question 2
A boat’s planner returns a path that passes 1 m from a buoy. The boat’s footprint is 2 m wide and it takes 20 s to stop from 3 m/s. Name two reasons the path is unsafe.
Explanation
The footprint (half-width 1 m) would touch the buoy with no margin, and the boat cannot stop in time: it needs about 30 m or more at 3 m/s even with ideal braking. Currents and the inability to stop mean a much larger clearance and a slower speed are needed.
Question 3
Which parts of the Scout stack would you expect to keep when moving to a quadruped in the same hospital, and which to replace?
Explanation
Keep: the global map of corridors and doors, goals, the behaviour tree and mission logic. Replace or extend: the local terrain representation (height, slope), the local motion layer (gait and footholds), and the recoveries (spin and back up are unsuitable).
What’s next
Next: navigation that is learned from data or steered by language, and what is not yet proven.
Related content
Nothing below is required to finish this lesson.
- BeforeM9-T4: Evaluating Navigation
Design an evaluation with repeatable scenarios, logged metrics and enough runs to trust the result.
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