On Motion Planning for Point-to-Point Maneuvers for a Class of Sailing Vehicles

Algorithm 1

Motion planning algorithm. Goal: To generate a sequence of control signals for the propulsive force.

1: start/end points 𝐱(0)=(𝑥₀,0), 𝐱(𝑇)=(𝑥_𝑇,0)

2: compare 𝑥₀ with 𝑥_min to check whether it needs to go

 backwards, if yes, go backwards and restart from step 1

3: solve TPBVP for input levels {𝐹,0,−𝐹} to get 𝑇₁,𝑇₂,𝑇₃, and 𝑥_𝑡3

4: 𝐢𝐟𝑥_𝑡3=𝑥_𝑇

5:  case 1: apply input levels {𝐹,0,−𝐹} with durations {𝑇₁,𝑇₂,𝑇₃}

6: 𝐞𝐥𝐬𝐞𝐢𝐟𝑥_𝑡3>𝑥_𝑇

7:  case 2: solve TPBVP for input levels {𝐹,−𝐹,0,−𝐹}

   and apply them with obtained durations {𝑇₁,𝑇₂,𝑇₃,𝑇₄}

8: else (i.e., 𝑥_𝑡3<𝑥_𝑇)

9:  case 3: solve TPBVP for input levels {𝐹,0,𝐹,−𝐹} and apply

   them with obtained durations {𝑇₁,𝑇₂,𝑇₃,𝑇₄}

10:𝐞𝐧𝐝