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Thus the RCM constraint can be satisfied and modulated by resolving the joint angle variable \(\theta \).4 Simplified RNN for Redundancy Resolution with RCM ConstraintsIn this section, the modeling and theoretical analysis of the proposed SIMPLIFIED RNN for redundancy resolution with RCM constraints are addressed.4.1 Optimization ParadigmIn order to deal with the RCM constrained redundancy resolution issue, in this work, Lagrange function which is simultaneously associated with the kinematic objective function and the RCM constraint is defined as follows$$\begin{aligned} \begin{aligned} L=&\dot{\theta }^T\dot{\theta }/2+c_2\dot{k}^2/2+\lambda _1^T[\dot{k}(r_A-r_B)+kJ_1\dot{\theta }+(1-k)J_2\dot{\theta }\\&+c_1(r_P-r_P(0))]+\lambda _2^T[J_1{\dot{\theta }}+c_3(r_A-r_d)-\dot{r}_d] \end{aligned} \end{aligned}$$ (10) where \(\lambda _1\) and \(\lambda _2\) denote the Lagrange multiplier vectors. The partial derivatives of the Lagrange function with respect to the unknown variables \(({\dot{\theta }},\dot{k},\lambda _1,\lambda _2)\) are$$\begin{aligned} \left\{ \begin{array}{ll} \frac{\partial L}{\partial {\dot{\theta }}}={\dot{\theta }}+[kJ_1+(1-k)J_2]^T\lambda _{1}+J_1^T\lambda _2\\ \frac{\partial L}{\partial \dot{k}}=c_2\dot{k}+ \lambda _{1}^T(r_A-r_B)\\ \frac{\partial L}{\partial \lambda _{1}}=(kJ_1+(1-k)J_2)\dot{\theta }+\dot{k}(r_A-r_B)\\ ~~~~~~~+c_1(r_P-r_P(0))\\ \frac{\partial L}{\partial \lambda _{2}}=J_1{\dot{\theta }}+c_3(r_A-r_d)-\dot{r}_d \end{array} \right. \end{aligned}$$ (11) According to the Karush-Kuhn-Tucker (KKT) conditions [25] , the optimization above can be solved by force the following equations$$\begin{aligned} \left\{ \begin{array}{ll} \frac{\partial L}{\partial {\dot{\theta }}}=0\\ \frac{\partial L}{\partial \dot{k}}=0\\ \frac{\partial L}{\partial \lambda _{1}}=0\\ \frac{\partial L}{\partial \lambda _{2}}=0 \end{array} \right. \end{aligned}$$ (12) to be zero and obtain the desired solution \(({\dot{\theta }}^*,\dot{k}^*,\lambda _1^*,\lambda _2^*)\) for satisfying the optimization objective and constraints.4.2 Original ZD-based RNN MethodIn order to solve such optimization paradigm which reflects the redundancy resolution with RCM constraints, according to the general design principle of the ZD-based RNN model to make the aforementioned partial derivatives of the Lagrange function being 0, we thus need to construct the following error-monitoring function$$\begin{aligned} \begin{aligned} \Xi&=\begin{bmatrix} {\dot{\theta }}+[kJ_1+(1-k)J_2]^T\lambda _{1}+J_1^T\lambda _2\\ c_2\dot{k}+ \lambda _{1}^T(r_A-r_B)\\ (kJ_1+(1-k)J_2)\dot{\theta }+\dot{k}(r_A-r_B)+c_1(r_P-r_P(0))\\ J_1{\dot{\theta }}+c_3(r_A-r_d)-\dot{r}_d \end{bmatrix}\\&=AZ+B \end{aligned} \end{aligned}$$ (13) where$$\begin{aligned} A= & {} \begin{bmatrix} I_{n\times n} &{} 0_{n\times 1} &{} kJ_1^T+(1-k)J_2^T &{} J_1^T\\ 0 &{} c_2 &{} r_A^T-r_B^T &{} 0_{1\times m} \\ kJ_1+(1-k)J_2 &{} r_A-r_B &{} 0 &{} 0 \\ J_1 &{} 0_{m\times 1} &{} 0 &{} 0 \end{bmatrix} \end{aligned}$$ (14) $$\begin{aligned} Z= & {} \begin{bmatrix} {\dot{\theta }}\\ \dot{k}\\ \lambda _1\\ \lambda _2 \end{bmatrix}~~\text {and}~~B=\begin{bmatrix} 0_{n\times 1}\\ 0\\ 0_{m\times 1}\\ c_3(r_A-r_d)-\dot{r}_d \end{bmatrix} \end{aligned}$$ (15) Our goal of applying ZD-based method is to force \(\varXi =0\) eventually and thus the resultant optimal solution of Z can be got.Based on the design discipline of the ZD method, we have the following error-processing formula for redundancy resolution of manipulator with RCM constraints$$\begin{aligned} \dot{\varXi }=-\gamma \varPsi (\varXi ) \end{aligned}$$ (16) where the convergence scaling parameters can be configured as \(\gamma >0\) for unity, \(\varPsi (\cdot ):R^{(n+7)\times (n+7)}\rightarrow R^{(n+7)\times (n+7)}\) denotes the general nonlinear activation function array with its entries being monotonously-increasing odd functions. Therefore, we would have the following ZD-based neural network model for redundancy resolution of manipulator with RCM constraints$$\begin{aligned} \dot{A}Z+A\dot{Z}+\dot{B}=-\gamma \varPsi (AZ+B) \end{aligned}$$ (17) Due to existence of time derivative of coefficient matrix A in the system equation above, such ZD model needs to obtain the time-derivatives of Jacobian matrices analytically during its solution to update the model states,i.e., the coefficient matrix \(\dot{A}\) that is consisted of Jacobian matrices \(\dot{J}_1\) and \(\dot{J}_2\). However, the analytical time-derivative

Chamsoft Posts: 11 Joined: Tue Jun 24, 2008 6:12 pm Dot Net 4.5 download size Hi,If I want to install the dot net framework 4.5 on a client PC I can download a combined 32/64 bit offline installer from the MS website which is just under 50Mb: when I create a project in InstallAware and include these 2 application runtimes it creates 2 web media blocks which are 83MB and 95MB. Why are these so much larger than the MS download? And why do I have to deal with 2 separate files when the MS installer combines both into a single file?Here's the link to MS download page: ... k(v=vs.110).aspx FrancescoT Site Admin Posts: 5361 Joined: Sun Aug 22, 2010 4:28 am Re: Dot Net 4.5 download size Postby FrancescoT » Wed Apr 23, 2014 11:28 am Dear User,the Net Runtime packages included with InstallAware also include other required runtime components.These are not included with the official distributed package .... they are instead downloaded during the package verification process.Hope this clarifies your doubt.Regards chamsoft Posts: 11 Joined: Tue Jun 24, 2008 6:12 pm Re: Dot Net 4.5 download size Postby chamsoft » Thu Apr 24, 2014 12:59 am Hi Francesco, according to the MS download page the only thing not contained in their offline installer are the language packs..."Offline installer (stand-alone redistributable) contains all the required components for installing the .NET Framework but does not contain language packs. This download is larger than the web installer. The offline installer does not require an Internet connection. After you run the offline installer, you can download the stand-alone language packs to install language support. Use the offline installer if you cannot rely on having a consistent Internet connection."From: I don't need anything other than the English version I would prefer to use

DotNetVersionLister is community tool available at GitHub. You don’t need to manually download or install anything. It can all be done using one line of command in PowerShell. To check .NET Framework version in Windows 11, follow the steps below.1. Search for Windows PowerShell via Start. Then, right-click the top result and select Run as administrator.2. In the PowerShell window, enter the following command.Install-Module -Name DotNetVersionLister -Scope CurrentUser #-Force3. If you have never installed NuGet provider which the module requires, you will be prompted to install it. Type Y and hit Enter to continue.4. When asked if you are sure you want to install the module, type Y and hit Enter to install it.5. After installing the module, execute the following command to view the .NET Framework version in Windows 11.Get-STDotNetVersionIf you get error that says “The ‘Get-STDotNetVersion’ command was found in the module‘DotNetVersionLister’, but the module could not be loaded“, it is because the Execution Policy is set to Restricted. This is to protect your PC from scripts that do not trust. You can temporary set the Execution Policy to unrestricted by typing the following command.Set-Executionpolicy UnrestrictedType Y and hit Enter to confirm the changes. Then, execute the get dot net version command to view the installed .NET Framework version.Get-STDotNetVersionAfter viewing your .NET version, set the execution policy back to restricted again. After entering the command below, type Y and hit Enter to confirm the changes.Set-Executionpolicy RestrictedCheck .NET version using Get-ChildItem commandIf you prefer not to install any module, you can use the following command instead to check the version of .NET Framework installed on your PC. The following command will work in both Windows PowerShell and Windows Terminal.Get-ChildItem 'HKLM:\SOFTWARE\Microsoft\NET Framework Setup\NDP' -Recurse | Get-ItemProperty -Name version -EA 0 | Where { $_.PSChildName -Match '^(?!S)\p{L}'} | Select PSChildName, versionMethod 2: Check .NET version via Command PromptTo check .NET Framework version via Command Prompt in Windows 11, follow the steps below.1. Click Start. Search for Command Prompt or CMD and run it as administrator.2. In the elevated Command Prompt window, enter the following command.reg query "HKLM\SOFTWARE\Microsoft\Net Framework Setup\NDP" /sThis command

\(k=0\) is configured, then \(r_P=r_B\); when \(k=1\) is configured, then \(r_P=r_A\); when \(0, \(r_P\) is strictly between points \(r_A\) and \(r_B\). The redundancy resolution for kinematic control of the manipulator needs to finish the two tasks, 1) let the end-effector track the desired path accurately; and 2) satisfy the RCM constraint to make \(r_P\) vary in a very small range or almost static during motion planning and control. In an application scenario, the last link (e.g., \(r_A-r_B\)) of the manipulator can penetrate a small hole (e.g., \(r_P\)) and simultaneously make the end-effector (e.g., \(r_A\)) perform the path tracking task.3 Problem FormulationAs the RCM constraint makes point \(r_P\) is between \(r_A\) and \(r_B\), \(r_P\) can be depicted by the equation \(r_p-r_B=k(r_A-r_B)\). Since \(r_A\) and \(r_B\) are obtained through the forward kinematics with resolved joint angles \(\theta \), thus the state variable pair \((\theta , k)\) can describe the redundancy resolution of the manipulator with RCM constraints. By differentiating the both sides of equation \(r_p-r_B=k(r_A-r_B)\) which depicts the RCM constraint, one can obtain$$\begin{aligned} \dot{r}_P-\dot{r}_B=\dot{k}(r_A-r_B)+k(\dot{r}_A-\dot{r}_B) \end{aligned}$$ (3) When combining it with the aforementioned Eq. (1), one can further have$$\begin{aligned} \dot{r}_P-J_2\dot{\theta }=\dot{k}(r_A-r_B)+k(J_1-J_2)\dot{\theta } \end{aligned}$$ (4) As the position of RCM point \(r_P\) can be described by the following linear combination between \(r_A\) and \(r_B\)$$\begin{aligned} r_P=k(r_A-r_B)+r_B \end{aligned}$$ (5) Combining the aforementioned equations, then we have$$\begin{aligned} \dot{k}(r_A-r_B)+kJ_1\dot{\theta }+(1-k)J_2\dot{\theta }+\dot{r}_P=0 \end{aligned}$$ (6) i.e.,$$\begin{aligned} \begin{aligned} \dot{k}(r_A-r_B)+[kJ_1+(1-k)J_2]\dot{\theta }+\dot{r}_P=0 \end{aligned} \end{aligned}$$ (7) where we can call the equality above as the RCM constraint for redundancy resolution.Based on the derivations and discussions above, we propose the quadratic programming formulation for redundancy resolution of manipulators with RCM constraints as follows$$\begin{aligned} \begin{aligned}&\arg \min _{\theta ,k}~~\dot{\theta }^T\dot{\theta }/2+c_2\dot{k}^2/2\\&\text {s.t.}\left\{ \begin{array}{ll} \dot{k}(r_A-r_B)+[kJ_1+(1-k)J_2]\dot{\theta }+\dot{r}_P=0\\ J_1\dot{\theta }+c_3(r_A-r_d)-\dot{r}_d=0 \end{array} \right. \end{aligned} \end{aligned}$$ (8) where \(c_2>0\) and \(c_3>0\) denote the scaling parameters for the objective function and the last equality constraint respectively. In order to satisfy RCM constraints during redundancy resolution for kinematic control, the time-derivative \(\dot{r}_P\) of \(r_P\) should follow some rules to make \(r_P\) converge to a constant position value.As the point \(r_P\) should not hold static as much as possible to sanctify the RCM constraint, then the time derivative of \(r_P\) can be concisely depicted by$$\begin{aligned} \dot{r}_P=-c_1(r_P-r_P(0)) \end{aligned}$$ (9) to make the RCM point \(r_P\) converge to a fixed position \(r_P(0)\), where \(c_1\ge 0\) is used to scale the convergence of \(r_P\) which shows how the corresponding RCM constraint’s dynamic response changes.In the proposed optimization formulation for redundancy resolution with RCM constraints, the position of \(r_P\) is dynamically adjusted by parameter k with simultaneous positions \(r_A\) and \(r_B\). The initial value k(0) is chosen according to the specific scenarios for safe manipulation, e.g., when \(t=0\), \(r_P\) can be chosen in the middle of the line \(A-B\), and thus \(k(0)=0.5\). To maintain the RCM constraint, \({\dot{\theta }}\) and \(\dot{k}\) are used as decision variables, and the variable which really controls the manipulator is \(\dot{\theta }\) as the control input action. In practice, we can therefore solve \(\dot{k}\) and substitute it into the aforementioned proposed optimization formulation and