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Our group H OLDING B IDART - F RANCE S OFTWARE B IDART - F RANCE C OMMERCIAL, S ALES, M ARKETING, SUPPORT B ARCELONA - S PAIN S OFTWARE P ORTLAND - USA C HARTS B IDART - F RANCE 75 E MPLOYES T URNOVER 2012: 6.2 M€ (+10%)

Radar Overlay Strong collaboration with FURUNO Japan (1st worldwide marine electronics manufacturer).

Cameras FLIR (IR, night vision…)

Isochrones for minimum time route optimization Wind polar Wave polar Set sail Weather prediction (wind, waves) Currents Optimal route

DEMO

Isochrone : Dynamic programming N Objective: Maximize distance for a given time interval ∆t DStep n →Isochrone at time ζ Reference : Knmi publicatie met nummer : On minimal-time ship routing S.J. Bijlsma 1975

N D Wind Polars Isochrone : Dynamic programming

N D a d1d1 d2d2 d3d3 d4d4 What is the shorter path ? Isochrone : Dynamic programming

N D Wind polar Direct construction of next point : normal to isochrone == normal to polar Isochrone : Dynamic programming

N D Repeat for all isochrone point, you construct next isochrone. Isochrone : Dynamic programming

Next isochrone (dash) Optimization becomes a geometrical optimization. Not easy to resolve, in good computational time, taking into account numerical precision. Multiple path for optimal route at intersection point. Isochrone : Dynamic programming

Route optimization for motor boats Main goal: fuel consumption optimization. But also limit weather conditions. Several types of boats – Motor – Motor with sail assistance – Motor Sailing – Sailing

3D Routing New problem : find best course (2d) and best motor speed (power) to minimize fuel consumption. Motor and MotorSail boats have round speed polars (motor always on) => isochrones are isodistance (shortest path).

Fuel Consumption models Motor : – Hydro & areo dynamic forces + motor consumption curve. – Approximation 2 nd degree from speed inside speed limits (18-25kts) : Conso t/nm = *V V (not linear) Motor Sailing : mutilple Wind polar curves (for each motor power / sail %).

Fast Marching Method Ordered Upwind Method We wanted a new method for 2D & 3D (more easy to implement than 3D geometric calculation). Differential equation : Consumption = f(x,y,t,course,motor power). Front propagation. Strong anisotropy : wind and wind polar (sailing) or waves.

Ordered Upwind Method Considered are sorted according to cost. Reference : SIAM J. Numer. Anal., 41(1), 325–363. (39 pages) Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms

Ordered Upwind Method Smallest Considered is removed from Sorted Queue. It becomes the Last Accepted.

Ordered Upwind Method All Neighbors of Last Accepted are updated. Cost and Arrival Time are computed.

Ordered Upwind Method Again, smallest Considered => Last Accepted

Ordered Upwind Method The Front advanced with 2 new Accepted. Loop until arrival point is reached.

3D OUM

OUM : 3 update methods Direct Cost : from a node to horizontal, vertical or diagonal node. Enumeration : minimise over 20 angles (original method from Vladimirsky) Gradiant : from downwind gradiant, select best speed vector in polar, use it to compute upwind.

Enumeration Linear cost interpolation between U2 & U3. 20 angles tried for minimization.

Gradiant, when 3 accepted neighboors

DEMO

Experience Difficult to validate results : reference solution. Gradiant was working during unit testing, we found problems during integration. Parallel algorithm is not evidence. Software optimization is needed for interactive simulations.