Final changes

paper.md

@@ -34,14 +34,14 @@ ARC-OPT supports the software developer in designing robot controllers by provid
 
 # Description
 
-![ARC-OPT library overview](wbc_overview.png)
+![ARC-OPT library overview\label{fig:overview}](wbc_overview.png)
 
-ARC-OPT separates the implementation of controllers, robot models, solvers, and scenes, which allows a modular composition of the WBC problem:
+Figure \ref{fig:overview} shows an overview of the ARC-OPT library. ARC-OPT separates the implementation of controllers, robot model, solver, and scene, which allows a modular composition of the WBC problem:
 
 * A **controller** implements a function in the robot's task space, e.g., for maintaining balance, avoiding an obstacle, or following a trajectory. ARC-OPT provides various controllers in joint or Cartesian space, like PD-Controllers, or repulsive potential fields.
 * The **scene** sets up the QP, where the costs can be configured at runtime, and the constraints are specific for the implemented scene. Different scenes are currently implemented on velocity, acceleration and torque level.
 * The **robot model** computes the kinematic and dynamic information that the scene requires to set up the QP, like Jacobians, mass-inertia matrices, and gravity terms. ARC-OPT implements various robot models based on Pinocchio [@carpentier2019pinocchio], RBDL [@Felis2016], KDL [@kdl2021], and Hyrodyn [@2019_Kumar_HyRoDynApproach_IDETC].
-* The **solver** solves the QP, which has been set up in the scene, and produces the required control input for the robot joints. ARC-OPT provides various QP solvers based on open-source implementations, e.g.,  qpOASES [@Ferreau2014], eiquadprog [@Eiquadprog2021], proxQP [@bambade2022], and qpSwift [@pandala2019qpswift].
+* The **solver** solves the QP set up in the scene and generates the required control input for the robot joints. ARC-OPT provides various QP solvers based on open-source implementations, e.g.,  qpOASES [@Ferreau2014], eiquadprog [@Eiquadprog2021], proxQP [@bambade2022], and qpSwift [@pandala2019qpswift].
 
 Apart from this, ARC-OPT implements various concepts typically used in WBC, like floating base dynamics, friction cone constraints, cost weighting, and task hierarchies.
 
@@ -56,17 +56,17 @@ $$\begin{array}{cc}
        & \boldsymbol{\tau}_m \leq \boldsymbol{\tau} \leq \boldsymbol{\tau}_M \\
 \end{array}$$
 
-where $\mathbf{J}$ is the robot Jacobian, $\dot{\mathbf{v}}_d$ the desired task space acceleration,  $\ddot{\mathbf{q}},\dot{\mathbf{q}},\mathbf{q}$ the joint accelerations, velocities and positions, $\mathbf{H}$ the mass-inertia matrix, $\mathbf{h}$ the vector of gravity and Coriolis terms, $\boldsymbol{\tau}$ 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 $\mathbf{J}$ is the robot Jacobian, $\dot{\mathbf{v}}_d$ 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 $\dot{\mathbf{v}}_d$:
 
 $$
 \dot{\mathbf{v}}_d = \dot{\mathbf{v}}_r + \mathbf{K}_d(\mathbf{v}_r-\mathbf{v}) + \mathbf{K}_p(\mathbf{x}_r-\mathbf{x})
 $$
 
 where $\mathbf{K}_p,\mathbf{K}_d$ are gain matrices, $\mathbf{x},\mathbf{v}$ the end effector position and velocity, $\dot{\mathbf{v}}_r,\mathbf{v}_r,\mathbf{x}_r$ the reference acceleration, velocity, and position. This example is implemented for a 7 DoF KUKA iiwa robot arm in the ARC-OPT tutorials\footnote{\url{https://github.com/ARC-OPT/wbc/blob/master/tutorials/kuka_iiwa/cart_pos_ctrl_dynamic.cpp}}.
 
-The ARC-OPT library for Whole-Body Control has been used in various scientific works [@Mronga2022],[@Mronga2021],[@Mronga2020],[@Popescu2022], and evaluated on different robots.
+The ARC-OPT library for Whole-Body Control has been used in various scientific works [@Mronga2022],[@Mronga2021],[@Mronga2020],[@Popescu2022], and evaluated on different robots, like, e.g., the RH5 humanoid [@Eer2021DesignAA] shown in Figure \ref{fig:rh5}.
 
-![RH5 Humanoid robot [@Eer2021DesignAA] standing on one leg using the ARC-OPT library](rh5_one_leg.png)
+![RH5 Humanoid robot standing on one leg using the ARC-OPT library\label{fig:rh5}(rh5_one_leg.png)
 
 
 # Acknowledgements