The increasing prevalence of robotic arms in various applications highlights the need for energy-efficient operation. Trajectory optimization, encompassing both path and time scaling, aims to minimize objective functions such as time, energy, or jerk. While minimizing time improves productivity, minimizing energy reduces wear and tear and operational costs. Minimizing jerk reduces vibrations and positioning errors. This paper focuses on minimum energy trajectory planning, assuming a predefined path (waypoints) and optimizing the time scaling using PSO. The goal is to find optimal movement parameters that satisfy velocity and acceleration constraints while minimizing energy consumption and operation time.

Existing research explores various trajectory optimization approaches. Minimum time trajectory planning directly reduces manufacturing time, while minimum energy planning reduces mechanical stress and energy costs. Minimum jerk planning minimizes vibrations and errors. Some studies combine these objectives for better results, such as optimal time-jerk trajectory planning using improved butterfly optimization algorithm for Delta parallel robots or minimum time-energy path planning for collision avoidance in multi-robot systems. However, this research focuses specifically on time scaling optimization for energy efficiency using PSO, rather than path generation.

The study uses a trapezoidal motion profile for point-to-point movements between waypoints. Two movement types are considered: MoveL (linear motion) and MoveJ (joint motion). Time scaling is optimized using a trapezoidal velocity profile, characterized by constant acceleration, constant velocity, and constant deceleration phases. The optimization process employs the PSO algorithm. The objective function combines energy consumption and cycle time with equal weight. The PSO algorithm iteratively updates particle velocities and positions based on personal best and global best solutions to find optimal values for velocity (v) and acceleration (a) for each segment of the trajectory. The algorithm considers constraints on v and a to ensure a feasible trapezoidal profile. A 6-DOF UR5 robotic arm is used for experimental validation, and simulations are performed in MATLAB to model the robot's dynamic behavior with the determined parameters. Two trajectories with linear segments and direction changes are tested to assess the method's effectiveness.

The experimental results validate the proposed method. The velocity profile obtained matches the theoretical trapezoidal profile. Figure 4 shows the joint acceleration at the lowest fitness function value, indicating a successful optimization. Figure 5 shows normalized values of cycle time and energy consumption as functions of end-effector velocity. The optimal end-effector velocity is found to be around 0.18 mm/s². Table 1 summarizes the fitness function values for best, worst, and average velocities. Choosing the best velocity yields a 78.22% improvement compared to the worst, while the average improvement compared to a random velocity is 49%. This demonstrates the effectiveness of the PSO algorithm in finding movement parameters that significantly reduce energy consumption and cycle time.

The findings demonstrate that PSO is a viable method for optimizing the movement of robotic arms to achieve energy efficiency and reduced operation times. The 49% average improvement in efficiency highlights the potential for significant energy savings in industrial robotic applications. The approach focuses on time scaling optimization within a predefined trajectory, which is a practical and relevant approach for many real-world robotic tasks. The use of a real-world robotic arm for validation adds credibility to the results and demonstrates the applicability of the proposed method in practical scenarios.

This paper presented a PSO-based methodology for optimizing robotic arm movements to minimize energy consumption and operation time. Experimental results using a UR5 robot showed a 49% average improvement in efficiency. Future research could explore different optimization algorithms, incorporate more complex trajectory types, or consider additional factors like payload variations and environmental conditions.

The study focused on a specific type of robotic arm and a limited set of trajectories. The results might not be directly generalizable to other robots or more complex tasks. The optimization process considered only two objective functions (energy and cycle time), and the weighting between them could be adjusted for different priorities. External factors affecting energy consumption, such as environmental temperature, were not accounted for.