A Balanced Positional Control Architecture for a 12-DoF Quadruped Robot through Simulation-validation and Hardware Testing

Abstract: A multi-joint enabled robot requires extensive mathematical calculations to determine the end effector's position with respect to the other connective joints involved and their corresponding frames in a specific coordinate system. If a control architecture employs fewer positional constraints which cannot precisely determine the end effector's position in all quadrants of a 2D Cartesian plane then the robot is generally under-constrained, leading to challenges in accurate positioning to the end-effector across the entire plane. Consequently, only a subset of the end effector's degree of freedom (DoF) can be assigned for the robot's leg position for pose and trajectory estimation purposes. This paper introduces a novel approach and proposes an algorithm to consider a balanced control of the robot's leg position in a coordinate system so the robot's leg can be precisely determined and the DoF is not limited. Mathematical derivation of the joint angles is derived with forward and inverse kinematics, and Python-based simulation has been done to verify and simulate the robot's locomotion. Using Python-based code for serial communication with a micro-controller unit makes this approach more effective for demonstrating its application on a prototype leg its movement has been realized. The experimental prototype leg exhibits a commendable 78.9% accuracy with the simulated result, validating the robustness of our algorithm in practical scenarios. A comprehensive assessment of the control algorithm with random and continuous data point test has been conducted to ensure performance, so the algorithm can as well be deployed in a physical robot.

• The paper introduces a balanced control architecture for a 12-DoF quadruped, validated through both simulation and hardware testing.
• It employs detailed kinematic analysis using forward and inverse models to accurately map joint rotations to foot positions.
• Simulations in Python and prototype hardware integration confirm the model's reliability, advancing bio-inspired robotic locomotion.

Introduction to Kinematic Analysis in Robotics

Kinematic analysis plays an integral role in robotics, particularly for multi-joint robots like quadruped systems which mirror biological movement. In efforts of enhancing movement preciseness and controlled actuation, the study discusses the sophisticated mathematics behind the motion of robot legs. Such analysis involves two primary computations: forward kinematics, where joint angles determine the position of the robot's 'foot', and inverse kinematics, a reverse process that computes the required joint angles to achieve a desired foot position.

The Mechanics of Forward Kinematics

Forward kinematics focuses on understanding where the robot's foot will be based on given joint angles using the robot's coordinate system. Essential to this process are rotational matrices and translational matrices, which represent the movements and rotations of robot limbs in space. Denavit-Hartenberg parameters play a crucial role as well, providing a structured framework to simplify the complex relationships between the robot's joints and segments. By applying these mathematical tools, the research sought to formulate a transformation matrix, encapsulating the full range of the leg's potential positions.

Inverse Kinematics and Its Computational Approach

Moving from prescribing motions to dictating end goals, inverse kinematics is crucial for programming the robot's movement toward desired positions. The research devises mathematical models to dictate the robot's joint angles when given specific coordinates for the foot's position, factoring in elements like potential rotations (yaw, pitch, and roll) of the robot's body. This modeling is particularly important as joint angle data are often transmitted within robotic systems as pulse width modulated (PWM) signals, which then dictate the physical steering of the robotic joints.

Simulation, Analysis, and Hardware Integration

Using Python in a Jupyter notebook environment allowed researchers to test their kinematics code through simulation before applying it to hardware, ensuring accuracy and real-world viability of their algorithms. A prototype leg was then built, controlled by a microcontroller which received joint angle data through serial communication. The results indicated that the prototype's movements aligned with the simulation's predicted angles, affirming the reliability of the developed kinematic models.

Concluding the Study's Contributions

The paper culminates with an affirmation on the significance of kinematic analysis for the advancement of bio-inspired robotic locomotion. It delivers complete methods to analyze the movements of individual robot legs, guiding future robotics research and development. By establishing successful kinematic algorithms, the study paves the way for more refined real-world applications and robotics capable of precise, controlled movements across challenging terrains.