技术领域technical field
本发明涉及一种用于生成四足仿生机器人连续自由步态的方法，使用该方法，四足仿生机器人可以快速、稳定地通过包含不可落足区域的复杂地形，属于机器人控制技术领域。The invention relates to a method for generating a continuous free gait of a quadruped bionic robot. By using the method, a quadruped bionic robot can quickly and stably pass through complex terrain including areas where feet cannot be settled, and belongs to the technical field of robot control.
背景技术Background technique
四足机器人能够在崎岖度较高的自然地形上，甚至是一些对于轮式和履带式机器人无法跨越的复杂地形环境中稳定行走。在复杂的自然地形环境中往往存在着不适于四足机器人落足的区域，当机器人落足于这些区域时，极易发生足底滑动、沉陷等影响机器人稳定性的情况。因而，四足机器人在包含不可落足区域的地形上行走时，就必须能够准确获取地形信息，进而通过相应的处理，获得地形中的不适于机器人落足的不可落足区域，并基于此，提出相应的步态规划方法。Quadruped robots can walk stably on rough natural terrain, even in complex terrain environments that cannot be crossed by wheeled and tracked robots. In the complex natural terrain environment, there are often areas that are not suitable for quadruped robots to land. When the robot lands in these areas, it is very easy for the soles of the feet to slip and sink, which will affect the stability of the robot. Therefore, when a quadruped robot walks on a terrain that includes a non-footholding area, it must be able to accurately obtain terrain information, and then through corresponding processing, obtain the non-footholding area in the terrain that is not suitable for the robot to land on. Based on this, A corresponding gait planning method is proposed.
四足机器人落足点是离散的，为保证机器人稳定地通过包含不可落足区域的崎岖地形，并且避免落足于地形中的不可落足区域，四足机器人必须使用非周期性静步态——自由步态。The footholds of quadruped robots are discrete. In order to ensure that the robot can stably pass through the rough terrain including areas where footholds cannot be achieved, and to avoid landing in areas where footholds cannot be established in the terrain, quadruped robots must use non-periodic static gaits— - Free gait.
在四足机器人的相关研究领域中，自由步态规划是提高四足机器人地形适应性的关键因素。目前，国内外研究者们已经给出了多种自由步态的生成方法。1999年《Robotica》(《机器人》)在17(4):405-412发表的论文《Quadruped free gait generation based onthe primary/secondary gait》中，提出了一种名为“主要/次要”的自由步态生成方法，机器人在行走过程中，主要以周期性静步态行走，只有在无法使用周期性静步态行走时，才转而使用自由步态向前行走；2002年，《The International Journal of RoboticsResearch》(《国际机器人研究杂志》)在21(2):115-130发表的论文《Free gaits forquadruped robots over irregular terrain》提出了三种不同类型的自由步态：自由蟹行步态、自由自转步态和自由转向步态，机器人使用这三种自由步态能够在包含不可落足区域的地形上以任意方向上前进；2015年，在《四足机器人越障自由步态规划与控制研究》中提出了一种基于图搜素算法生成自由步态的方法。在这些步态规划中，普遍存在着未给出具体的对地形信息获取和处理的问题，而准确处理地形信息，是使四足机器人避免落足于地形中不可落足区域的前提。另外，在这些自由步态规划中，机器人的重心只沿前进方向上移动，稳定性不高，限制了机器人的地形适应性。中国专利文献CN104267720A公开了《一种四足仿生机器人的自由步态生成方法》，使用该步态生成方法可生成一种非连续自由步态，当机器人以这种步态行走时，存在着平均运动速度较低的不足。该步态生成方法是基于提前给定地形中的可选落足点进行规划的，未给出根据地形信息自主分析地形中不可落足点区域的算法，与实际应用需求贴合度不高。另外，在自由步态规划中，迈步顺序的确定方法对机器人运动性能的影响较大，而在该步态生成方法中，仅以运动学裕度作为迈步顺序确定的依据，未综合考虑影响机器人运动性能的其他因素。In the related research fields of quadruped robots, free gait planning is a key factor to improve the terrain adaptability of quadruped robots. At present, researchers at home and abroad have given a variety of free gait generation methods. In the paper "Quadruped free gait generation based on the primary/secondary gait" published by "Robotica" ("Robot") at 17(4):405-412 in 1999, a free gait called "primary/secondary" was proposed. Gait generation method. During the walking process, the robot mainly walks with a periodic static gait. Only when the periodic static gait cannot be used, it turns to walk forward with a free gait; in 2002, "The International Journal The paper "Free gaits forquadruped robots over irregular terrain" published in 21(2):115-130 of Robotics Research ("International Robotics Research Journal") proposed three different types of free gaits: free crab gait, free Autorotation gait and free steering gait, the robot can use these three free gaits to move forward in any direction on the terrain that contains unfootable areas; A method for generating free gaits based on a graph search algorithm is proposed in . In these gait planning, there is a common problem of not giving specific terrain information acquisition and processing, and accurate processing of terrain information is the prerequisite for quadruped robots to avoid landing in areas that cannot be settled in the terrain. In addition, in these free gait plans, the center of gravity of the robot only moves in the forward direction, and the stability is not high, which limits the terrain adaptability of the robot. Chinese patent document CN104267720A discloses "A Free Gait Generation Method for a Quadruped Bionic Robot". Using this gait generation method, a discontinuous free gait can be generated. When the robot walks with this gait, there is an average Insufficient movement speed is low. This gait generation method is based on the planning of optional footholds in the terrain given in advance, and does not provide an algorithm for autonomously analyzing areas of non-footholds in the terrain based on terrain information, which does not meet the actual application requirements. In addition, in free gait planning, the method of determining the step sequence has a greater impact on the robot's kinematic performance, while in this gait generation method, only the kinematics margin is used as the basis for determining the step sequence, and the impact on the robot is not considered comprehensively. Other Factors of Athletic Performance.
有鉴于此，为提高四足机器人在包含不可落足区域的地形上行走时的自主性，必须给出通过处理地形信息获得地形中不可落足区域的处理方法；同时，对于四足仿生机器人自由步态生成中迈步顺序的确定、重心移动规划等方面，需综合考虑四足仿生机器人在行走过程中的稳定性、快速性和灵活性，以提高四足仿生机器人的地形适应性为目标，生成符合实际需求的自由步态。In view of this, in order to improve the autonomy of the quadruped robot when walking on the terrain containing the unfootable area, it is necessary to give a processing method to obtain the unfootable area in the terrain by processing the terrain information; at the same time, for the quadruped bionic robot to freely In terms of the determination of the step sequence and the center of gravity movement planning in gait generation, it is necessary to comprehensively consider the stability, speed and flexibility of the quadruped bionic robot in the walking process, with the goal of improving the terrain adaptability of the quadruped bionic robot. A free gait that meets practical needs.
发明内容Contents of the invention
本发明针对现有四足机器人自由步态生成方法存在的诸多不足，提供一种四足仿生机器人连续自由步态生成方法。该方法是基于对地形信息的准确识别与处理给出的，应用该方法，可使机器人避免出现因落足于不可落足区域而造成失稳的情况，从而自主、稳定、快速地通过复杂的崎岖地形。Aiming at the many shortcomings in existing methods for generating free gaits of quadruped robots, the invention provides a method for generating continuous free gaits of quadruped bionic robots. This method is based on the accurate identification and processing of terrain information. By applying this method, the robot can avoid the situation of instability caused by landing in an unfeasible area, so that it can autonomously, stably and quickly pass through complex terrain. rough terrain.
本发明提供的连续自由步态规划方法，是基于对地形信息的准确识别与处理给出的。通过对地形信息的处理，四足仿生机器人可以明确其自身位置与地形中不可落足区域的相对位置关系，结合最优落足点选取算法，可以有效地保证机器人避免落足于不可落足区域；为保证机器人在行走过程中具有足够的稳定裕度，机器人通过四足支撑阶段的重心摆动，以增加机器人的稳定裕度；机器人在使用自由步态行走时，其迈步顺序是不固定的，在四足支撑相中，综合考虑机器人重心投影与支撑多边形的关系及各足摆动时相对应的重心移动量，以确定机器人在行走过程中的迈步顺序，能够在保证机器人灵活运动的同时，保证机器人以最小的移动量维持其自身的稳定性；另外，为提高四足机器人的平均运动速度，规划机器人的躯干沿前进方向以给定的速度不断地向前运动。The continuous free gait planning method provided by the present invention is based on accurate identification and processing of terrain information. Through the processing of terrain information, the quadruped bionic robot can clarify the relative positional relationship between its own position and the non-footholding area in the terrain, combined with the optimal foothold point selection algorithm, it can effectively ensure that the robot avoids footholding in the non-footholding area ; In order to ensure that the robot has sufficient stability margin during the walking process, the robot swings through the center of gravity of the quadruped support stage to increase the stability margin of the robot; when the robot walks with free gait, its step sequence is not fixed, In the quadruped support phase, the relationship between the projection of the center of gravity of the robot and the support polygon and the corresponding movement of the center of gravity when each foot swings are comprehensively considered to determine the step sequence of the robot during the walking process, which can ensure the flexible movement of the robot while ensuring The robot maintains its own stability with the minimum amount of movement; in addition, in order to increase the average movement speed of the quadruped robot, the torso of the robot is planned to move forward continuously at a given speed along the forward direction.
本发明的四足仿生机器人连续自由步态生成方法，具体包括以下步骤：The continuous free gait generation method of the quadruped bionic robot of the present invention specifically comprises the following steps:
(1)获得地形点云数据，对点云数据进行简化和栅格化，并得到地形的高程图；根据地形的高程图，计算每个栅格对应的方差，对比预先设立的阈值，判断地形中的不可落足区域；(1) Obtain terrain point cloud data, simplify and rasterize the point cloud data, and obtain the terrain elevation map; calculate the variance corresponding to each grid according to the terrain elevation map, and compare the preset threshold to judge the terrain in the non-footholding area;
(2)计算机器人各足选定为摆动足时，为保证机器人在足摆动阶段的稳定性，所需要的重心调整量；(2) Calculate the center of gravity adjustment required to ensure the stability of the robot during the foot swing phase when each foot of the robot is selected as the swing foot;
(3)根据机器人各足的位置，以减小机器人重心移动的次数和重心沿侧方向上的移动量为原则，选定摆动足；(3) According to the position of each foot of the robot, the swing foot is selected on the principle of reducing the number of times the center of gravity of the robot moves and the amount of movement of the center of gravity along the lateral direction;
(4)机器人按照计算的重心调整量主动调整重心至目标位置；(4) The robot actively adjusts the center of gravity to the target position according to the calculated center of gravity adjustment;
(5)结合地形信息与机器人的位置信息，根据最优落足点选择算法为摆动足选择地形中的相应位置点作为最优落足点；(5) Combining the terrain information and the position information of the robot, according to the optimal foothold point selection algorithm, select the corresponding position point in the terrain for the swing foot as the optimal foothold point;
(6)摆动足摆动至最优落足点，当摆动足的足底触底传感器检测到触地，转到步骤(2)，重复整个过程。(6) The swinging foot swings to the optimal foothold point. When the sole touch sensor of the swinging foot detects that it touches the ground, go to step (2) and repeat the whole process.
所述步骤(1)中对点云数据进行简化和栅格化的过程是：The process of simplifying and rasterizing the point cloud data in the step (1) is:
①确定单个栅格的尺寸，长×宽为m×n(单位mm)；① Determine the size of a single grid, the length × width is m × n (unit: mm);
②按照确定的栅格尺寸，将点云数据进行栅格化处理；② Rasterize the point cloud data according to the determined grid size;
③分别求出每个栅格中点数据对应的拟合平面；③ Calculate the fitting plane corresponding to the point data in each grid respectively;
④以栅格中点所对应的拟合平面的高度值，作为该栅格的高程值。④ Take the height value of the fitting plane corresponding to the midpoint of the grid as the elevation value of the grid.
所述步骤(2)中判断地形中的不可落足区域的过程是：The process of judging the unacceptable area in the terrain in the step (2) is:
通过建立评估模型，以评估每个栅格的崎岖度，在评估某个栅格的崎岖度时，连同这个栅格以及栅格周围(P*Q-1)个栅格共同组成评估模型，其中，P和Q均是奇数；By establishing an evaluation model to evaluate the roughness of each grid, when evaluating the roughness of a certain grid, together with this grid and the surrounding (P*Q-1) grids to form an evaluation model, where , both P and Q are odd numbers;
用E(i,j)表示栅格的高程值，则分别求得栅格(i,j)崎岖度的评估模型中栅格的平均高程值和高程值方差，如下式所示：Use E(i,j) to represent the elevation value of the grid, then obtain the average elevation value and variance of the elevation value of the grid in the evaluation model of the roughness of the grid (i,j), respectively, as shown in the following formula:
以栅格(i,j)评估模型的方差作为栅格的崎岖度评价值，计算得到每个栅格的崎岖度评价值后，与预先设定的阈值T相比较；如果某个栅格的崎岖度评价值满足下式，则认为该栅格所在的区域为不可落足区域：The variance of the grid (i, j) evaluation model is used as the roughness evaluation value of the grid, and after calculating the roughness evaluation value of each grid, it is compared with the preset threshold T; if a grid’s If the ruggedness evaluation value satisfies the following formula, the area where the grid is located is considered to be an unacceptable area:
S(i,j)2≥T。S(i,j)2 ≥T.
所述步骤(3)中选定摆动足的确定原则是：The determination principle of selected swing foot in the described step (3) is:
(1)如果不需要重心移动，某只足在摆动时，机器人即可满足最小稳定裕度约束以及运动约束时，则该足可被优先选择为摆动足；(1) If there is no need to move the center of gravity, when a foot is swinging, the robot can meet the minimum stability margin constraints and motion constraints, then this foot can be preferentially selected as the swing foot;
(2)如果所有的足均不符合第(1)条，则需根据计算的重心调整量，得到四只足分别选为摆动足时，所对应的重心调整量：Ly1、Ly2、Ly3以及Ly4；之后比较这四个重心调整量的大小，选择重心移动量最小相对应的足作为摆动足。(2) If all the feet do not comply with item (1), it is necessary to obtain the corresponding center of gravity adjustments when the four feet are respectively selected as swing feet according to the calculated center of gravity adjustments: Ly1 , Ly2 , Ly3 and Ly4 ; then compare the adjustments of the four center of gravity, and select the foot corresponding to the smallest movement of the center of gravity as the swing foot.
所述步骤(4)中的重心调整量计算过程是：The center of gravity adjustment calculation process in the described step (4) is:
在四足支撑调整阶段，计算四足机器人重心的调整量时，必须遵循以下两条规则：In the phase of quadruped support adjustment, when calculating the adjustment amount of the center of gravity of the quadruped robot, the following two rules must be followed:
(1)保证四足机器人在重心调整之后，摆动足摆动过程中，其稳定裕度不小于预先设定的最小稳定裕度Smin；(1) Ensure that the stability margin of the quadruped robot is not less than the preset minimum stability margin Smin during the swinging process of the swing foot after the center of gravity is adjusted;
(2)在满足规则(1)的同时，尽量减小侧方向上的重心调整量；(2) While satisfying rule (1), minimize the adjustment of the center of gravity in the lateral direction;
假设机器人沿前进方向上的运动速度为Vx，重心调整阶段的时间为t1，则得重心调整的目标位置点P1的横坐标x1需满足下式：Assuming that the moving speed of the robot along the forward direction is Vx , and the time of the center of gravity adjustment stage is t1 , then the abscissa x1 of the target position point P1 for center of gravity adjustment needs to satisfy the following formula:
xI＝Lx1＝Vx·t1，xI =Lx1 =Vx ·t1 ,
欲使四足机器人经四足支撑阶段的重心调整后，四足机器人的稳定裕度不小于最小稳定裕度Smin，则点P1的位置需满足下式：In order to make the quadruped robot's stability margin not less than the minimum stability margin Smin after the center of gravity adjustment of the quadruped robot is carried out in the quadruped support stage, the positionof point P1 needs to satisfy the following formula:
(Lx1+Lx2)≥Smin，(Lx1 +Lx2 )≥Smin ,
设重心调整阶段的时间为t2，则Lx2的值由下式求得：Assuming that the time of center of gravity adjustment stage is t2 , then the value of Lx2 is obtained by the following formula:
Lx2＝Vx·t2，Lx2 =Vx ·t2 ,
欲使四足机器人经足的摆动阶段后，四足机器人仍能保证其自身的稳定性，即稳定裕度不小于最小稳定裕度Smin，则迈步阶段结束后，重心投影的目标位置点P2需满足下式：If the quadruped robot can still guarantee its own stability after the swing phase of the legs, that is, the stability margin is not less than the minimum stability margin Smin , then after the step phase, the target position point P of the center of gravity projection2 must satisfy the following formula:
Lx3≥Smin，Lx3 ≥ Smin ,
为提高机器人在行走过程中的能耗，点P1和点P2满足式(Lx1+Lx2)≥Smin和Lx3≥Smin时，对应的最小移动量Ly，即为目标的重心调整量。In order to improve the energy consumption of the robot during walking, when point P1 and point P2 satisfy the formula (Lx1 +Lx2 )≥Smin and Lx3 ≥Smin , the corresponding minimum movement amount Ly is the target Center of gravity adjustment.
所述步骤(5)中的最优落足点选择算法，是：The optimal foothold selection algorithm in the step (5) is:
将可选落足点的坐标位置存储在数组C中，如下式所示：Store the coordinate position of the optional foothold in the array C, as shown in the following formula:
其中，ci代表的是摆动足第i个可选的落足点；xi和yi分别表示的是第i个可选落足点在世界坐标系{W}中的横纵坐标；Among them, ci represents thei -th optional foothold of the swing foot; xi and yi respectively represent the horizontal and vertical coordinates of the i-th optional foothold in the world coordinate system {W};
摆动足的最优落足点，必须满足以下两个条件：The optimal landing point of the swing foot must meet the following two conditions:
(1)最优落足点必须帮助摆动足获得尽量大的步长，这样有助于机器人提高其平均运动速度；(1) The optimal foothold point must help the swing foot to obtain as large a step length as possible, which will help the robot improve its average movement speed;
(2)最优落足点必须帮助机器人获得更大面积的稳定区域，这样有助于机器人提高其在运动过程中的稳定性；(2) The optimal foothold must help the robot obtain a larger area of stability, which will help the robot improve its stability during movement;
以Li(x,y)和Si(x,y)分别表示第i个可选的落足点被确定为最优落足点时，摆动足的步长以及对应的支撑三角形的面积，然后，建立最优落足点的评价函数，如下式所示：Let Li (x, y) and Si (x, y) represent the step length of the swing foot and the area of the corresponding support triangle when the i-th optional foothold is determined to be the optimal foothold, respectively, Then, establish the evaluation function of the optimal foothold point, as shown in the following formula:
F(x)＝wS·Li(x,y)+wL·Si(x,y)，F(x)=wS · Li (x, y) + wL · Si (x, y),
其中，wS和wL分别表示的是摆动足步长和机器人支撑三角形面积的权重系数；Among them, wS and wL represent the weight coefficients of the swing foot step length and the area of the robot support triangle, respectively;
根据数组C中存储的可选落足点的坐标，分别计算出每个可选落足点对应的评价函数的值，其中，最大评价函数的值对应的可选落足点即为摆动足的最优落足点。According to the coordinates of the optional foothold points stored in the array C, the value of the evaluation function corresponding to each optional foothold point is calculated respectively, wherein the optional foothold point corresponding to the value of the maximum evaluation function is the swing foot The best foothold.
本发明具有以下特点：The present invention has the following characteristics:
1.结合获取的地形点云信息，四足仿生机器人能够准确地识别地形中的不可落足区域；1. Combined with the obtained terrain point cloud information, the quadruped bionic robot can accurately identify the unacceptable areas in the terrain;
2.能够帮助机器人选择最优落足点，进而保证机器人在避开地形中不可落足区域的同时，增大机器人稳定性和平均运动速度；2. It can help the robot to choose the optimal foothold point, thereby ensuring that the robot can increase the stability and average movement speed of the robot while avoiding the non-footholding area in the terrain;
3.通过重心的主动调整，有效地增大四足机器人在行走过程中的稳定裕度，进而可提高四足机器人的地形适应性；3. Through the active adjustment of the center of gravity, the stability margin of the quadruped robot can be effectively increased during the walking process, thereby improving the terrain adaptability of the quadruped robot;
4.优化了迈步顺序确定方法，在确保机器人运动灵活性的同时，减小了运动过程中的侧向调整量，可有效地降低机器人的能耗；4. The method of determining the step sequence is optimized, while ensuring the flexibility of the robot's movement, it reduces the amount of lateral adjustment during the movement, which can effectively reduce the energy consumption of the robot;
5.机器人在运动过程中，躯干沿前进方向上以预先设定的速度不断向前运动，有效地提高了机器人的运动速度，使机器人在稳定的前提下，以最短的时间通过复杂地形。5. During the movement of the robot, the torso moves forward continuously at a preset speed along the forward direction, which effectively increases the movement speed of the robot and enables the robot to pass through complex terrain in the shortest time under the premise of stability.
附图说明Description of drawings
图1是十二自由度四足仿生机器人的仿真模型图。Figure 1 is a simulation model diagram of a quadruped bionic robot with 12 degrees of freedom.
图2是由TOF相机获取的崎岖地形的点云数据图。Figure 2 is a point cloud data map of rough terrain acquired by a TOF camera.
图3是栅格(i，j)中包含的点云数据图。Figure 3 is a graph of the point cloud data contained in the grid (i, j).
图4是栅格(i，j)中点云数据的拟合平面示意图。Fig. 4 is a schematic diagram of the fitting plane of the point cloud data in the grid (i, j).
图5是简化后崎岖地形的高程图。Figure 5 is an elevation map of simplified rough terrain.
图6是栅格崎岖度评价模型图。Fig. 6 is a diagram of a grid ruggedness evaluation model.
图7是崎岖地形上不可落足区域示意图。Fig. 7 is a schematic diagram of areas where footholds are not permitted on rough terrain.
图8是四足机器人最优落足点选择示例图。Fig. 8 is an example diagram of selecting the optimal foothold point for a quadruped robot.
图9是机器人重心调整量计算示例图。Fig. 9 is a diagram showing an example calculation of the center of gravity adjustment amount of the robot.
图10是摆动足选择方法示例图。Fig. 10 is an example diagram of a swing foot selection method.
具体实施方式detailed description
下面以图1所示的十二自由度四足机器人为例，对本发明的四足机器人连续自由步态的生成方法作详细描述。Taking the quadruped robot with 12 degrees of freedom as shown in FIG. 1 as an example, the method for generating the continuous free gait of the quadruped robot of the present invention will be described in detail below.
一.地形信息处理1. Terrain information processing
首先，通过光传输时间(Time Of Flight,TOF)三维激光相机获得地形的点云数据，如图2所示。将点云中各点在世界坐标系{W}中的位置，存储到数字P中，如下式(1)所示。First, the point cloud data of the terrain is obtained through a Time Of Flight (TOF) 3D laser camera, as shown in Figure 2. The position of each point in the point cloud in the world coordinate system {W} is stored in the number P, as shown in the following formula (1).
其中，pi(xi,yi,zi)表示的是点云中第i个点在世界坐标系中的坐标。Among them, pi (xi , yi ,zi ) represents the coordinates of the i-th point in the point cloud in the world coordinate system.
在地形信息的处理中，分为两个步骤，第一步是对地形数据的简化；第二步是对地形崎岖度的评估。In the processing of terrain information, it is divided into two steps, the first step is the simplification of terrain data; the second step is the evaluation of terrain roughness.
(1)地形数据简化(1) Terrain data simplification
为了减少点云数据，从而减小计算量，对点云数据做以下处理：In order to reduce the point cloud data, thereby reducing the amount of calculation, the point cloud data is processed as follows:
①确定单个栅格的尺寸，m×n(长×宽，单位mm)；① Determine the size of a single grid, m×n (length×width, in mm);
②按照确定的栅格尺寸，将点云数据进行栅格化处理；② Rasterize the point cloud data according to the determined grid size;
③分别求出每个栅格中点数据对应的拟合平面；③ Calculate the fitting plane corresponding to the point data in each grid respectively;
④以栅格中点所对应的拟合平面的高度值，作为该栅格的高程值。④ Take the height value of the fitting plane corresponding to the midpoint of the grid as the elevation value of the grid.
以图3所示的栅格(i，j)以及其中包含的点云数据作为实例，说明拟合平面的求解过程。Taking the grid (i, j) shown in Figure 3 and the point cloud data contained in it as an example, the solution process of the fitting plane is illustrated.
首先，给出拟合平面的方程，如下式(2)所示。First, the equation of the fitting plane is given, as shown in the following formula (2).
z＝A·x+B·y+C (2)z=A·x+B·y+C (2)
其中，A、B、C为待定系数。Among them, A, B, C are undetermined coefficients.
根据式(2)，可得到栅格中，各点到拟合平面的距离之和，如下式(3)所示。According to the formula (2), the sum of the distances from each point in the grid to the fitting plane can be obtained, as shown in the following formula (3).
其中，m表示的是在栅格(i，j)中的点数据的总数。Among them, m represents the total number of point data in the grid (i, j).
根据式(3)，可得到式(3)对各参数的偏导数，如式(4)所示。According to formula (3), the partial derivative of formula (3) with respect to each parameter can be obtained, as shown in formula (4).
为求得栅格中各点的拟合平面，构建如下式(5)所示的方程组。通过求得式(5)中方程组，可得到式(2)中参数。In order to obtain the fitting plane of each point in the grid, a system of equations as shown in the following formula (5) is constructed. By obtaining the equation group in equation (5), the parameters in equation (2) can be obtained.
根据式(2)、式(4)和式(5)，可得到如式(6)所示的矩阵方程。According to formula (2), formula (4) and formula (5), the matrix equation shown in formula (6) can be obtained.
进而，根据式(6)，可得到求解式(2)中各参数的矩阵方程，如下式(7)所示。Furthermore, according to formula (6), the matrix equation for solving each parameter in formula (2) can be obtained, as shown in formula (7) below.
求得参数A、B及C后，可得到图3中所示的栅格(i，j)中点云数据的拟合平面，如图4所示。After obtaining the parameters A, B and C, the fitting plane of the point cloud data in the grid (i, j) shown in Fig. 3 can be obtained, as shown in Fig. 4 .
通过式(7)求得式(2)中各系数后，可得到栅格(i，j)的高程值。After calculating the coefficients in formula (2) through formula (7), the elevation value of grid (i, j) can be obtained.
根据本部分给出的方法，将图2中所示的点云数据处理后，得到如图5中所示的高程图。According to the method given in this part, after processing the point cloud data shown in Figure 2, the elevation map shown in Figure 5 is obtained.
(2)地形崎岖度评估(2) Evaluation of terrain roughness
通过建立评估模型，以评估每个栅格的崎岖度。在评估某个栅格的崎岖度时，连同这个栅格以及栅格周围(P*Q-1)个栅格共同组成评估模型，其中，P和Q均是奇数。图6给出了评估栅格(i,j)崎岖度的评估模型示例，其中，P＝5，Q＝3。By establishing an evaluation model to evaluate the roughness of each grid. When evaluating the ruggedness of a certain grid, the evaluation model is composed of this grid and (P*Q-1) grids around the grid, where both P and Q are odd numbers. FIG. 6 shows an example of an evaluation model for evaluating the roughness of grid (i, j), where P=5 and Q=3.
用E(i,j)表示栅格的高程值，则可分别求得栅格(i,j)崎岖度的评估模型中栅格的平均高程值和高程值方差，如下式(9)所示。Using E(i, j) to represent the elevation value of the grid, the average elevation value and the variance of the elevation value of the grid in the evaluation model of the roughness of the grid (i, j) can be obtained respectively, as shown in the following formula (9) .
以栅格(i,j)评估模型的方差作为栅格的崎岖度评价值，计算得到每个栅格的崎岖度评价值后，与预先设定的阈值(T)相比较。如果某个栅格的崎岖度评价值满足式(10)，则认为该栅格所在的区域为不可落足区域。The variance of the grid (i, j) evaluation model is used as the roughness evaluation value of the grid, and the roughness evaluation value of each grid is calculated and compared with the preset threshold (T). If the ruggedness evaluation value of a grid satisfies formula (10), the area where the grid is located is considered to be an unacceptable area.
S(i,j)2≥T (10)S(i,j)2 ≥ T (10)
以图7给出的示例，使用上述方法得到地形的不可落足区域，如图7中白色区域为崎岖地形上四足机器人的不可落足区域。Taking the example given in Figure 7, using the above method to obtain the non-footholding area of the terrain, the white area in Figure 7 is the non-footholding area of the quadruped robot on the rough terrain.
二.最优落足点选择算法2. Optimal Foothold Selection Algorithm
结合图8给出的落足点选择示例，给出最优落足点选择算法。图8中所示的实线框为摆动足的有效工作区域，横纵虚线的交叉点为可选的落足点，阴影覆盖的区域为不可落足区域。将可选落足点的坐标位置存储在数组C中，如下式(11)所示。Combined with the foothold selection example shown in Figure 8, the optimal foothold selection algorithm is given. The solid line box shown in Figure 8 is the effective working area of the swing foot, the intersection of the horizontal and vertical dotted lines is the optional foothold point, and the area covered by the shadow is the non-footholding area. Store the coordinate positions of optional footholds in the array C, as shown in the following formula (11).
其中，ci代表的是摆动足第i个可选的落足点；xi和yi分别表示的是第i个可选落足点在世界坐标系{W}中的横纵坐标。Among them, ci represents thei -th optional foothold of the swing foot; xi and yi respectively represent the horizontal and vertical coordinates of the i-th optional foothold in the world coordinate system {W}.
摆动足的最优落足点，必须满足以下两个条件：The optimal landing point of the swing foot must meet the following two conditions:
(1)最优落足点必须帮助摆动足获得尽量大的步长，这样有助于机器人提高其平均运动速度；(1) The optimal foothold point must help the swing foot to obtain as large a step length as possible, which will help the robot improve its average movement speed;
(2)最优落足点必须帮助机器人获得更大面积的稳定区域，这样有助于机器人提高其在运动过程中的稳定性。(2) The optimal foothold must help the robot to obtain a larger area of stability, which will help the robot improve its stability during motion.
以Li(x,y)和Si(x,y)分别表示第i个可选的落足点被确定为最优落足点时，摆动足的步长以及对应的支撑三角形的面积，然后，建立最优落足点的评价函数，如式(12)所示。Let Li (x, y) and Si (x, y) represent the step length of the swing foot and the area of the corresponding support triangle when the i-th optional foothold is determined to be the optimal foothold, respectively, Then, establish the evaluation function of the optimal foothold, as shown in formula (12).
F(x)＝wS·Li(x,y)+wL·Si(x,y) (12)F(x)＝wS · Li (x, y) + wL · Si (x, y) (12)
其中，wS和wL分别表示的是摆动足步长和机器人支撑三角形面积的权重系数。Among them, wS and wL represent the weight coefficients of the swing foot step length and the area of the robot support triangle, respectively.
根据数组C中存储的可选落足点的坐标，可分别计算出每个可选落足点对应的评价函数的值，其中，最大评价函数的值对应的可选落足点即为摆动足的最优落足点。According to the coordinates of the optional foothold points stored in the array C, the value of the evaluation function corresponding to each optional foothold point can be calculated respectively, and the optional foothold point corresponding to the value of the maximum evaluation function is the swing foothold. the optimal foothold.
三.重心调整量计算3. Calculation of center of gravity adjustment
本发明给出的四足机器人自由步态规划方法中，使用纵向稳定裕度衡量机器人的稳定性。In the quadruped robot free gait planning method provided by the present invention, the stability of the robot is measured by the longitudinal stability margin.
在四足支撑阶段，机器人完成重心的主动调整，可以保证摆动足能够稳定地摆动至最优落足点。但是，重心在前进方向侧方向上的摆动，也提高了四足机器人的能耗。In the quadruped support stage, the robot completes the active adjustment of the center of gravity, which can ensure that the swing foot can swing stably to the optimal foothold point. However, the swing of the center of gravity on the side of the forward direction also increases the energy consumption of the quadruped robot.
因而，在四足支撑调整阶段，计算四足机器人重心的调整量时，必须遵循以下两条规则：Therefore, in the quadruped support adjustment phase, the following two rules must be followed when calculating the adjustment amount of the quadruped robot's center of gravity:
(1)保证四足机器人在重心调整之后，摆动足摆动过程中，其稳定裕度不小于预先设定的最小稳定裕度(Smin)；(1) Ensure that the stability margin of the quadruped robot is not less than the preset minimum stability margin (Smin ) during the swinging process of the swing foot after the center of gravity is adjusted;
(2)在满足规则(1)的同时，尽量减小侧方向上的重心调整量。(2) While satisfying the rule (1), minimize the adjustment of the center of gravity in the lateral direction.
假设机器人沿前进方向上的运动速度为Vx，重心调整阶段的时间为t1，则可得图9中，重心调整的目标位置点P1的横坐标x1需满足下式(13)。Assuming that the moving speed of the robot along the forward direction is Vx , and the time of the center of gravity adjustment stage is t1 , then in Figure 9, the abscissa x1 of the target position point P1 for center of gravity adjustment needs to satisfy the following formula (13).
xI＝Lx1＝Vx·t1 (13)xI =Lx1 =Vx ·t1 (13)
欲使四足机器人经四足支撑阶段的重心调整后，四足机器人的稳定裕度不小于最小稳定裕度Smin，则点P1的位置需满足下式(14)。In order to make the quadruped robot's stability margin not less than the minimum stability margin Smin after the center of gravity of the quadruped robot is adjusted in the quadruped support stage, the position of point P1 needs to satisfy the following formula (14).
(Lx1+Lx2)≥Smin (14)(Lx1 +Lx2 )≥Smin (14)
设重心调整阶段的时间为t2，则Lx2的值可由式(15)求得。Assuming that the time of center of gravity adjustment stage is t2 , then the value of Lx2 can be obtained by formula (15).
Lx2＝Vx·t2 (15)Lx2 =Vx t2 (15)
欲使四足机器人经足的摆动阶段后，四足机器人仍能保证其自身的稳定性，即稳定裕度不小于Smin，则迈步阶段结束后，重心投影的目标位置点P2需满足式(16)。In order for the quadruped robot to ensure its own stability after the foot swing stage, that is, the stability margin is not less than Smin , then after the stepping stage is over, the target position point P2 of the center of gravity projection needs to satisfy the formula (16).
Lx3≥Smin (16)Lx3 ≥Smin (16)
为提高机器人在行走过程中的能耗，点P1和点P2满足式(14)、式(16)时，对应的最小移动量Ly，即为目标的重心调整量。In order to improve the energy consumption of the robot during walking, when point P1 and point P2 satisfy Equation (14) and Equation (16), the corresponding minimum movement amount Ly is the center of gravity adjustment amount of the target.
四.迈步顺序的确定4. Determination of the order of steps
四足机器人在使用自由步态向前行走时，其迈步顺序是不固定的。因而，四足机器人需要在行走过程中自主确定其迈步顺序。When a quadruped robot walks forward with a free gait, its step sequence is not fixed. Therefore, the quadruped robot needs to determine its step sequence autonomously during the walking process.
本发明中给出的自由步态生成方法中，在确定迈步顺序时，要以减小四足机器人重心移动的次数和重心沿侧方向上的移动量为原则，以此提高四足机器人的能量利用率。In the free gait generation method given in the present invention, when determining the step sequence, it is necessary to reduce the number of times the center of gravity of the quadruped robot moves and the amount of movement of the center of gravity along the side direction, so as to improve the energy of the quadruped robot. utilization rate.
以图10所示的具体示例，介绍摆动足的确定原则。Taking the specific example shown in Figure 10, the principle of determining the swing foot is introduced.
(1)如果不需要重心移动，某只足在摆动时，机器人即可满足最小稳定裕度约束以及运动约束时，则该足可被优先选择为摆动足。这样，机器减少了重心的移动次数，可有效地降低能耗。(1) If there is no need to move the center of gravity, when a certain foot is swinging, the robot can satisfy the minimum stability margin constraints and motion constraints, then this foot can be preferentially selected as the swinging foot. In this way, the machine reduces the number of shifts of the center of gravity, which can effectively reduce energy consumption.
以如图10为例，当将1号足确定为摆动足时，机器人重心的投影不需要经过侧向的调整，即处于支撑三角形内，且满足式(17)。Take Figure 10 as an example, when the No. 1 foot is determined as the swing foot, the projection of the center of gravity of the robot does not need to be adjusted laterally, that is, it is in the supporting triangle and satisfies formula (17).
L≥Smin (17)L≥Smin (17)
另外，图10中L的值满足式(18)。In addition, the value of L in FIG. 10 satisfies the expression (18).
L≥[Vx·(t1+t2)+Smin] (18)L≥[Vx (t1 +t2 )+Smin ] (18)
由此可知，当将1号足确定为摆动足时，机器人重心的投影不需要经过侧向的调整，即可满足稳定性约束(式(17))和运动学约束(式(18))。因而，将1号足作为摆动足，这样可省去一次重心的调整运动，进而可减低能耗。It can be seen that when the No. 1 foot is determined as the swing foot, the projection of the center of gravity of the robot does not need to be adjusted laterally to satisfy the stability constraints (Eq. (17)) and kinematic constraints (Eq. (18)). Therefore, the No. 1 foot is used as the swing foot, which saves an adjustment movement of the center of gravity, thereby reducing energy consumption.
(2)如果所有的足均不符合规则(1)，则需根据“4重心调整量计算”中给出的重心调整量计算方法，得到四只足分别选为摆动足时，所对应的重心调整量：Ly1、Ly2、Ly3以及Ly4。之后比较这四个重心调整量的大小，选择重心移动量最小相对应的足作为摆动足。(2) If all the feet do not comply with the rule (1), it is necessary to obtain the corresponding centers of gravity when the four feet are respectively selected as swing feet according to the calculation method of the center of gravity adjustment given in "4 Calculation of center of gravity adjustment" Adjustment amounts: Ly1 , Ly2 , Ly3 and Ly4 . Then compare the size of these four center of gravity adjustments, and select the foot corresponding to the smallest center of gravity movement as the swing foot.
按照上述两条规则，四足机器人即可在行走过程中，自主地确定摆动足的摆动顺序，并最终形成适用于四足机器人在包含不可落足区域崎岖地形上行走时的迈步顺序。According to the above two rules, the quadruped robot can autonomously determine the swing sequence of the swing foot during the walking process, and finally form a step sequence suitable for the quadruped robot to walk on rough terrain including areas where feet cannot be settled.
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| CN201710017097.0ACN106695791B (en) | 2017-01-11 | 2017-01-11 | Continuous free gait generation method for quadruped bionic robot |
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| CN201710017097.0ACN106695791B (en) | 2017-01-11 | 2017-01-11 | Continuous free gait generation method for quadruped bionic robot |
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