• ?IK groups and IK elements

?　　VREP中使用IK groups和IK elements來進行正/逆運動學(xué)計算，一個IK group可以包含一個或者多個IK elements：

• IK groups: IK groups group one or more IK elements. To solve the kinematics of a simple kinematic chain, one IK group containing one IK element is needed. The IK group defines the overall solving properties (like what solving algorithm to use, etc.) for one or more IK elements.?
• IK elements: IK elements specify simple kinematic chains. One IK element represents one kinematic chain. A kinematic chain is a linkage containing at least one?joint object. In short, an IK element is made up by:
  • a base?(any type of?object, even a?joint. In that case however the joint is considered as rigid). It represents the start of the kinematic chain.
  • several links?(any type of object except joints). Joints which are not in?IK mode?are however also considered as links(in that case they behave as rigid joints (fixed value)).?
  • several joints. A joint which is not in?IK mode?is however not considered as a joint, but as a link (see above).?
  • a tip. The tip is always a?dummy?and is the last object in the considered kinematic chain (when going from the base to the tip). The tip dummy should be linked to a target dummy (see hereafter) and the link should be an?IK, tip-target?link type.?
  • a target. The target is always a dummy and represents the position and/or orientation the tip should adopt (or follow) during?simulation.?

　　?一個IK element代表一條運動鏈，最簡單的就是下面這種情況，即場景中只有一個串聯(lián)機械臂（一條運動鏈），那么進行逆運動學(xué)求解只需要一個IK group：

　　如果同一場景中有2個互不干擾的串聯(lián)機械臂，那么就需要2個IK group。下面這種情況IK group的求解順序?qū)Y(jié)果沒有影響：

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　　然而當(dāng)兩個運動鏈相互之間產(chǎn)生影響時，比如上圖中Target2固定到運動鏈1上時，求解順序就很重要了。必須先求解IK group1，求解的結(jié)果會直接影響Target2的位置，從而影響IK group2的求解：

　　下面是一種更復(fù)雜的情況：兩個運動鏈共享某一關(guān)節(jié)，先解算運動鏈1會帶著關(guān)節(jié)朝左移動從而影響運動鏈2的求解；而先解算運動鏈2會帶著關(guān)節(jié)朝右移動從而影響運動鏈1的求解。這種矛盾的情況下按順序解算就失去作用，需要同時求解兩個運動鏈。將兩個IK element放在同一IK group中就可以同時進行逆解計算：

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• 交互式驗證求解結(jié)果

　　簡單的串聯(lián)機械臂按照教程很容易搭建好逆運動學(xué)模型，模型和求解參數(shù)設(shè)定好以后可以通過拖拽/旋轉(zhuǎn)Target Dummy（或者操控球）來觀察機械臂的行為。下面以幫助文檔中的7自由度冗余機械臂為例進行操作，模型位于C:\Program Files\V-REP3\V-REP_PRO_EDU\tutorials\InverseKinematics中。?Try holding down the Ctrl or Shift-keys during manipulation：打開Object Position/Orientation操縱面板，選中操控球（manipSphere），在默認(rèn)視圖下按住鼠標(biāo)只能在X-Y平面內(nèi)進行位置的拖拽，如果同時按住Ctrl鍵則可切換到Z方向拖拽，這是一個很實用的功能。另外值得一提的是下面的Gif圖片使用ScreenToGif開源軟件制作，相當(dāng)良心！

　　打開Tools→User settings對話框，在Object manipulation中也可以自定義拖拽或旋轉(zhuǎn)物體時的步距/步距角：

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• 求解方法

　　The pseudoinverse tends to have stability problems in the neighborhoods?of singularities. At a singularity, the Jacobian matrix no longer has full row?rank, corresponding to the fact that there is a direction of movement of the?end effectors which is not achievable. If the configuration is exactly at a?singularity, then the pseudoinverse method will not attempt to move in an?impossible direction, and the pseudoinverse will be well-behaved. However,?if the configuration is close to a singularity, then the pseudoinverse method?will lead to very large changes in joint angles, even for small movements in?the target position.?

　　Try to drag the object as far as possible, and notice how the inverse kinematics task?breaks. Indeed, this happens when a configuration is singular or not reachable, however there are workarounds to this behavior: while the simulation is still running, select "IK_Group" in the inverse kinematics dialog list, then specify?DLS?for the?Calc. method?item. Drag the object out of reach and notice how the inverse kinematics resolution became more stable. Try adjusting the?Damping?item up and down. Basically, when damping is large, resolution becomes more stable but slower.?The damped least squares method(DLS) avoids many of the pseudo inverse?method’s problems with singularities and can give a numerically stable?method.

　　即使用偽逆矩陣法（Pseudo Inverse）進求解，在奇異位置處可能會出現(xiàn)問題，而DLS法在奇異位置處則更穩(wěn)定。

　　Practically, you can get the advantages of both resolution methods, all you need to do is define two identical "IK groups", where the first is not damped and the second is damped. Then, for the second "IK group", you can specify a conditional resolution (refer to the?Edit conditional parameters?item for more information). ?偽逆矩陣法收斂快，但是在奇異位置處存在問題；DLS法在奇異位置處計算結(jié)果更穩(wěn)定，但是運算較慢。因此可以將兩者結(jié)合起來使用，在IK Group中添加undamped的偽逆矩陣法和damped的DLS法。選中damped IK group，點開Edit conditional parameters對話框，在Perform if...條件欄中進行配置：如果undamped方法失敗，則執(zhí)行damped方法。

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• 約束

　　Make sure that all items are checked in the?Constraints?section (check als?Alpha-Beta?and?Gamma). Indeed, we want our "tip" dummy to follow our "target" dummy in position and orientation.?Sometimes it is however not possible to correctly specify the constraints for a tip, and in that case the IK group's calculation method should be a damped method (e.g. DLS method) with an appropriately selected damping factor. A damped resolution method should also be selected when a target can't possibly be reached (out of reach, or close to a singular configuration). Damping can result in more stable calculations, but keep in mind that damping will always slow down the IK calculations (more iterations will be needed to put the tip into place). ?正確理解和施加約束對于運動學(xué)逆解的求解相當(dāng)重要，如果約束的數(shù)目比機構(gòu)自由度要多則會造成過約束，這時有些求解方法就會失敗。

　　在IK element的Constraints選項欄中勾選X、Y、Z可以分別對笛卡爾坐標(biāo)系下的三個位置分量進行約束，但是姿態(tài)的三個分量只有兩個選項框可以勾選：Turning Alpha-Beta constraint on, will match the tip's z-axis orientation with the target's z-axis orientation, while keeping a free rotation around the z-axis if Gamma constraint is off. When Alpha-Beta constraint AND Gamma constraint are turned on, then the tip will try to adopt exactly the same orientation as its associated target. （V-rep中物體姿態(tài)以X-Y-Z歐拉角的方式確定。即以指定的參考系為初始姿態(tài)，然后按X-Y-Z的順序依次繞自身的坐標(biāo)軸旋轉(zhuǎn)Alpha,Beta,Gamma角度后得到）

• Alpha-beta on and Gamma off

　　很多工業(yè)機械臂只有4個自由度(包括沿X,Y,Z方向的平移和繞Z軸的旋轉(zhuǎn)自由度)，如SCARA機器人，其末端的Z軸指向是固定不變的（因此要約束Alpha-beta，即繞X-Y軸的旋轉(zhuǎn)）。

• Alpha-beta and Gamma on

?　　對于自由度等于或大于6的機械臂，在其靈活工作空間內(nèi)的點可以任意姿態(tài)到達(dá)，因此可以約束所有的自由度。

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• collections

　　A collection is a user-defined collection of?scene objects. A collection has to contain at least one object and is considered to be an?entity?(objects are also entities). Collections are useful when referring to several objects like a robot for instance. V-REP supports?calculations?based not only on objects, but also on collections. For instance the?collision detection module?allows registering following collision pair: (collection A; object B). The collision checking algorithm will then check whether the collection A (any object composing it) collides with object B.

　　VREP中可以將場景里的物體組成一個集合(collection)，后續(xù)的一些操作，比如碰撞檢測時就可以選取定義好的集合。將物體添加進集合有多種方式，以這個冗余機器人為例，在工具欄中打開Collections對話框，點擊Add new collection按鈕，添加一個新的集合并將其命名為redundantRob。然后選中機器人的根節(jié)點redundantRobot，同時勾選Tree of selected object和Base included，點擊Add把機器人整個加入進collection中。為了驗證可以點Visualize selected collection按鈕，用顏色來顯示加入集合中的物體：

　　VREP提供多種靈活的選取方法（參考幫助文檔的Collections頁面），上面這種操作只需要選取根節(jié)點即可將整個運動鏈上的物體加入集合，比一個個物體單獨添加要方便很多：

　　In above example, if object 1 is removed from the scene, the element is not valid anymore and will also be removed. Object 1 is the element's defining object.

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參考：

Inverse kinematics tutorial

Solving IK and FK for any type of mechanism

External kinematics (auxiliary API)

轉(zhuǎn)載于:https://www.cnblogs.com/21207-iHome/p/7420733.html

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