###### Abstract  
In this paper, a multi-objective integrated trajectory planning method based on an improved butterfly optimization algorithm (IBOA) is proposed, to improve the dynamic performance of the Delta parallel pickup robot in high-speed pick-and-place processes. The main objective of the present study is to improve dynamic positioning accuracy and running stability at high speeds and high accelerations. On the one hand, the intention is to ensure smooth motions using the trajectory planning method, and on the other hand to improve the picking efficiency. To this end, the pick-and-place trajectory of the robot is constructed by using NURBS curves in Cartesian space. Taking the time and jerk as the optimization objectives, a trajectory optimization method based on the improved butterfly optimization algorithm (IBOA) is proposed. The IBOA is based on the butterfly optimization algorithm (BOA); a circle chaotic sequence is introduced to replace the random initial population of the original BOA, and the fractional differential is used to improve the convergence speed of the BOA. Then, the problem of parallel segment deformation of the optimized trajectory is solved. Finally, a three-degrees-of-freedom Delta robot is used to evaluate the performance of the posed algorithm. The obtained results show that, compared with other optimization algorithms, IBOA reduces the optimization time by 16.2%, and the maximum jerk is reduced by 87.6%. The results are better than the optimization results of other algorithms by 14.1% and 27.2%. The robot motion simulation results show that IBOA can effectively reduce the vibration acceleration of the end platform. polynomial interpolation, B-spline interpolation, Lame curves, and PH curves [7; 8; 9; 10]. Compared with other trajectory planning methods, the non-uniform rational B-spline (NURBS) interpolation method has remarkable advantages such as local controllability. Moreover, the high-order derivability of this method provides continuity of the jerk, which is a favorable feature for motions for complex continuous tasks [11]. Accordingly, the NURBS method has been widely used in diverse applications. To shorten the running time, reduce the jerk, and decrease the energy consumption during robot operation, it is of significant importance to optimize the robot trajectory. With the development of intelligent optimization algorithms in the past few decades, numerous algorithms such as particle swarm algorithms [12], ant colony algorithms [13], gray wolf algorithms [14], and convex optimization algorithms [15] have been proposed to optimize the robot trajectory. Further investigations revealed that such algorithms offer an effective scheme for solving the optimization problem of the objective function, but the accuracy and efficiency of the solution often depend on the convergence rate of the algorithm. For instance, conventional intelligent optimization algorithms have a long searching time and are easily trapped in a local optimum [16]. Aiming at resolving these difficulties, numerous modified methods have been proposed. In this regard, [PERSON] et al. [17] used the 4-3-4 polynomial function to fit the running track and combined the genetic algorithm and particle swarm optimization algorithms to optimize the running time of the robot. Based on the fifth NURBS curve, [PERSON] [18] proposed the improved harmony search algorithm and obtained a smooth and time-optimal robot running trajectory. Taking the running time of the trajectory as the constraint, a smooth trajectory is obtained by optimizing the five-degree and three-degree B-spline trajectories, respectively, using the HS algorithm. However, only the single-objective optimization of running time is analyzed. [PERSON] et al. [19] applied the improved cuckoo search algorithm to optimize the motion time of the trajectory fitted using the 3-5-3 polynomial function. This paper mainly focuses on the research in joint space.