  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.
