Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
Fundamentals of Robotics: Analysis and Control
Fundamentals of Robotics: Analysis and Control
Introduction to Robotics: Mechanics and Control
Introduction to Robotics: Mechanics and Control
Robotics: Basic Analysis and Design
Robotics: Basic Analysis and Design
Robot Modelling: Control and Applications with Software
Robot Modelling: Control and Applications with Software
Understanding Digital Signal Processing (2nd Edition)
Understanding Digital Signal Processing (2nd Edition)
Theory of Applied Robotics: Kinematics, Dynamics, and Control
Theory of Applied Robotics: Kinematics, Dynamics, and Control
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Large and fragile systems may require motion trajectories with the highest attainable degree of smoothness. This paper introduces a method to create infinitely continuous motion profiles based on convolving an infinitely continuous FIR kernel with an underlying rate-limited position profile. Conventional motion profiling is limited to blending polynomial between linear segments. Due to the issues of controlling unwanted inflections and the computing of the polynomial coefficient, blending polynomials are usually limited to third order with special cases up to seventh order. Beyond third order, closed form equations do not exists for the coefficients, requiring a set of equations to be solved for each blend. With third order polynomials the highest derivative that can be controlled is jerk. While maximum jerk can be controlled, change in jerk is instantaneous. This inherent instantaneous change in jerk can send shock waves though a system with the possibility of causing damage. The infinitely continuous profiles introduced in this paper overcomes all the shortcomings of polynomial blending. With FIR smoothing of an underlying rate-limited position profile, only a single kernel is needed to be computed off-line before motion starts. The entire process of motion generation consists of rate-limiting desired position updates and then filtering them with an infinitely continuous FIR kernel. The output is an infinitely continuous profile that allows real-time updates of velocity. Two methods are introduced to create the kernels. In the first method the duration of the kernel is minimized for a given maximum value of any derivative. In the second method the maximum value of any derivative is minimized for a given kernel duration. The use of the convolution instead of polynomial fitting to create profiles is simpler, eliminates special cases, and allows real-time updates of velocity while producing maximally smooth profiles.