From 334e8a86776c782004f4dcaf0d89fc06f9f21dc9 Mon Sep 17 00:00:00 2001 From: Dennis Mronga Date: Thu, 28 Nov 2024 13:24:19 +0100 Subject: [PATCH] Update paper.md --- paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper.md b/paper.md index 749a4441..b044b504 100644 --- a/paper.md +++ b/paper.md @@ -58,7 +58,7 @@ $$\begin{array}{cc} & \boldsymbol{\tau}_m \leq \boldsymbol{\tau} \leq \boldsymbol{\tau}_M \\ \end{array}$$ -where \mathbf{w}^i are task weights for the i-th task, $\mathbf{J}^i$ is the respective robot Jacobian, $\dot{\mathbf{v}}^i_d$ the desired task space acceleration, $\mathbf{q},\dot{\mathbf{q}},\ddot{\mathbf{q}}$ the joint positions, velocities, and accelerations $\mathbf{H}$ the mass-inertia matrix, $\mathbf{h}$ the vector of gravity and Coriolis forces, $\boldsymbol{\tau}$ the robot joint torques, $\mathbf{f}$ the contact wrenches, $\mathbf{J}_c$ the contact Jacobian, and $\boldsymbol{\tau}_m,\boldsymbol{\tau}_M$ the joint torque limits. To implement a simple Cartesian position controller for, e.g., controlling the end effector of a robot manipulator, the following PD-controller can be used to generate $\dot{\mathbf{v}}_d$: +where $\mathbf{w}^i$ are task weights for the i-th task, $\mathbf{J}^i$ is the respective robot Jacobian, $\dot{\mathbf{v}}^i_d$ the desired task space acceleration, $\mathbf{q},\dot{\mathbf{q}},\ddot{\mathbf{q}}$ the joint positions, velocities, and accelerations $\mathbf{H}$ the mass-inertia matrix, $\mathbf{h}$ the vector of gravity and Coriolis forces, $\boldsymbol{\tau}$ the robot joint torques, $\mathbf{f}$ the contact wrenches, $\mathbf{J}_c$ the contact Jacobian, and $\boldsymbol{\tau}_m,\boldsymbol{\tau}_M$ the joint torque limits. To implement a simple Cartesian position controller for, e.g., controlling the end effector of a robot manipulator, the following PD-controller can be used to generate $\dot{\mathbf{v}}_d$: $$ \dot{\mathbf{v}}_d = \dot{\mathbf{v}}_r + \mathbf{K}_d(\mathbf{v}_r-\mathbf{v}) + \mathbf{K}_p(\mathbf{x}_r-\mathbf{x})