Theory & Background

Each leg has 3 revolute joints: hip abduction/adduction (side motion), hip flexion/extension (fore-aft), knee flexion. The 3-link chain (coxa-femur-tibia) forms a 3R kinematic chain in 3D space. Forward kinematics: toe position from joint angles via DH matrix multiplication. Inverse kinematics: given toe position (x,y,z), compute joint angles. Closed-form solution for 3R chain with geometric decomposition into sub-problems.

Components & Requirements

10 components required for this project.

#	Component	Purpose	Qty
1	Dynamixel XL430-W250 Servos	12 joint motors (3 per leg)	x12
2	Raspberry Pi 4 (8GB)	Main computer for ROS	x1
3	Intel RealSense D435i	Depth camera for terrain mapping	x1
4	Custom Aluminum Frame	Rigid lightweight body structure	x1
5	Dynamixel U2D2 Interface	Servo bus to USB communication	x1
6	IMU (Vectornav VN-100)	High-accuracy attitude reference	x1
7	LiPo 14.8V 10000mAh	Motor power supply	x1
8	Force/Torque Sensors (ATI Mini45)	Foot contact force measurement	x4
9	Compact DC-DC Converters	5V/12V distribution from battery	x3
10	Emergency Stop Button	Safety cutoff	x1

Step-by-Step Implementation

Follow these 3 steps carefully.

1

12-DOF Leg Kinematics (3R Chain)

Each leg has 3 revolute joints: hip abduction/adduction (side motion), hip flexion/extension (fore-aft), knee flexion. The 3-link chain (coxa-femur-tibia) forms a 3R kinematic chain in 3D space. Forward kinematics: toe position from joint angles via DH matrix multiplication. Inverse kinematics: given toe position (x,y,z), compute joint angles. Closed-form solution for 3R chain with geometric decomposition into sub-problems.

2

Trot Gait Implementation

Trot gait: diagonal leg pairs move together (FR+RL, FL+RR alternating). Each cycle: first diagonal pair in stance (on ground, providing support), second diagonal in swing (lifted, moving forward). Timing: 50% duty cycle, symmetric. Generate foot trajectories: swing foot follows a cycloidal curve (smooth lift-forward-plant). Stance foot: moves backward at body speed (propulsion). Adjust body height to maintain ground clearance during swing.

3

Terrain Adaptation with Depth Camera

Process depth camera point cloud to estimate terrain height map. For each foot placement point, sample the height map to know exact ground level. Adjust foot target height accordingly — step higher on raised terrain, avoid holes. Implement a foothold planner: evaluate candidate footholds around desired placement point, score based on flatness, stability, and distance from edges. Select highest-scored safe foothold.

Code & Implementation

Core code for quadruped_gait.py:

quadruped_gait.py
  Python

import numpy as np

class QuadrupedGait:
    def __init__(self, body_length=0.3, body_width=0.2, leg_length=0.15):
        self.L = body_length; self.W = body_width; self.l = leg_length
        # Default foot positions (FR, FL, RR, RL) relative to body center
        self.stance_feet = np.array([
            [ L/2,  -W/2, -l],  # FR
            [ L/2,   W/2, -l],  # FL
            [-L/2,  -W/2, -l],  # RR
            [-L/2,   W/2, -l],  # RL
        ])

    def trot_trajectory(self, t, stride=0.1, freq=1.0, height=0.05):
        """Returns foot positions at time t for trot gait"""
        phase = (t * freq) % 1.0
        foot_pos = self.stance_feet.copy()
        # Diagonal pairs: FR+RL in phase, FL+RR antiphase
        for i, swing_phase in enumerate([phase, phase+0.5, phase+0.5, phase]):
            sp = swing_phase % 1.0
            if sp < 0.5:  # Swing phase
                foot_pos[i][0] += stride * (sp * 2 - 0.5)  # X swing
                foot_pos[i][2] += height * np.sin(np.pi * sp * 2)  # Z lift
            else:  # Stance phase
                foot_pos[i][0] -= stride * (sp - 0.5) * 2  # X pushback
        return foot_pos

Testing & Troubleshooting

Test Quadruped Robot by verifying each subsystem individually before full integration.

!

Troubleshooting Tips

Verify power voltages, check ground connections, use serial monitor for debug.

Real-World Applications

*Inspection of industrial facilities on rough terrain

*Agricultural field monitoring

*Search and rescue on disaster terrain

*Military logistics on battlefield terrain

*Mining and construction site inspection

*Space rover concept for rough planets

*Elderly care in domestic environments

*Research platform for locomotion algorithms

Extensions & Next Steps

Implement whole-body control for dynamic movements (jumping, spinning)
Add manipulation arm for quadruped combined with manipulation
Implement reinforcement learning for adaptive gait on unknown terrain
Add mapping and autonomous navigation for inspection missions
Build a mini-cheetah style backflip and dynamic behavior

Interactive Playground

Coming Soon

An interactive simulator will be available here — simulate circuits and run code in-browser without hardware.

Frequently Asked Questions

How does a quadruped compare to a wheeled robot for rough terrain?

Quadrupeds can step over obstacles up to leg-height, climb stairs, traverse gaps, and adapt foot placement to uneven surfaces. They have near-zero ground clearance requirements (can step on isolated footholds). Wheels are much faster on flat surfaces, mechanically simpler, and more energy-efficient on smooth terrain. Quadrupeds excel where ground is unpredictable: rubble, stairs, off-road terrain, or when precise foot placement around obstacles is required.

Introduction