12-DOF Quadruped Robo-Dog with Inverse Kinematics Gait
Construct an open-source 4-legged quadruped robot with 3-DOF per leg, dynamic trot gaits, and IMU body stabilization.
Step-by-step guide to building a dynamic 12-DOF quadruped robot. Covers foot trajectory generation (Bézier curves), analytical 3-DOF leg inverse kinematics, trot/walk state machines, and active roll/pitch IMU body posture compensation.
Bill of Materials (BOM) & Components
| Component | Specifications | Qty | Estimated Cost |
|---|---|---|---|
| High-Torque Metal Gear Coreless Digital Servos (25kg.cm) | Stainless steel gears, 0.08s/60° speed, 7.4V | 12 | $220 |
| Teensy 4.1 / ESP32-S3 Microcontroller | 600MHz ARM Cortex-M7 for 1000Hz IK solver | 1 | $35 |
| PCA9685 16-Channel 12-Bit PWM I2C Servo Driver | Dedicated hardware PWM timing generation | 1 | $8 |
| 2S 7.4V 5000mAh 50C Hardcase LiPo Battery | Capable of supplying 30A peak current for sudden leg landings | 1 | $35 |
| Custom Carbon-Fiber & 3D Printed Leg Assemblies | Lightweight structural carbon tubes with TPU rubber foot pads | 1 | $60 |
Electrical & Architecture Summary
Microcontroller calculates 12 joint angles in real time via analytical IK, outputting PWM angles to PCA9685 drivers. Onboard BNO055 IMU provides feedback for posture stabilization.
Step-by-Step Assembly & Configuration
Leg Kinematics & Mechanical Assembly
Assemble Coxa, Femur, and Tibia links for all 4 legs (Front-Left, Front-Right, Rear-Left, Rear-Right). Ensure horn alignment at exact 90-degree reference positions.
- Zero all 12 servos electronically before screwing servo horns.
- Install high-traction TPU rubber feet to prevent slipping on smooth floors.
Analytical 3-DOF Leg Inverse Kinematics Formulation
Implement the algebraic IK solver that translates Cartesian foot targets (x, y, z) into Coxa (θ₁), Femur (θ₂), and Tibia (θ₃) joint angles.
- Formulate trigonometric law of cosines for knee and hip joints.
- Validate workspace boundaries to prevent reaching unreachable singular positions.
Bézier Curve Foot Trajectory & Trot Gait Generation
Generate smooth swing-phase foot trajectories using 12-point cubic Bézier curves and execute diagonal pair trot gaits.
- Pair FL+RR and FR+RL legs for diagonal trot stance/swing coordination.
- Adjust swing clearance height to step cleanly over obstacles.