Add basic shooting-on-the-fly implementation

This makes a bunch of simplistic assumptions about how the dynamics of
the shot work, but it'll probably get us pretty close initially and is
easy to implement and understand as-is.

Change-Id: I2ee8fa9d2681e4dec0e490395027d8860f58e521
diff --git a/y2020/control_loops/superstructure/turret/aiming.cc b/y2020/control_loops/superstructure/turret/aiming.cc
index 97331f3..7aaefac 100644
--- a/y2020/control_loops/superstructure/turret/aiming.cc
+++ b/y2020/control_loops/superstructure/turret/aiming.cc
@@ -10,6 +10,32 @@
 
 using frc971::control_loops::Pose;
 
+// Shooting-on-the-fly concept:
+// The current way that we manage shooting-on-the fly endeavors to be reasonably
+// simple, until we get a chance to see how the actual dynamics play out.
+// Essentially, we assume that the robot's velocity will represent a constant
+// offset to the ball's velocity over the entire trajectory to the goal and
+// then offset the target that we are pointing at based on that.
+// Let us assume that, if the robot shoots while not moving, regardless of shot
+// distance, the ball's average speed-over-ground to the target will be a
+// constant s_shot (this implies that if the robot is driving straight towards
+// the target, the actual ball speed-over-ground will be greater than s_shot).
+// We will define things in the robot's coordinate frame. We will be shooting
+// at a target that is at position (target_x, target_y) in the robot frame. The
+// robot is travelling at (v_robot_x, v_robot_y). In order to shoot the ball,
+// we need to generate some virtual target (virtual_x, virtual_y) that we will
+// shoot at as if we were standing still. The total time-of-flight to that
+// target will be t_shot = norm2(virtual_x, virtual_y) / s_shot.
+// we will have virtual_x + v_robot_x * t_shot = target_x, and the same
+// for y. This gives us three equations and three unknowns (virtual_x,
+// virtual_y, and t_shot), and given appropriate assumptions, can be solved
+// analytically. However, doing so is obnoxious and given appropriate functions
+// for t_shot may not be feasible. As such, instead of actually solving the
+// equation analytically, we will use an iterative solution where we maintain
+// a current virtual target estimate. We start with this estimate as if the
+// robot is stationary. We then use this estimate to calculate t_shot, and
+// calculate the next value for the virtual target.
+
 namespace {
 // The overall length and width of the field, in meters.
 constexpr double kFieldLength = 15.983;
@@ -30,6 +56,16 @@
 // The amount (in meters) that the inner port is set back from the outer port.
 constexpr double kInnerPortBackset = 0.743;
 
+// Average speed-over-ground of the ball on its way to the target. Our current
+// model assumes constant ball velocity regardless of shot distance.
+// TODO(james): Is this an appropriate model? For the outer port it should be
+// good enough that it doesn't really matter, but for the inner port it may be
+// more appropriate to do something more dynamic--however, it is not yet clear
+// how we would best estimate speed-over-ground given a hood angle + shooter
+// speed. Assuming a constant average speed over the course of the trajectory
+// should be reasonable, since all we are trying to do here is calculate an
+// overall time-of-flight (we don't actually care about the ball speed itself).
+constexpr double kBallSpeedOverGround = 15.0;  // m/s
 
 // Minimum distance that we must be from the inner port in order to attempt the
 // shot--this is to account for the fact that if we are too close to the target,
@@ -62,6 +98,22 @@
   fbb.Finish(builder.Finish());
   return fbb.Release();
 }
+
+// This implements the iteration in the described shooting-on-the-fly algorithm.
+// robot_pose: Current robot pose.
+// robot_velocity: Current robot velocity, in the absolute field frame.
+// target_pose: Absolute goal Pose.
+// current_virtual_pose: Current estimate of where we want to shoot at.
+Pose IterateVirtualGoal(const Pose &robot_pose,
+                        const Eigen::Vector3d &robot_velocity,
+                        const Pose &target_pose,
+                        const Pose &current_virtual_pose) {
+  const double air_time =
+      current_virtual_pose.Rebase(&robot_pose).xy_norm() / kBallSpeedOverGround;
+  const Eigen::Vector3d virtual_target =
+      target_pose.abs_pos() - air_time * robot_velocity;
+  return Pose(virtual_target, target_pose.abs_theta());
+}
 }  // namespace
 
 Pose InnerPortPose(aos::Alliance alliance) {
@@ -86,21 +138,13 @@
 
 Aimer::Aimer() : goal_(MakePrefilledGoal()) {}
 
-void Aimer::Update(const Status *status, aos::Alliance alliance, Mode mode) {
+void Aimer::Update(const Status *status, aos::Alliance alliance,
+                   WrapMode wrap_mode, ShotMode shot_mode) {
   const Pose robot_pose({status->x(), status->y(), 0}, status->theta());
   const Pose inner_port = InnerPortPose(alliance);
   const Pose outer_port = OuterPortPose(alliance);
   const Pose robot_pose_from_inner_port = robot_pose.Rebase(&inner_port);
-  const double inner_port_angle = robot_pose_from_inner_port.heading();
-  const double inner_port_distance = robot_pose_from_inner_port.xy_norm();
-  aiming_for_inner_port_ =
-      (std::abs(inner_port_angle) < kMaxInnerPortAngle) &&
-      (inner_port_distance > kMinimumInnerPortShotDistance);
-  const Pose goal =
-      (aiming_for_inner_port_ ? inner_port : outer_port).Rebase(&robot_pose);
-  const double heading_to_goal = goal.heading();
-  CHECK(status->has_localizer());
-  distance_ = goal.xy_norm();
+
   // TODO(james): This code should probably just be in the localizer and have
   // xdot/ydot get populated in the status message directly... that way we don't
   // keep duplicating this math.
@@ -111,25 +155,64 @@
       drivetrain::GetDrivetrainConfig().Tlr_to_la() *
       Eigen::Vector2d(status->localizer()->left_velocity(),
                       status->localizer()->right_velocity());
-  // X and Y dot are negated because we are interested in the derivative of
-  // (target_pos - robot_pos).
-  const double xdot = -linear_angular(0) * std::cos(status->theta());
-  const double ydot = -linear_angular(0) * std::sin(status->theta());
-  const double rel_x = goal.rel_pos().x();
-  const double rel_y = goal.rel_pos().y();
+  const double xdot = linear_angular(0) * std::cos(status->theta());
+  const double ydot = linear_angular(0) * std::sin(status->theta());
+
+  const double inner_port_angle = robot_pose_from_inner_port.heading();
+  const double inner_port_distance = robot_pose_from_inner_port.xy_norm();
+  aiming_for_inner_port_ =
+      (std::abs(inner_port_angle) < kMaxInnerPortAngle) &&
+      (inner_port_distance > kMinimumInnerPortShotDistance);
+
+  // This code manages compensating the goal turret heading for the robot's
+  // current velocity, to allow for shooting on-the-fly.
+  // This works by solving for the correct turret angle numerically, since while
+  // we technically could do it analytically, doing so would both make it hard
+  // to make small changes (since it would force us to redo the math) and be
+  // error-prone since it'd be easy to make typos or other minor math errors.
+  Pose virtual_goal;
+  {
+    const Pose goal = aiming_for_inner_port_ ? inner_port : outer_port;
+    virtual_goal = goal;
+    if (shot_mode == ShotMode::kShootOnTheFly) {
+      for (int ii = 0; ii < 3; ++ii) {
+        virtual_goal =
+            IterateVirtualGoal(robot_pose, {xdot, ydot, 0}, goal, virtual_goal);
+      }
+      VLOG(1) << "Shooting-on-the-fly target position: "
+              << virtual_goal.abs_pos().transpose();
+    }
+    virtual_goal = virtual_goal.Rebase(&robot_pose);
+  }
+
+  const double heading_to_goal = virtual_goal.heading();
+  CHECK(status->has_localizer());
+  distance_ = virtual_goal.xy_norm();
+
+  // The following code all works to calculate what the rate of turn of the
+  // turret should be. The code only accounts for the rate of turn if we are
+  // aiming at a static target, which should be close enough to correct that it
+  // doesn't matter that it fails to account for the
+  // shooting-on-the-fly compensation.
+  const double rel_x = virtual_goal.rel_pos().x();
+  const double rel_y = virtual_goal.rel_pos().y();
   const double squared_norm = rel_x * rel_x + rel_y * rel_y;
+
   // If squared_norm gets to be too close to zero, just zero out the relevant
   // term to prevent NaNs. Note that this doesn't address the chattering that
   // would likely occur if we were to get excessively close to the target.
+  // Note that x and y terms are swapped relative to what you would normally see
+  // in the derivative of atan because xdot and ydot are the derivatives of
+  // robot_pos and we are working with the atan of (target_pos - robot_pos).
   const double atan_diff = (squared_norm < 1e-3)
                                ? 0.0
-                               : (rel_x * ydot - rel_y * xdot) / squared_norm;
+                               : (rel_y * xdot - rel_x * ydot) / squared_norm;
   // heading = atan2(relative_y, relative_x) - robot_theta
   // dheading / dt = (rel_x * rel_y' - rel_y * rel_x') / (rel_x^2 + rel_y^2) - dtheta / dt
   const double dheading_dt = atan_diff - linear_angular(1);
 
   double range = kTurretRange;
-  if (mode == Mode::kAvoidEdges) {
+  if (wrap_mode == WrapMode::kAvoidEdges) {
     range -= 2.0 * kAntiWrapBuffer;
   }
   // Calculate a goal turret heading such that it is within +/- pi of the