Global optimum motion profiles for enhanced energy efficiency in industrial positioning applications

Point-to-point mechanisms are widely used in industry. The electric motors driving these mechanisms are responsible for a significant portion of the global energy consumption. Therefore, it is essential to consider methods and technologies to reduce their energy consumption. Motion profile optimization offers a cost-effective opportunity to reduce energy consumption without the need for additional hardware adaptations or investments. Hence, it is crucial to discover the global optimum, representing the overall best solution across the entire design space, to ensure that the full optimization potential is realized, rather than settling for a local optimum, which may only represent a superior solution within a limited region of the design space. The latter remains a challenge in the current literature. This paper introduces a novel approach that utilizes interval analysis to guarantee the discovery of the global optimum within the design space. It achieves this by dividing the design space into smaller intervals, employing interval arithmetic to evaluate the functions over these intervals, and systematically eliminating and refining the intervals to pinpoint the location of the global optimum. However, to use interval analysis, a bounded design space is required. Therefore, this paper describes the motion profile using polynomials expressed in the Chebyshev basis, offering the advantage of a bounded design space and a minimal number of design parameters compared to polynomials expressed in the classical basis. Additionally, this paper shows that symbolically formulating the motion profile allows linearization of the kinematic constraints, enhancing the computational efficiency and convergence speed of interval analysis. Furthermore, a method for reducing the initial design space is introduced, as the initial bounded design space tends to overestimate the feasible design space. Refining the design space enables interval analysis to require fewer evaluations, facilitating faster optimization. To allow wide industrial adoption of the proposed method, the system properties $J\left(\theta \right)$ and $T_l\left(\theta \right)$ are extracted from CAD simulations to build the objective function. Finally, measurements indicate a reduction in root-mean-square (rms) torque of a pick-and-place unit by up to 38.4% and a reduction in energy consumption of up to 51.2%, validating the proposed approach’s effectiveness.