Movement Optimization of Robotic Arms for Energy and Time Reduction using Evolutionary Algorithms

The paper addresses the challenge of high energy consumption and operational efficiency in robotic arms used across manufacturing, healthcare, and other domains. Trajectory is defined as the robot position over time, combining path (geometric description of end-effector locations) and time scaling (timing between positions). Traditional objectives in trajectory optimization include minimizing time, energy, and jerk. Minimizing time improves productivity; minimizing energy reduces mechanical stress and cost; minimizing jerk reduces vibrations and joint positioning errors. The study focuses on minimizing energy consumption and operation time using particle swarm optimization (PSO), under the assumption that the path (waypoints) is task-defined (e.g., pick-and-place). The research concentrates on optimizing time scaling and movement parameters (movement type, speed, acceleration) while respecting velocity and acceleration constraints, with the goal of reducing energy use and cycle time for a 6-DoF robotic arm.

The paper references prior work on industrial robot trajectory optimization targeting objectives such as minimum time, energy, and jerk. Examples include: joint optimization of time and jerk using improved butterfly optimization for Delta parallel robots, and minimum time-energy path planning for multi-robot systems with collision avoidance in unknown environments. Reviews highlight that minimizing time boosts throughput while increasing energy, whereas minimizing energy can increase cycle time; jerk minimization reduces vibrations and positioning errors. Trapezoidal motion profiles are cited as standard for industrial robots, providing the fastest straight-line motion under bounded velocity and acceleration. PSO is referenced as a simple, fast-converging metaheuristic suitable for large-scale optimization.

Trajectory execution is modeled as point-to-point motion between task-defined waypoints, using industrially common trapezoidal velocity profiles characterized by acceleration, constant-velocity, and deceleration phases. Movement types considered include MoveL (Cartesian linear path), MoveP (process motion with constant speed through multiple waypoints), and MoveJ (joint-space coordinated motion). For experiments, MoveJ is used to follow waypoint sequences in joint space. Time scaling uses a trapezoidal profile parameterized by maximum velocity v, acceleration a, and total time T, subject to dependencies ensuring feasibility (e.g., ensuring trapezoidal rather than triangular profiles and satisfying path completion constraints). Only two of v, a, and T can be independently selected; constraints ensure that velocity and acceleration limits are respected and the profile remains trapezoidal when intended. Optimization objectives: (1) minimize total operation time (cycle time) over all waypoint-to-waypoint moves; (2) minimize energy consumption aggregated across all six joints. Because these objectives trade off (faster motions may consume more energy), a scalar fitness function is defined as the sum of squared normalized terms for cycle time and energy, assigning equal weight to both. Optimization algorithm: Particle Swarm Optimization (PSO) searches over movement parameters (primarily v and a for each point-to-point segment) within feasible bounds. Each particle encodes a candidate set of parameters. At each iteration, particles update velocities and positions using inertia, cognitive, and social terms based on personal best and global (or neighborhood) best solutions. For each candidate, a MATLAB dynamic model of a 6-DoF manipulator simulates the trajectory with the specified trapezoidal profile to compute cycle time and energy, which are normalized and combined into the fitness. The process iterates until convergence to the lowest fitness configuration. The resulting optimal parameters are then validated on a physical Universal Robots UR5 platform.

- The PSO-selected parameters produce velocity profiles consistent with a trapezoidal time-scaling model observed in experiments. - The optimal end-effector velocity identified via simulation is approximately 0.18 mm/s^2, close to the intersection point of the normalized objective curves (~0.2 mm/s^2). - Fitness values reported: best 0.0443; average 0.0869; worst 0.2119. - Improvement relative to worst-case velocity is about 78.22% in the combined fitness. - Compared to a random velocity choice, the average improvement in the combined metric (reflecting reduced energy consumption and cycle time) is approximately 49%. - Experimental validation on a UR5 robot demonstrates up to 49% efficiency improvement when choosing the optimized velocity rather than a random setting.

The results show that optimizing time-scaling parameters with PSO effectively balances the trade-off between energy consumption and cycle time for point-to-point tasks. By adhering to trapezoidal profiles and actuator constraints, the method identifies operating points that substantially reduce energy use without unduly increasing cycle time, and vice versa. The close agreement between simulated optimal velocity and the intersection of the normalized objective curves indicates the fitness formulation captures the intended trade-off. Validation on the UR5 confirms practical applicability, suggesting that optimizing movement type, speed, and acceleration can meaningfully extend manipulator longevity and reduce operational costs in industrial scenarios where waypoints are predetermined.

The paper presents a PSO-based methodology to optimize movement parameters (movement type, speed, acceleration) for a 6-DoF robotic arm following waypoint-defined trajectories, with the goal of minimizing energy consumption and operation time under velocity and acceleration constraints. Using trapezoidal time scaling and a combined fitness capturing both objectives with equal weight, the approach identifies an optimal operating point that achieves substantial efficiency gains. Experiments with a UR5 robot indicate that selecting the optimized end-effector velocity yields an average improvement of about 49% over a random velocity choice.