MATLAB Implementation of 5th-Degree Polynomial Interpolation for Robotic Trajectory Planning

Fifth-degree polynomial interpolation plays a crucial role in robotic trajectory planning. This interpolation method helps beginners better understand robotic motion representation and trajectory planning concepts by fitting a series of data points into a smooth polynomial curve. The implementation typically involves solving for six coefficients (a0 to a5) that define the polynomial equation: θ(t) = a0 + a1*t + a2*t² + a3*t³ + a4*t⁴ + a5*t⁵, where t represents time and θ(t) denotes the joint angle or position. MATLAB's polyfit function can be employed to calculate these coefficients based on boundary conditions including initial/final positions, velocities, and accelerations. The generated polynomial ensures smooth robotic motion with continuous position, velocity, and acceleration profiles, making it suitable for applications requiring jerk-free movement. Additionally, fifth-degree polynomial interpolation finds applications in other domains such as image processing and data fitting, where high-order smoothness is required.