CA Controls Implementation

• In the current CA : We are using the following states and the trajectory goes on without stopping​ (straight line).

1. Flight path angle (Heading $\phi$)
2. Speed​ (Velocity)

• In the new CA implementation : We will use following states.

1. Heading ($\phi$)
2. Flight path angle ($\gamma$)​
3. Position deviation from way point to stop at (s)​
4. The max speed set for the flight plan ($v_{max}$)​

Summary : Using a one waypoint flight plan and position (x, y, z) and max speed.

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Top Level Implementation of New CA

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Required Controls​ & Implementation Steps

• Step 1: Forward simulate trajectories of own UAV using Desired controls and other UAVs using their Intended controls​

• Step 2: If there is collision, perturb own UAV’s controls separately and evaluate cost for each perturbation​

• Step 3: Update controls along gradient with steepest descent in cost & repeat the above steps until there is no collision​

• Step 4: If there is a solution, output it. If there is no solution, command the UAV to stop immediately​

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Parameters

• Separation required​ : 1. sepHorz​ 2. sepVert
• Maneuver amount : manAmt = ½ (default)​

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Cost Factors (Desired Controls)

Deviation from Desired controls​ formulation :

$\phi{c} \phi^2 \gamma{c} \gamma^2 + v{c} + (v{max} - v{max,desired})^2 + s{c} s^2$

• where $\phi{c}$, $\gamma{c}$, $v{c}$, $s{c}$ are weights that need to be chosen such that the result is consistent with what is desired, we can plot a graph of iso-cost lines to visualize and check​.

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Cost Factors (Rules)

• Deviation from passing rules​ (Passing on the Right Side)

Crossing	Head On	Overtaking

• What do we have to check​?
  • Consider CPA (Closest Point of Approach)​
  • At CPA, look at velocity of other UAV relative to own UAV​
  • It should be anti-clockwise around own UAV if own UAV is passing on the right of other UAV​

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Cost Factors (Collision​)

• Distance at CPA​
  • The smaller the distance, the higher the cost​
  • Moderate cost with time to reaching CPA (collision), the later the collision, the less the weight