CN118393901A - An air pump control optimization method for a tree-climbing robot - Google Patents
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Abstract
Description
技术领域Technical Field
本发明属于气泵PID控制技术领域，具体涉及一种用于爬树机器人的气泵控制优化方法。The invention belongs to the technical field of air pump PID control, and in particular relates to an air pump control optimization method for a tree climbing robot.
背景技术Background technique
气动爬树机器人结合了柔软材料、仿生结构等，大大地改善了刚性机器人的运动适应性和附着可靠性，使得机器人拥有在在森林、杆状物设备等非结构化环境中进行爬行作业的能力，在森林高空勘察、资源勘探和重大灾难营救等领域具有广阔的应用前景；然而，现有的爬树机器人在控制气压以实现稳定爬升和移动时，存在控制精度低、能耗高等问题，因此，如何优化气压控制以提高爬树机器人的工作效率和稳定性，是一个亟待解决的技术难题。Pneumatic tree-climbing robots combine soft materials, bionic structures, etc., which greatly improve the motion adaptability and adhesion reliability of rigid robots, enabling the robots to perform crawling operations in unstructured environments such as forests and pole-shaped equipment. They have broad application prospects in fields such as high-altitude forest surveys, resource exploration, and major disaster rescue. However, existing tree-climbing robots have problems such as low control accuracy and high energy consumption when controlling air pressure to achieve stable climbing and movement. Therefore, how to optimize air pressure control to improve the working efficiency and stability of tree-climbing robots is a technical problem that needs to be solved urgently.
气动爬树机器人主要通过气泵输出气压控制机器人的四个力臂，主要难点在于：①气动爬树机器人的力臂关节内主要由弹性材料制成，其形变极其容易受外界负载的影响，导致自适应较差；②气动爬树机器人非线性控制使得动力学建模变得极其困难，导致其控制、定位效果不佳；③柔性材料与抓取目标接触时的被动变形也使得形状检测变得尤为困难。The pneumatic tree-climbing robot mainly controls the four lever arms of the robot through the air pressure output by the air pump. The main difficulties are: ① The lever arm joints of the pneumatic tree-climbing robot are mainly made of elastic materials, and their deformation is easily affected by external loads, resulting in poor adaptability; ② The nonlinear control of the pneumatic tree-climbing robot makes dynamic modeling extremely difficult, resulting in poor control and positioning effects; ③ The passive deformation of the flexible material when it comes into contact with the grasping target also makes shape detection particularly difficult.
气动爬树机器人在实际操作过程中，需要精确控制气泵以维持稳定的气压，通过气压实现爬树机器人力臂控制，从而确保其稳定爬升；PID控制器因其简单易实现和较好的控制效果，被广泛应用于各种爬树机器人控制中，然而，PID控制参数的优化一直是一个挑战，参数的精确性影响着爬树机器人力臂控制。In the actual operation of a pneumatic tree-climbing robot, it is necessary to precisely control the air pump to maintain a stable air pressure, and to achieve the tree-climbing robot's arm control through the air pressure, thereby ensuring its stable climbing. PID controllers are widely used in various tree-climbing robot controls because of their simplicity, ease of implementation and good control effects. However, the optimization of PID control parameters has always been a challenge, and the accuracy of the parameters affects the tree-climbing robot's arm control.
人工原优化算法（APO）是一种新颖的仿生元启发式算法，其设计灵感来源于自然界中的原生动物，模拟了它们的觅食、休眠和繁殖行为。算法的全局搜索阶段包括自养模式和异养行为；算法局部开发阶段包括睡眠模式和繁殖行为；人工原优化算法（APO）虽然在解决工程优化问题上表现出色，但也存在一些缺陷，例如：参数调整困难和对大规模问题适应性有限的缺点，影响算法的收敛精度和寻优效率。The Artificial Proto-Optimization (APO) algorithm is a novel bionic meta-heuristic algorithm, which is inspired by protozoa in nature and simulates their foraging, dormancy and reproduction behaviors. The global search phase of the algorithm includes autotrophic mode and heterotrophic behavior; the local development phase of the algorithm includes sleep mode and reproduction behavior; Although the Artificial Proto-Optimization (APO) algorithm performs well in solving engineering optimization problems, it also has some defects, such as: difficulty in parameter adjustment and limited adaptability to large-scale problems, which affect the convergence accuracy and optimization efficiency of the algorithm.
发明内容Summary of the invention
本发明的目的在于：针对上述背景技术中爬树机器人的气泵控制机器人力臂存在的问题，本发明利用改进的人工原优化算法对爬树机器人的气泵控制的PID闭环算法优化，提供气泵PID闭环算法的鲁棒性，从而提高对机器人力臂的控制精度和反应速度，解决爬树机器人在工作过程中由于力臂的灵敏度和自适应能力差导致的工作效率低下的问题。The purpose of the present invention is to: address the problems existing in the air pump control of the robot arm of the tree-climbing robot in the above-mentioned background technology. The present invention optimizes the PID closed-loop algorithm of the air pump control of the tree-climbing robot by using an improved artificial original optimization algorithm, and provides the robustness of the air pump PID closed-loop algorithm, thereby improving the control accuracy and response speed of the robot arm, and solving the problem of low working efficiency of the tree-climbing robot due to poor sensitivity and adaptability of the arm during operation.
为了实现上述目的，本发明采用了如下技术方案：一种用于爬树机器人的气泵控制优化方法，包括爬树机器人的气泵控制系统，利用压力传感器采集爬树机器人力臂与树木之间的压力数据，并通过PID控制器调整气泵的输出气压，提高机器人力臂实施弯曲度的精确性和鲁棒性，具体步骤为。In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme: an air pump control optimization method for a tree-climbing robot, including an air pump control system of the tree-climbing robot, using a pressure sensor to collect pressure data between the tree-climbing robot's arm and the tree, and adjusting the output air pressure of the air pump through a PID controller to improve the accuracy and robustness of the robot's arm's bending. The specific steps are as follows.
S1、根据气压、树径、爬升速度的关系，建立爬树机器人的气泵控制数学模型。S1. According to the relationship among air pressure, tree diameter and climbing speed, a mathematical model of air pump control for the tree climbing robot is established.
S2、建立爬树机器人的气泵控制系统，控制系统包括气泵控制单元和执行单元。S2. Establish an air pump control system for the tree-climbing robot. The control system includes an air pump control unit and an execution unit.
S3、对人工原优化算法改进，利用改进的人工原优化算法优化爬树机器人的气泵PID闭环控制算法，改进人工原优化算法，具体步骤为：S3. Improve the artificial original optimization algorithm. Use the improved artificial original optimization algorithm to optimize the air pump PID closed-loop control algorithm of the tree climbing robot. Improve the artificial original optimization algorithm. The specific steps are:
S31、改进人工原种群休眠和繁殖的比例因子，调整人工原优化算法的局部开 发阶段的种群规模，调整局部开发阶段与全局搜索阶段的算法位置更新策略； S31. Improve the proportional factors of dormancy and reproduction of artificial original populations , adjust the population size of the local development phase of the artificial original optimization algorithm, and adjust the algorithm position update strategy in the local development phase and the global search phase;
S32、基于人工原种群的多样性和人工原位置的最优解的变化，通过引入动态调整 机制，改进人工原优化算法的觅食因子； S32. Based on the diversity of the artificial original population and the changes in the optimal solution of the artificial original position, the foraging factor of the artificial original optimization algorithm is improved by introducing a dynamic adjustment mechanism ;
S33、利用改进的觅食因子对人工原优化算法的全局搜索阶段的位置更新数 学模型改进； S33. Using improved foraging factors Improvement of the mathematical model for position update in the global search phase of the artificial original optimization algorithm;
S34、提出一种"均匀统计搜索"初始化方法，对人工原种群位置进行均匀初始化，利用改进的人工原优化算法优化爬树机器人的气泵PID闭环控制算法；S34. A "uniform statistical search" initialization method is proposed to uniformly initialize the positions of the artificial original population, and the air pump PID closed-loop control algorithm of the tree climbing robot is optimized using the improved artificial original optimization algorithm;
S4、利用压力传感器采集爬树机器人力臂与树木之间的实时压力数据P(t)，计算爬树机器人力臂与树木之间的目标压力值Pa与实时压力数据P(t)的误差值e(t)。S4. Use a pressure sensor to collect real-time pressure data P(t) between the tree-climbing robot arm and the tree, and calculate the error value e(t) between the target pressure value Pa between the tree-climbing robot arm and the tree and the real-time pressure data P(t).
S5、根据误差值e(t)和PID控制器的参数Kp、Ki、Kd，计算气泵PID控制输出值u(t)，将输出值u(t)转换为气泵的控制信号，使气泵调整气体输出，控制机器人力臂。S5. Calculate the air pump PID control output value u ( t ) according to the error value e ( t ) and the parameters Kp , Ki , and Kd of the PID controller, and convert the output value u ( t ) into a control signal of the air pump so that the air pump adjusts the gas output and controls the robot arm.
更具体地，爬树机器人的气泵控制数学模型为：More specifically, the air pump control mathematical model of the tree climbing robot is:
（1）； (1);
式（1）中，Y(t)为爬树机器人力臂的变化度，m为机器人的质量（kg），g为重力加速度（9.81 m/s²），μ为摩擦系数，W(t)为不同时间段的树径，d(t)为不同时间段机器人力臂与树的接触宽度，kv为速度，t为时间单位为秒，u(t)为气泵PID控制输出值。In formula (1), Y(t) is the degree of change of the force arm of the tree climbing robot, m is the mass of the robot (kg), g is the acceleration of gravity (9.81 m/s²), μ is the friction coefficient, W(t) is the tree diameter at different time periods, d(t) is the contact width between the robot force arm and the tree at different time periods, kv is the speed, t is the time unit in seconds, and u(t) is the output value of the air pump PID control.
更具体地，爬树机器人的气泵控制系统包括气泵控制单元和执行单元，其中气泵控制单元包括气泵控制器，气泵控制器采用PID闭环控制算法，将爬树机器人力臂与树木之间的实时压力数据差值e(t)输入到气泵控制器中，经过公式计算出爬树机器人的气泵PID控制输出值u(t)，将气泵PID控制输出值u(t)输入到爬树机器人的气泵控制数学模型，即公式（1）中，从而改变爬树机器人力臂的变化度，同时压力传感器采集爬树机器人力臂与树木之间的实时压力数据P(t)，返回计算爬树机器人力臂与树木之间的实时压力数据差值e(t)，直至t达到控制最大时间T，实现爬树机器人的闭环控制，执行单元为一个永磁电机，为爬树机器人提供气体驱动机器人力臂。More specifically, the air pump control system of the tree climbing robot includes an air pump control unit and an execution unit, wherein the air pump control unit includes an air pump controller. The air pump controller adopts a PID closed-loop control algorithm to input the real-time pressure data difference e(t) between the force arm of the tree climbing robot and the tree into the air pump controller. The air pump PID control output value u ( t ) of the tree - climbing robot is calculated and input into the air pump control mathematical model of the tree-climbing robot, i.e., formula (1), so as to change the degree of change of the tree-climbing robot's lever arm. At the same time, the pressure sensor collects the real-time pressure data P(t) between the tree-climbing robot's lever arm and the tree, and returns to calculate the real-time pressure data difference e(t) between the tree-climbing robot's lever arm and the tree until t reaches the maximum control time T, thus realizing the closed-loop control of the tree-climbing robot. The execution unit is a permanent magnet motor, which provides gas to drive the robot's lever arm for the tree-climbing robot.
更具体地，原人工原优化算法的人工原种群休眠和繁殖的比例因子决定了人 工原种群休中眠和繁殖的个体数量占总种群数量的比例，其是简单随机决定的，无法及时 响应种群状态的变化，本发明基于种群多样性和适应度变化率动态调整休眠和繁殖的比 例，调整人工原优化算法的睡眠和繁殖阶段的种群规模，使算法更灵活，能够更好地平衡探 索和开发，提升优化效率和效果；其中，种群多样性通过计算人工原个体之间的距离衡量， 改进的人工原种群休眠和繁殖的比例因子数学模型为： More specifically, the ratio factor of dormancy and reproduction of the artificial original population of the original artificial original optimization algorithm is The ratio of the number of individuals sleeping and reproducing in the artificial original population to the total population is determined by simple randomness and cannot respond to changes in the population state in a timely manner. The present invention dynamically adjusts the ratio of sleep and reproduction based on population diversity and fitness change rate, adjusts the population size of the sleep and reproduction stages of the artificial original optimization algorithm, makes the algorithm more flexible, can better balance exploration and development, and improves optimization efficiency and effect; wherein, population diversity is measured by calculating the distance between artificial original individuals, and the improved artificial original population sleep and reproduction ratio factor The mathematical model is:
(2)； (2);
式（2）中，为第iter次迭代改进的人工原种群休眠和繁殖的比例因 子，为第i个个体在种群中的适应度值排名，N为人工原最大规模，为第iter次迭 代的当前种群的多样性，为初始种群的多样性。利用种群多样性指标调整整体休眠和 繁殖比例，避免过早收敛到局部最优解。 In formula (2), The ratio factor of dormancy and reproduction of the artificial original population improved for the iterth iteration, is the fitness ranking of the ith individual in the population, N is the maximum size of the artificial original, is the diversity of the current population at the iter iteration, is the diversity of the initial population. The population diversity index is used to adjust the overall dormancy and reproduction ratio to avoid premature convergence to the local optimal solution.
更具体地，基于人工原种群的多样性和人工原位置的适应度的变化，通过引入动 态调整机制，改进人工原优化算法的觅食因子，改进的觅食因子数学模型为： More specifically, based on the diversity of the artificial original population and the changes in the fitness of the artificial original position, the foraging factor of the artificial original optimization algorithm is improved by introducing a dynamic adjustment mechanism. , improved foraging factor The mathematical model is:
（3）； (3);
式（3）中，为第iter次迭代的改进的觅食因子，为改进的觅食因 子最小值，取值为0，为改进的觅食因子最大值，取值为2；为当前迭代次数，为最大迭代次数，为动态调整机制。 In formula (3), is the improved foraging factor for the iter-th iteration, is the minimum value of the improved foraging factor, which is 0. is the maximum value of the improved foraging factor, which is 2; is the current iteration number, is the maximum number of iterations, It is a dynamic adjustment mechanism.
更具体地，动态调整机制基于人工原种群熵值变化率和最优解变化率设计，数学模型为：More specifically, the dynamic adjustment mechanism Based on the design of the change rate of the entropy value of the artificial original population and the change rate of the optimal solution, the mathematical model is:
（4）； (4);
式（4）中，为第iter+1次迭代人工原种群位置的熵值，为 第iter次迭代人工原种群位置的熵值，为初始人工原种群位置的熵值，为第iter次迭代种群最优解适应度值，为先前种群最优解适应度 值，取值为0.001，其中，人工原种群位置的熵值计算公式为：， 式中的N为最大种群规模，为第i个人工原出现的概率，通过位置适应度值归一化得到。 In formula (4), is the entropy value of the artificial original population position at the iter+1th iteration, is the entropy value of the artificial original population position at the iter-th iteration, is the entropy value of the initial artificial original population position, is the fitness value of the optimal solution of the iter-th iteration population, is the fitness value of the previous population optimal solution, The value is 0.001, where the entropy value calculation formula of the artificial original population position is: , where N is the maximum population size, is the probability of the i-th artifact appearing, which is obtained by normalizing the position fitness value.
更具体地，与原始觅食因子相比，改进后的动态调整觅食因子引入了种群熵值和 最优解变化的关系，使觅食因子的调整更加复杂和多样化；利用改进的觅食因子对人 工原优化算法的全局搜索阶段的位置更新数学模型改进，使得算法能够动态适应搜索过程 中的变化，更有效地在早期阶段进行探索，在后期阶段进行开发，加速了收敛过程，提高了 对复杂环境下爬树机器人的适应性。More specifically, compared with the original foraging factor, the improved dynamically adjusted foraging factor introduces the relationship between the population entropy value and the change of the optimal solution, making the adjustment of the foraging factor more complex and diversified; using the improved foraging factor Improvements to the mathematical model for position updates during the global search phase of the artificial original optimization algorithm enable the algorithm to dynamically adapt to changes during the search process, more effectively explore in the early stages and exploit in the later stages, accelerate the convergence process, and improve the adaptability of the tree-climbing robot in complex environments.
更具体地，利用改进的觅食因子改进的人工原优化算法的全局搜索阶段的位 置更新数学模型为： More specifically, using the improved foraging factor The position update mathematical model of the global search phase of the improved artificial original optimization algorithm is:
（5）； (5);
式（5）中，为第i个人工原的新位置，为第iter次迭代第i个人工原 的位置，为第iter次迭代随机人工原的位置，为人工原邻居对的数量，为一个大小为1×dim的觅食映射向量，向量内的值取值为1，为自养模式的权重，为异养模式的权重，rand为0到1内的随机数，为第k个配对邻居中随机选择的人 工原位置，其中k大于i，为第k个配对邻居中随机选择的人工原位置，其中k小于i；为第k个配对邻居中选择的第i-k个人工原位置，为第k个配对邻居中选择 的第i+k个人工原位置；为自养和异养行为的分界参数，为第iter次迭代 的改进的觅食因子。 In formula (5), is the new position of the i-th artifact, is the position of the i-th artificial original in the iter-th iteration, Random for the iterth iteration The location of the artificial is the number of artificial original neighbor pairs, is a foraging mapping vector of size 1×dim, and the value in the vector is 1. is the weight of the autotrophic mode, is the weight of the heterotrophic mode, rand is a random number between 0 and 1, is a randomly selected artificial original position among the k-th paired neighbors, where k is greater than i, is the artificial original position randomly selected from the kth paired neighbors, where k is less than i; is the ikth artificial original position selected from the kth pairing neighbor, The i+kth artificial original position is selected from the kth pairing neighbors; is the dividing parameter between autotrophic and heterotrophic behavior, is the improved foraging factor for the iter-th iteration.
更具体地，利用改进的人工原优化算法优化爬树机器人的气泵PID闭环控制算法 时，需要设计目标函数指导算法对气泵PID闭环控制算法的优化，爬树机器人的气泵控制主 要考虑通过控制爬树机器人的气泵输出值，从而提高爬树机器人力臂的变化度的精度，使 调整后的力臂半径与树木的半径差值尽可能的小，从而使得爬树机器人工作更稳定，因而 将爬树机器人力臂与树木之间的目标压力值Pa与实时压力数据P(t)的误差值e(t)和爬树 机器人力臂的变化度Y(t)考虑在内设计目标函数，目标函数数学模型为： More specifically, when the improved artificial original optimization algorithm is used to optimize the air pump PID closed-loop control algorithm of the tree-climbing robot, it is necessary to design an objective function to guide the algorithm to optimize the air pump PID closed-loop control algorithm. The air pump control of the tree-climbing robot mainly considers controlling the air pump output value of the tree-climbing robot, thereby improving the accuracy of the change degree of the tree-climbing robot's force arm, so that the difference between the adjusted force arm radius and the radius of the tree is as small as possible, thereby making the tree-climbing robot work more stably. Therefore, the error value e(t) between the target pressure value Pa between the tree-climbing robot's force arm and the tree and the real-time pressure data P(t) and the change degree Y(t) of the tree-climbing robot's force arm are taken into consideration to design the objective function. The objective function The mathematical model is:
（6）； (6);
式（6）中，T为控制最大时间，为爬树机器人力臂的变化度Y(t)的权重，Y(t)为爬树机器人力臂的变化度。In formula (6), T is the maximum control time, is the weight of the degree of change Y(t) of the tree-climbing robot’s force arm, and Y(t) is the degree of change of the tree-climbing robot’s force arm.
更具体地，利用改进的人工原优化算法优化爬树机器人的气泵PID闭环控制算法，通过改进的人工原优化算法对爬树机器人的气泵PID闭环控制算法的比例系数Kp、积分系数Ki、微分系数Kd，具体步骤为：More specifically, the improved artificial original optimization algorithm is used to optimize the air pump PID closed-loop control algorithm of the tree climbing robot. The proportional coefficient Kp, integral coefficient Ki, and differential coefficient Kd of the air pump PID closed-loop control algorithm of the tree climbing robot are adjusted by the improved artificial original optimization algorithm. The specific steps are:
步骤一、设置改进的人工原优化算法的人工原规模N，最大迭代次数Max_iter、问题维度dim，上界UB和下界LB；Step 1: Set the artificial original scale N, the maximum number of iterations Max_iter, the problem dimension dim, the upper bound UB and the lower bound LB of the improved artificial original optimization algorithm;
步骤二、按照公式（7）利用"均匀统计搜索"初始化方法，对人工原种群进行均匀初始化，使得人工原个体覆盖整个改进的人工原优化算法的搜索空间；对改进的人工原优化算法的搜索空间的上界UB和下界LB限制；Step 2: According to formula (7), the "uniform statistical search" initialization method is used to uniformly initialize the artificial original population, so that the artificial original individuals cover the entire search space of the improved artificial original optimization algorithm; the upper bound UB and lower bound LB of the search space of the improved artificial original optimization algorithm are restricted;
（7）； (7);
式（7）中，为第i个人工原个体第j维的初始化后的位置，其中，;，为人工原个体的下限位置，为人工原个体 的上限位置，为上次迭代的全局最佳人工原个体位置，rand(0,1)为0到1内的随 机数； In formula (7), is the initialized position of the jth dimension of the ith artificial original individual, where ; , is the lower limit position of the artificial original individual, is the upper limit position of the artificial original individual, is the global best artificial original individual position of the last iteration, rand(0,1) is a random number between 0 and 1;
步骤三、将搜索空间内的人工原个体位置与爬树机器人的气泵PID闭环控制算法的Kp、Ki、Kd组成的向量建立三维映射；Step 3: Establish a three-dimensional mapping between the position of the artificial original individual in the search space and the vector composed of Kp, Ki, and Kd of the air pump PID closed-loop control algorithm of the tree-climbing robot;
步骤四、利用目标函数计算第iter次迭代人工原种群中每个人工原个体的位置适应度值，将种群中较小的适应度值对应的人工原个体位置作为当前迭代的最佳位置；Step 4: Use the objective function to calculate the position fitness value of each artificial original individual in the iter-th iteration artificial original population, and take the position of the artificial original individual corresponding to the smaller fitness value in the population as the best position of the current iteration;
步骤五、建立改进的人工原优化算法在全局搜索阶段和局部开发阶段的种群位置更新数学模型，更新人工原个体位置，具体步骤为：Step 5: Establish a mathematical model for updating the population position of the improved artificial primitive optimization algorithm in the global search stage and the local development stage, and update the position of the artificial primitive individuals. The specific steps are as follows:
S351、利用公式（2）计算第iter次迭代改进的人工原种群休眠和繁殖的比例因子，设置大小为的种群范围，若当前迭代第i个个 体在种群范围内，则第i个个体位置更新执行步骤S352；否则执行步骤S353； S351. Use formula (2) to calculate the proportional factor of dormancy and reproduction of the artificial original population improved in the iterth iteration , set the size to If the i-th individual in the current iteration is within the population range, the position of the i-th individual is updated and executed in step S352; otherwise, step S353 is executed;
S352、模型人工原的休眠和繁殖行为，按照公式（8）建立算法局部收敛阶段的人工原个体位置更新数学模型；S352, modeling the dormancy and reproduction behavior of artificial atom, and establishing a mathematical model for the position update of artificial atom individuals in the local convergence stage of the algorithm according to formula (8);
（8）； (8);
式（8）中，为第i个人工原的新位置，为第iter次迭代第i个人工原 的位置，rand为0到1内的随机数，为休眠和繁殖的分界参数，当大于rand时，执 行人工原的休眠位置更新数学模型，否则，执行人工原的繁殖位置更新数学模型； In formula (8), is the new position of the i-th artifact, is the position of the ith artificial source in the iterth iteration, rand is a random number between 0 and 1, is the boundary parameter between dormancy and reproduction. When it is greater than rand, the mathematical model of the dormant position of the artificial source is updated, otherwise, the mathematical model of the reproductive position of the artificial source is updated;
S353、模型人工原的搜索行为，通过改进的觅食因子改进的人工原优化算法 的全局搜索阶段的位置更新数学模型，即公式（5）建立算法全局搜索阶段人工原个体位置 数学模型； S353, Modeling the Search Behavior of Artificial Protozoa, by Improving the Foraging Factor The mathematical model for updating the position of the artificial atom in the global search phase of the improved artificial atom optimization algorithm, that is, formula (5) establishes the mathematical model for the position of the artificial atom in the global search phase of the algorithm;
步骤六、再次利用目标函数计算位置更新后的人工原种群中每个个体的位置适应度值，将当前得到的最小适应度值对应的个体位置作为全局最佳人工原个体位置；Step 6: Use the objective function again to calculate the position fitness value of each individual in the artificial original population after the position update, and take the individual position corresponding to the currently obtained minimum fitness value as the global optimal artificial original individual position;
步骤七、执行iter=iter+1，判断当前迭代次数iter是否满足iter=Max_iter，若满足，则将全局最小适应度值对应的人工原个体位置输出并解析为爬树机器人的气泵PID闭环控制算法的Kp、Ki、Kd参数值，否则执行步骤二的按照公式（7）利用"均匀统计搜索"初始化方法，对人工原种群进行均匀初始化。Step 7: Execute iter=iter+1 to determine whether the current number of iterations iter satisfies iter=Max_iter. If so, the position of the artificial original individual corresponding to the global minimum fitness value is output and parsed as the Kp, Ki, and Kd parameter values of the air pump PID closed-loop control algorithm of the tree-climbing robot. Otherwise, execute step 2 and use the "uniform statistical search" initialization method according to formula (7) to uniformly initialize the artificial original population.
相对于现有技术，本发明的有益效果为：基于种群多样性和适应度变化率动态调整人工原优化算法的休眠和繁殖的比例，使算法更灵活，能够更好地平衡探索和开发阶段，提升了算法优化效率和效果；通过改进的觅食因子和动态调整机制，使得全局搜索阶段的位置更新更加精确，加速了算法的收敛过程，并在复杂环境下提高了爬树机器人的适应性，本发明通过使用改进的人工原优化算法对爬树机器人的气泵控制的PID闭环算法进行优化，显著提升了对机器人力臂的控制精度和反应速度，解决了由于力臂的灵敏度和自适应能力差导致的工作效率低下的问题；同时，通过精确控制气泵输出，保持气压稳定，从而确保爬树机器人在非结构化环境如森林和杆状物设备中稳定爬升，增强了爬树机器人的适应性和可靠性。Compared with the prior art, the beneficial effects of the present invention are as follows: the dormancy and reproduction ratio of the artificial original optimization algorithm is dynamically adjusted based on population diversity and fitness change rate, making the algorithm more flexible, and being able to better balance the exploration and development stages, thereby improving the algorithm optimization efficiency and effect; through the improved foraging factor and dynamic adjustment mechanism, the position update in the global search stage is made more accurate, the convergence process of the algorithm is accelerated, and the adaptability of the tree-climbing robot is improved in complex environments. The present invention optimizes the PID closed-loop algorithm of the air pump control of the tree-climbing robot by using the improved artificial original optimization algorithm, thereby significantly improving the control accuracy and reaction speed of the robot's force arm, and solving the problem of low work efficiency caused by poor sensitivity and adaptability of the force arm; at the same time, by precisely controlling the air pump output and maintaining stable air pressure, the tree-climbing robot is ensured to climb stably in unstructured environments such as forests and pole-shaped equipment, thereby enhancing the adaptability and reliability of the tree-climbing robot.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为利用改进人工原优化算法优化爬树机器人的气泵控制的方法步骤图；FIG1 is a step diagram of a method for optimizing the air pump control of a tree climbing robot using an improved artificial original optimization algorithm;
图2为利用改进的人工原优化算法优化爬树机器人的气泵PID闭环控制算法的方法流程图；FIG2 is a flow chart of a method for optimizing the air pump PID closed-loop control algorithm of a tree-climbing robot using an improved artificial original optimization algorithm;
图3为改进的人工原优化算法与标准人工原优化算法对爬树机器人的气泵PID闭环控制算法的Kp、Ki、Kd整定的结果对比图；FIG3 is a comparison diagram of the results of Kp, Ki, and Kd setting of the air pump PID closed-loop control algorithm of the tree-climbing robot using the improved artificial original optimization algorithm and the standard artificial original optimization algorithm;
图4为改进的人工原优化算法与标准人工原优化算法用于爬树机器人的气泵PID闭环控制算法的适应度函数变化对比图；FIG4 is a comparison diagram of the fitness function changes of the improved artificial primitive optimization algorithm and the standard artificial primitive optimization algorithm for the air pump PID closed-loop control algorithm of the tree climbing robot;
图5为不同控制方法用于爬树机器人的气泵控制的效果对比图。FIG5 is a comparison diagram of the effects of different control methods on the air pump control of the tree climbing robot.
具体实施方式Detailed ways
面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例；基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.
本发明提供一种技术方案：一种用于爬树机器人的气泵控制优化方法，包括爬树机器人的气泵控制系统，利用压力传感器采集爬树机器人力臂与树木之间的压力数据，并通过PID控制器调整气泵的输出气压，提高机器人力臂实施变化度的精确性和鲁棒性，首先如图1所示，爬树机器人的气泵控制具体步骤为。The present invention provides a technical solution: an air pump control optimization method for a tree-climbing robot, including an air pump control system of the tree-climbing robot, which uses a pressure sensor to collect pressure data between the tree-climbing robot's arm and the tree, and adjusts the output air pressure of the air pump through a PID controller to improve the accuracy and robustness of the degree of change of the robot's arm. First, as shown in Figure 1, the specific steps of the air pump control of the tree-climbing robot are as follows.
S1、根据气压、树径、爬升速度的关系，建立爬树机器人的气泵控制数学模型。S1. According to the relationship among air pressure, tree diameter and climbing speed, a mathematical model of air pump control for the tree climbing robot is established.
进一步地，爬树机器人的气泵控制数学模型为：Furthermore, the air pump control mathematical model of the tree climbing robot is:
（1）； (1);
式（1）中，Y(t)为爬树机器人力臂的变化度，m为机器人的质量（kg），g为重力加速度（9.81 m/s²），μ为摩擦系数，W(t)为不同时间段的树径，d(t)为不同时间段机器人力臂与树的接触宽度，kv为速度，t为时间单位为秒，u(t)为气泵PID控制输出值。In formula (1), Y(t) is the degree of change of the force arm of the tree climbing robot, m is the mass of the robot (kg), g is the acceleration of gravity (9.81 m/s²), μ is the friction coefficient, W(t) is the tree diameter at different time periods, d(t) is the contact width between the robot force arm and the tree at different time periods, kv is the speed, t is the time unit in seconds, and u(t) is the output value of the air pump PID control.
S2、建立爬树机器人的气泵控制系统，控制系统包括气泵控制单元和执行单元。S2. Establish an air pump control system for the tree-climbing robot. The control system includes an air pump control unit and an execution unit.
进一步地，爬树机器人的气泵控制系统的气泵控制单元和执行单元，其中气泵控制单元包括气泵控制器，气泵控制器采用PID闭环控制算法，将爬树机器人力臂与树木之间的实时压力数据差值e(t)输入到气泵控制器中，经过公式计算出爬树机器人的气泵PID控制输出值u(t)，将气泵PID控制输出值u(t)输入到爬树机器人的气泵控制数学模型，即公式（1）中，从而改变爬树机器人力臂的变化度，同时压力传感器采集爬树机器人力臂与树木之间的实时压力数据P(t)，返回计算爬树机器人力臂与树木之间的实时压力数据差值e(t)，直至t达到控制最大时间T，实现爬树机器人的闭环控制，执行单元为一个永磁电机，为爬树机器人提供气体驱动机器人力臂。Furthermore, the air pump control unit and the execution unit of the air pump control system of the tree climbing robot, wherein the air pump control unit includes an air pump controller, and the air pump controller adopts a PID closed-loop control algorithm, inputs the real-time pressure data difference e(t) between the force arm of the tree climbing robot and the tree into the air pump controller, and then uses the formula The air pump PID control output value u ( t ) of the tree - climbing robot is calculated and input into the air pump control mathematical model of the tree-climbing robot, i.e., formula (1), so as to change the degree of change of the tree-climbing robot's lever arm. At the same time, the pressure sensor collects the real-time pressure data P(t) between the tree-climbing robot's lever arm and the tree, and returns to calculate the real-time pressure data difference e(t) between the tree-climbing robot's lever arm and the tree until t reaches the maximum control time T, thus realizing the closed-loop control of the tree-climbing robot. The execution unit is a permanent magnet motor, which provides gas to drive the robot's lever arm for the tree-climbing robot.
S3、对人工原优化算法改进，利用改进的人工原优化算法优化爬树机器人的气泵PID闭环控制算法，具体步骤为S31到步骤S34。S3. Improve the artificial original optimization algorithm, and use the improved artificial original optimization algorithm to optimize the air pump PID closed-loop control algorithm of the tree climbing robot. The specific steps are S31 to step S34.
S31、改进人工原种群休眠和繁殖的比例因子，调整人工原优化算法的局部开 发阶段的种群规模，调整局部开发阶段与全局搜索阶段的算法位置更新策略；进一步地，本 发明基于种群多样性和适应度变化率动态调整休眠和繁殖的比例，调整人工原优化算法的 睡眠和繁殖阶段的种群规模，使算法更灵活，能够更好地平衡探索和开发，提升优化效率和 效果；其中，种群多样性通过计算人工原个体之间的距离衡量，改进的人工原种群休眠和繁 殖的比例因子数学模型为： S31. Improve the proportional factors of dormancy and reproduction of artificial original populations , adjust the population size of the local development stage of the artificial prototype optimization algorithm, and adjust the algorithm position update strategy in the local development stage and the global search stage; further, the present invention dynamically adjusts the proportion of dormancy and reproduction based on population diversity and fitness change rate, adjusts the population size of the sleep and reproduction stages of the artificial prototype optimization algorithm, makes the algorithm more flexible, can better balance exploration and development, and improves optimization efficiency and effect; wherein, population diversity is measured by calculating the distance between artificial prototype individuals, and the improved artificial prototype population dormancy and reproduction ratio factor The mathematical model is:
(2)； (2);
式（2）中，为第iter次迭代改进的人工原种群休眠和繁殖的比例因 子，为第i个个体在种群中的适应度值排名，N为人工原最大规模，为第iter次迭 代的当前种群的多样性，为初始种群的多样性。利用种群多样性指标调整整体休眠和 繁殖比例，避免过早收敛到局部最优解。 In formula (2), The ratio factor of dormancy and reproduction of the artificial original population improved for the iterth iteration, is the fitness ranking of the ith individual in the population, N is the maximum size of the artificial original, is the diversity of the current population at the iter iteration, is the diversity of the initial population. The population diversity index is used to adjust the overall dormancy and reproduction ratio to avoid premature convergence to the local optimal solution.
S32、基于人工原种群的多样性和人工原位置的最优解的变化，通过引入动态调整 机制，改进人工原优化算法的觅食因子；改进的觅食因子数学模型为： S32. Based on the diversity of the artificial original population and the changes in the optimal solution of the artificial original position, the foraging factor of the artificial original optimization algorithm is improved by introducing a dynamic adjustment mechanism ; Improved foraging factor The mathematical model is:
（3）； (3);
式（3）中，为第iter次迭代的改进的觅食因子，为改进的觅食因 子最小值，取值为0，为改进的觅食因子最大值，取值为2；为当前迭代次数，为最大迭代次数，为动态调整机制。 In formula (3), is the improved foraging factor for the iter-th iteration, is the minimum value of the improved foraging factor, which is 0. is the maximum value of the improved foraging factor, which is 2; is the current iteration number, is the maximum number of iterations, It is a dynamic adjustment mechanism.
进一步地，动态调整机制基于人工原种群熵值变化率和最优解变化率设计，数学模型为：Furthermore, the dynamic adjustment mechanism Based on the design of the change rate of the entropy value of the artificial original population and the change rate of the optimal solution, the mathematical model is:
（4）； (4);
式（4）中，为第iter+1次迭代人工原种群位置的熵值，为第iter次迭代人工原种群位置的熵值，为初始人工原种群位置的熵 值，为第iter次迭代种群最优解适应度值，为先前种群最优解适应 度值，取值为0.001，其中，人工原种群位置的熵值计算公式为：，式中的N为最大种群规模，为第i个人工原出现的概率，通过 位置适应度值归一化得到。 In formula (4), is the entropy value of the artificial original population position at the iter+1th iteration, is the entropy value of the artificial original population position at the iter-th iteration, is the entropy value of the initial artificial original population position, is the fitness value of the optimal solution of the iter-th iteration population, is the fitness value of the previous population optimal solution, The value is 0.001, where the entropy value calculation formula of the artificial original population position is: , where N is the maximum population size, is the probability of the i-th artifact appearing, which is obtained by normalizing the position fitness value.
S33、利用改进的觅食因子对人工原优化算法的全局搜索阶段的位置更新数 学模型改进；改进的人工原优化算法的全局搜索阶段的位置更新数学模型为： S33. Using improved foraging factors The position update mathematical model of the global search phase of the artificial original optimization algorithm is improved; the position update mathematical model of the global search phase of the improved artificial original optimization algorithm is:
（5）； (5);
式（5）中，为第i个人工原的新位置，为第iter次迭代第i个人工原 的位置，为第iter次迭代随机人工原的位置，为人工原邻居对的数量，为一个大小为1×dim的觅食映射向量，向量内的值取值为1，为自养模式的权重，为异养模式的权重，rand为0到1内的随机数，为第k个配对邻居中随机选择的人 工原位置，其中k大于i，为第k个配对邻居中随机选择的人工原位置，其中k小于i；为第k个配对邻居中选择的第i-k个人工原位置，为第k个配对邻居中选择 的第i+k个人工原位置；为自养和异养行为的分界参数，为第iter次迭代 的改进的觅食因子。 In formula (5), is the new position of the i-th artifact, is the position of the i-th artificial original in the iter-th iteration, Random for the iterth iteration The location of the artificial is the number of artificial original neighbor pairs, is a foraging mapping vector of size 1×dim, and the value in the vector is 1. is the weight of the autotrophic mode, is the weight of the heterotrophic mode, rand is a random number between 0 and 1, is a randomly selected artificial original position among the k-th paired neighbors, where k is greater than i, is the artificial original position randomly selected from the kth paired neighbors, where k is less than i; is the ikth artificial original position selected from the kth pairing neighbor, The i+kth artificial original position is selected from the kth pairing neighbors; is the dividing parameter between autotrophic and heterotrophic behavior, is the improved foraging factor for the iter-th iteration.
S34、提出一种"均匀统计搜索"初始化方法，对人工原种群位置进行均匀初始化，利用改进的人工原优化算法优化爬树机器人的气泵PID闭环控制算法，通过改进的人工原优化算法对爬树机器人的气泵PID闭环控制算法的比例系数Kp、积分系数Ki、微分系数Kd，如图2所示，具体步骤为：S34. A "uniform statistical search" initialization method is proposed to uniformly initialize the position of the artificial original population, and the improved artificial original optimization algorithm is used to optimize the air pump PID closed-loop control algorithm of the tree-climbing robot. The proportional coefficient Kp, integral coefficient Ki, and differential coefficient Kd of the air pump PID closed-loop control algorithm of the tree-climbing robot are optimized by the improved artificial original optimization algorithm, as shown in Figure 2. The specific steps are:
步骤一、设置改进的人工原优化算法的人工原规模N，最大迭代次数Max_iter、问题维度dim，上界UB和下界LB；Step 1: Set the artificial original scale N, the maximum number of iterations Max_iter, the problem dimension dim, the upper bound UB and the lower bound LB of the improved artificial original optimization algorithm;
步骤二、按照公式（7）利用"均匀统计搜索"初始化方法，对人工原种群进行均匀初始化，使得人工原个体覆盖整个改进的人工原优化算法的搜索空间；对改进的人工原优化算法的搜索空间的上界UB和下界LB限制；Step 2: According to formula (7), the "uniform statistical search" initialization method is used to uniformly initialize the artificial original population, so that the artificial original individuals cover the entire search space of the improved artificial original optimization algorithm; the upper bound UB and lower bound LB of the search space of the improved artificial original optimization algorithm are restricted;
（7）； (7);
式（7）中，为第i个人工原个体第j维的初始化后的位置，其中，;，为人工原个体的下限位置，为人工原个体 的上限位置，为上次迭代的全局最佳人工原个体位置，rand(0,1)为0到1内的随 机数； In formula (7), is the initialized position of the jth dimension of the ith artificial original individual, where ; , is the lower limit position of the artificial original individual, is the upper limit position of the artificial original individual, is the global best artificial original individual position of the last iteration, rand(0,1) is a random number between 0 and 1;
步骤三、将搜索空间内的人工原个体位置与爬树机器人的气泵PID闭环控制算法的Kp、Ki、Kd组成的向量建立三维映射；Step 3: Establish a three-dimensional mapping between the position of the artificial original individual in the search space and the vector composed of Kp, Ki, and Kd of the air pump PID closed-loop control algorithm of the tree-climbing robot;
步骤四、利用目标函数计算第iter次迭代人工原种群中每个人工原个体的位置适应度值，将种群中较小的适应度值对应的人工原个体位置作为当前迭代的最佳位置；Step 4: Use the objective function to calculate the position fitness value of each artificial original individual in the iter-th iteration artificial original population, and take the position of the artificial original individual corresponding to the smaller fitness value in the population as the best position of the current iteration;
步骤五、建立改进的人工原优化算法在全局搜索阶段和局部开发阶段的种群位置更新数学模型，更新人工原个体位置，具体步骤为：Step 5: Establish a mathematical model for updating the population position of the improved artificial primitive optimization algorithm in the global search stage and the local development stage, and update the position of the artificial primitive individuals. The specific steps are as follows:
S351、利用公式（2）计算第iter次迭代改进的人工原种群休眠和繁殖的比例因子，设置大小为的种群范围，若当前迭代第i个个 体在种群范围内，则第i个个体位置更新执行步骤S352；否则执行步骤S353； S351. Use formula (2) to calculate the proportional factor of dormancy and reproduction of the artificial original population improved in the iterth iteration , set the size to If the i-th individual in the current iteration is within the population range, the position of the i-th individual is updated and executed in step S352; otherwise, step S353 is executed;
S352、模型人工原的休眠和繁殖行为，按照公式（8）建立算法局部收敛阶段的人工原个体位置更新数学模型；S352, modeling the dormancy and reproduction behavior of artificial atom, and establishing a mathematical model for the position update of artificial atom individuals in the local convergence stage of the algorithm according to formula (8);
（8）； (8);
式（8）中，为第i个人工原的新位置，为第iter次迭代第i个人工原 的位置，rand为0到1内的随机数，为休眠和繁殖的分界参数，当大于rand时，执 行人工原的休眠位置更新数学模型，否则，执行人工原的繁殖位置更新数学模型； In formula (8), is the new position of the i-th artifact, is the position of the ith artificial source in the iterth iteration, rand is a random number between 0 and 1, is the boundary parameter between dormancy and reproduction. When it is greater than rand, the mathematical model of the dormant position of the artificial source is updated, otherwise, the mathematical model of the reproductive position of the artificial source is updated;
S353、模型人工原的搜索行为，通过改进的觅食因子改进的人工原优化算法 的全局搜索阶段的位置更新数学模型，即公式（5）建立算法全局搜索阶段人工原个体位置 数学模型； S353, Modeling the Search Behavior of Artificial Protozoa, by Improving the Foraging Factor The mathematical model for updating the position of the artificial atom in the global search phase of the improved artificial atom optimization algorithm, that is, formula (5) establishes the mathematical model for the position of the artificial atom in the global search phase of the algorithm;
步骤六、再次利用目标函数计算位置更新后的人工原种群中每个个体的位置适应度值，将当前得到的最小适应度值对应的个体位置作为全局最佳人工原个体位置；Step 6: Use the objective function again to calculate the position fitness value of each individual in the artificial original population after the position update, and take the individual position corresponding to the currently obtained minimum fitness value as the global optimal artificial original individual position;
步骤七、执行iter=iter+1，判断当前迭代次数iter是否满足iter=Max_iter，若满足，则将全局最小适应度值对应的人工原个体位置输出并解析为爬树机器人的气泵PID闭环控制算法的Kp、Ki、Kd参数值，否则执行步骤二的按照公式（7）利用"均匀统计搜索"初始化方法，对人工原种群进行均匀初始化。Step 7: Execute iter=iter+1 to determine whether the current number of iterations iter satisfies iter=Max_iter. If so, the position of the artificial original individual corresponding to the global minimum fitness value is output and parsed as the Kp, Ki, and Kd parameter values of the air pump PID closed-loop control algorithm of the tree-climbing robot. Otherwise, execute step 2 and use the "uniform statistical search" initialization method according to formula (7) to uniformly initialize the artificial original population.
更进一步地，利用改进的人工原优化算法优化爬树机器人的气泵PID闭环控制算 法时，需要设计目标函数指导算法对气泵PID闭环控制算法的优化，爬树机器人的气泵控制 主要考虑通过控制爬树机器人的气泵输出值，从而提高爬树机器人力臂的变化度的精度， 使调整后的力臂半径与树木的半径差值尽可能的小，从而使得爬树机器人工作更稳定，因 而将爬树机器人力臂与树木之间的目标压力值Pa与实时压力数据P(t)的误差值e(t)和爬 树机器人力臂的变化度Y(t)考虑在内设计目标函数，目标函数数学模型为： Furthermore, when the improved artificial original optimization algorithm is used to optimize the air pump PID closed-loop control algorithm of the tree-climbing robot, it is necessary to design an objective function to guide the algorithm to optimize the air pump PID closed-loop control algorithm. The air pump control of the tree-climbing robot mainly considers controlling the air pump output value of the tree-climbing robot, thereby improving the accuracy of the change degree of the tree-climbing robot's force arm, so that the difference between the adjusted force arm radius and the radius of the tree is as small as possible, so that the tree-climbing robot can work more stably. Therefore, the error value e(t) between the target pressure value Pa between the tree-climbing robot's force arm and the tree and the real-time pressure data P(t) and the change degree Y(t) of the tree-climbing robot's force arm are taken into consideration to design the objective function. The objective function The mathematical model is:
（6）； (6);
式（6）中，T为控制最大时间，为爬树机器人力臂的变化度Y(t)的权重，Y(t)为爬树机器人力臂的变化度。In formula (6), T is the maximum control time, is the weight of the degree of change Y(t) of the tree-climbing robot’s force arm, and Y(t) is the degree of change of the tree-climbing robot’s force arm.
S4、利用压力传感器采集爬树机器人力臂与树木之间的实时压力数据P(t)，计算爬树机器人力臂与树木之间的目标压力值Pa与实时压力数据P(t)的误差值e(t)。S4. Use a pressure sensor to collect real-time pressure data P(t) between the tree-climbing robot arm and the tree, and calculate the error value e(t) between the target pressure value Pa between the tree-climbing robot arm and the tree and the real-time pressure data P(t).
S5、根据误差值e(t)和PID控制器的参数Kp、Ki、Kd，计算气泵PID控制输出值u(t)，将输出值u(t)转换为气泵的控制信号，使气泵调整气体输出，形成目标气压值，控制机器人力臂。S5. Calculate the air pump PID control output value u ( t ) according to the error value e ( t ) and the parameters Kp , Ki , and Kd of the PID controller, and convert the output value u ( t ) into a control signal of the air pump, so that the air pump adjusts the gas output to form a target air pressure value and controls the robot arm.
更进一步地，在Matlab中设计改进的人工原优化算法（FAPO）和标准人工原优化算法（APO）的代码，设置人工原种群规模N=40，最大迭代次数Max_iter=60、问题维度dim=3，上界UB=[60,100,15]和下界LB=[0,0,0]；利用目标函数和爬树机器人的气泵控制系统在Simulink中搭建爬树机器人的气泵控制仿真模型，仿真模型包括气泵PID控制参数输入模块、目标函数模块以及爬树机器人的气泵控制数学模型频域表达式模块，即受控函数模块；将最佳PID闭环控制算法的参数输入到气泵PID控制参数输入模块中，根据公式（6）搭建好目标函数模块，爬树机器人的气泵控制数学模型频域表达式设计为二阶复频域形式，数学模型为：Furthermore, the codes of the improved artificial primitive optimization algorithm (FAPO) and the standard artificial primitive optimization algorithm (APO) were designed in Matlab, with the artificial primitive population size N=40, the maximum number of iterations Max_iter=60, the problem dimension dim=3, the upper bound UB=[60,100,15] and the lower bound LB=[0,0,0] set; using the objective function The air pump control system of the tree-climbing robot is used to build the air pump control simulation model of the tree-climbing robot in Simulink. The simulation model includes the air pump PID control parameter input module, the objective function module and the frequency domain expression module of the air pump control mathematical model of the tree-climbing robot, that is, the controlled function module. The parameters of the optimal PID closed-loop control algorithm are input into the air pump PID control parameter input module. The objective function module is built according to formula (6). The frequency domain expression of the air pump control mathematical model of the tree-climbing robot is designed to be a second-order complex frequency domain form. The mathematical model is:
，式中，s为复频域参数。 , where s is the complex frequency domain parameter.
更进一步地，运行Matlab和Siulink系统仿真，得到如图3所示的随迭代次数增加得到的爬树机器人的气泵PID闭环控制算法的最佳Kp、Ki、Kd参数值，以及如图4所示，在改进的人工原优化算法（FAPO）和标准人工原优化算法（APO）在整定爬树机器人的气泵PID闭环控制算法控制参数过程中每次迭代最佳适应度值的变化对比图，最终，如图5所示，在Siumlink输出不同控制方法用于爬树机器人的气泵控制效果对比图。Furthermore, Matlab and Siulink system simulations are run to obtain the optimal Kp, Ki, and Kd parameter values of the air pump PID closed-loop control algorithm of the tree-climbing robot as the number of iterations increases, as shown in Figure 3, and a comparison chart of the changes in the optimal fitness value of each iteration in the process of adjusting the control parameters of the air pump PID closed-loop control algorithm of the tree-climbing robot using the improved artificial primitive optimization algorithm (FAPO) and the standard artificial primitive optimization algorithm (APO), as shown in Figure 4. Finally, as shown in Figure 5, a comparison chart of the air pump control effects of different control methods used for the tree-climbing robot is output in Siumlink.
更进一步地，在迭代60次，得到爬树机器人的气泵PID闭环控制算法的最佳Kp、Ki、Kd参数值，如图3所示，改进的人工原优化算法（FAPO）对爬树机器人的气泵PID闭环控制算法整定得到的最佳Kp=4.36、Ki=1.02、Kd=1.31；标准人工原优化算法（APO）对爬树机器人的气泵PID闭环控制算法整定得到的最佳Kp=8.41、Ki=1.02、Kd=2.75。Furthermore, after 60 iterations, the optimal Kp, Ki, and Kd parameter values of the air pump PID closed-loop control algorithm of the tree-climbing robot were obtained, as shown in Figure 3. The improved artificial primitive optimization algorithm (FAPO) tuned the air pump PID closed-loop control algorithm of the tree-climbing robot to obtain the optimal Kp=4.36, Ki=1.02, and Kd=1.31; the standard artificial primitive optimization algorithm (APO) tuned the air pump PID closed-loop control algorithm of the tree-climbing robot to obtain the optimal Kp=8.41, Ki=1.02, and Kd=2.75.
更进一步地，适应度值反应了算法对爬树机器人的气泵PID闭环控制算法的控制参数整定的性能， 适应度值越小，说明对爬树机器人的气泵PID闭环控制算法的控制参数整定的性能越好，适应度值越大，则性能越差；如图4所示，改进的人工原优化算法（FAPO）的整定适应度值相较于标准人工原优化算法（APO）的整定适应度值，在迭代初期就具有较小值，说明改进的人工原优化算法（FAPO）对爬树机器人的气泵PID闭环控制算法的控制参数整定开始就性能较好，随迭代次数的增加，在迭代次数10内，改进的人工原优化算法（FAPO）的整定适应度值下降速度更快，说明其整定速度更快，最后，在整个迭代整定过程中，改进的人工原优化算法（FAPO）的整定适应度值相较于标准人工原优化算法（APO）的整定适应度值一致更小，说明改进的人工原优化算法（FAPO）整定精度更高，综上可以说明改进的人工原优化算法（FAPO）性能更好。Furthermore, the fitness value reflects the performance of the algorithm in setting the control parameters of the air pump PID closed-loop control algorithm of the tree-climbing robot. The smaller the fitness value, the better the performance of the control parameter tuning of the air pump PID closed-loop control algorithm of the tree-climbing robot, and the larger the fitness value, the worse the performance; as shown in Figure 4, the tuning fitness value of the improved artificial primitive optimization algorithm (FAPO) has a smaller value at the beginning of the iteration compared with the tuning fitness value of the standard artificial primitive optimization algorithm (APO), indicating that the improved artificial primitive optimization algorithm (FAPO) has a better performance in the control parameter tuning of the air pump PID closed-loop control algorithm of the tree-climbing robot. With the increase of the number of iterations, within the number of iterations of 10, the tuning fitness value of the improved artificial primitive optimization algorithm (FAPO) decreases faster, indicating that its tuning speed is faster. Finally, in the entire iterative tuning process, the tuning fitness value of the improved artificial primitive optimization algorithm (FAPO) is consistently smaller than the tuning fitness value of the standard artificial primitive optimization algorithm (APO), indicating that the improved artificial primitive optimization algorithm (FAPO) has a higher tuning accuracy. In summary, it can be shown that the improved artificial primitive optimization algorithm (FAPO) has better performance.
更进一步，如图5所示显示了APO-PID和FAPO-PID算法在控制爬树机器人的气泵效果性能对比；设定目标气压为2个单位压强，相较于APO-PID方法，FAPO-PID方法的上升时间较短，这意味着FAPO-PID方法能够更快地达到目标气压设定值；同时，从图中可以看出，FAPO-PID的超调量比APO-PID小，几乎不存在超调量，在2秒左右时，FAPO-PID控制爬树机器人的气泵输出气压值达到目标值，此时FAPO-PID方法下气泵输出气体形成的气压为1.8，超调量为0.2，这表明FAPO-PID算法的稳定性更高，调节过程中波动较少，最后，都趋于相同的稳态值2单位气压压强值时，FAPO-PID算法的稳态误差更小，表明本发明提出的方法能够更精确地达到设定目标值。Furthermore, as shown in Figure 5, a performance comparison of the APO-PID and FAPO-PID algorithms in controlling the air pump of a tree-climbing robot is shown; the target air pressure is set to 2 units of pressure. Compared with the APO-PID method, the FAPO-PID method has a shorter rise time, which means that the FAPO-PID method can reach the target air pressure setting value faster; at the same time, it can be seen from the figure that the overshoot of FAPO-PID is smaller than that of APO-PID, and there is almost no overshoot. At about 2 seconds, the air pump output pressure value of the tree-climbing robot controlled by FAPO-PID reaches the target value. At this time, the air pressure formed by the air pump output gas under the FAPO-PID method is 1.8, and the overshoot is 0.2, which shows that the FAPO-PID algorithm has higher stability and less fluctuations during the adjustment process. Finally, when they all tend to the same steady-state value of 2 units of air pressure, the steady-state error of the FAPO-PID algorithm is smaller, indicating that the method proposed in the present invention can more accurately reach the set target value.
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