Firmware simulation, Unity project, and sim-verified robot fixes

Simulation
- sim/: the unchanged robot firmware compiled into hexapod_sim.dll
  against PC stand-ins (Arduino, Servo, Wire + register-level MPU6050,
  RF24 with matching-config radio), a kinematic body model (support
  plane + planted-foot odometry) that also drives the simulated IMU,
  and a headless smoke test (sim_smoke). build.ps1 builds and tests.
- Hexapod_Simulation_Unity/ folded in (history kept in a bundle
  outside the repo). Assets/HexapodSim loads the DLL, drives the
  existing leg rig, and offers joystick / keyboard / robot-serial
  input plus a test panel.

Robot (all found or confirmed in the simulation)
- Config.h geometry taken from the Unity model.
- IK femur elevation sign, gait stance direction, body pose
  rotation direction, yaw lever arm.
- Stance feet integrated from the current command; gait restarts at
  mid-stance; heading integrates the applied turn rate, only while
  walking.
- Leg clearance and reach checks (Limits::feetFeasible); walk command
  and body pose scaled as a whole, pose scale rate-limited, planted
  feet guarded so the body never snaps or legs collide.
- Robot-gyro self-leveling as an integrator.
- Heading mode: steering relative to the body; S walks backward.
- Standing height from the remote (STANCE_HEIGHT_RANGE_MM).

Protocol v3 (reflash both boards)
- CmdPacket gains body_height (22 bytes).

Remote
- Height slider (Nextion hHeight/nHeight, serial [ ]).
- Fixed unspecified I2C read order in RemoteIMU.

LEGACY/: owner's old Nextion HMI and remote hardware assets.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

2026-current/robot/Kinematics.cpp

@@ -39,8 +39,9 @@ JointAngles Kinematics::solve(int i, const FootTarget& target) {
   cos_tibia = constrain(cos_tibia, -1.0f, 1.0f);
   float tibia_rad = -(PI - acos(cos_tibia));   // knee-down convention; flip sign if yours mounts the other way
 
-  // Femur angle: elevation to the foot, plus the triangle's femur-side angle.
-  float elevation = atan2(-local_z, horiz);
+  // Femur angle: elevation to the foot (Z up, so a foot below the hip gives a
+  // negative elevation), plus the triangle's femur-side angle.
+  float elevation = atan2(local_z, horiz);
   float cos_femur_tri = (FEMUR_LEN_MM * FEMUR_LEN_MM + dist * dist - TIBIA_LEN_MM * TIBIA_LEN_MM)
                          / (2.0f * FEMUR_LEN_MM * dist);
   cos_femur_tri = constrain(cos_femur_tri, -1.0f, 1.0f);
@@ -57,11 +58,32 @@ JointAngles Kinematics::solve(int i, const FootTarget& target) {
   return out;
 }
 
+void Kinematics::jointPositions(int i, const JointAngles& a, FootTarget out[4]) {
+  float yaw = radians(LEG_MOUNT_ANGLE_DEG[i] + a.coxa_deg);
+  float femur = radians(a.femur_deg);
+  float tibia = radians(a.femur_deg + a.tibia_deg);   // tibia angle is relative to the femur
+  float cx = cos(yaw), cy = sin(yaw);
+  float r_knee = COXA_LEN_MM + FEMUR_LEN_MM * cos(femur);
+  float z_knee = FEMUR_LEN_MM * sin(femur);
+  float r_foot = r_knee + TIBIA_LEN_MM * cos(tibia);
+  float z_foot = z_knee + TIBIA_LEN_MM * sin(tibia);
+  float mx = LEG_MOUNT_X_MM[i], my = LEG_MOUNT_Y_MM[i];
+  out[0] = { mx, my, 0 };
+  out[1] = { mx + cx * COXA_LEN_MM, my + cy * COXA_LEN_MM, 0 };
+  out[2] = { mx + cx * r_knee, my + cy * r_knee, z_knee };
+  out[3] = { mx + cx * r_foot, my + cy * r_foot, z_foot };
+}
+
+static float g_stance_height_mm = STANCE_HEIGHT_MM;
+
+void Kinematics::setStanceHeight(float mm) { g_stance_height_mm = mm; }
+float Kinematics::stanceHeight() { return g_stance_height_mm; }
+
 FootTarget Kinematics::neutralStance(int i) {
   float a = radians(LEG_MOUNT_ANGLE_DEG[i]);
   FootTarget t;
   t.x = LEG_MOUNT_X_MM[i] + cos(a) * (COXA_LEN_MM + STANCE_RADIUS_MM);
   t.y = LEG_MOUNT_Y_MM[i] + sin(a) * (COXA_LEN_MM + STANCE_RADIUS_MM);
-  t.z = -STANCE_HEIGHT_MM;
+  t.z = -g_stance_height_mm;
   return t;
 }