# A Human-Inspired Control Strategy for Improving Seamless Robot-To-Human Handovers
## 2 Design of the Robotic Human-Inspired Control Strategy for HRH
### Coordinate Registration in the HRH System  
This section proposes all coordinate registration for the HRH system. It consists of the robot base frame (robot reference frame) [R], the robot end-effector frame [A], object (held by the robot) frame [T], RGBD camera frame [C], human frame [H] and handover location frame [L]. All relative frames in the HRH system are drawn in Figure 4. It is to be noted that all the reference frames are in Cartesian coordinates. According to the human frame [H] can be located by a tracking control based on the head_pose_estimation package [42] as mentioned previously. A human head is identified based on a personalized template by the spherical kernel using a supervised learning algorithm, namely a discriminative random regression forests (DRRF) technique. The human nose tip vector is a crucial aspect that can describe the changes of the head pose neatly. Subsequently, the nose tip frame is appropriately used as the human reference frame [H]. Then, it can be noted that the handover location frame [L] is associated with the human (nose tip) frame [H].  
The frame relationship between the object held by the robot and the human hand is the chief requirement implemented to successfully control the robot movements in the HRH tasks. The Transformation matrix has been investigated to identify the posture of the object [T] held by the HSR end-effector [A] relative to the robot reference frame [R]. It can be implied that the robot should manipulate the held object to the receiver naturally at the handover location (incorporating Equation (1)). The Transformation matrix of the handover location frame [L] relative to the robot base frame [R] can be determined based on (1) the  
Figure 3: (**a**) The dual-wheel caster-drive robot base and (**b**) the robot join configuration.  
[L] referenced by the [C] and (2) the [L] referenced via [R]. Hence, their relationship can be written as Equation (14).  
\[\frac{R}{T}T=\frac{R}{A}T\cdot\frac{A}{T}T=\frac{R}{C}T\cdot\frac{C}{H}T\cdot \frac{H}{L}T\cdot\frac{L}{T}T \tag{14}\]  
where \({}^{i}_{j}T\) denotes the coordinate transformation from the \(j\) frame relative to the \(i\) frame. The \({}^{R}_{T}T\) can be solved using the robot forward kinematics equations. The \({}^{C}_{H}T\) can be measured by the tracking system. The \({}^{C}_{C}T\) can be adopted from the robot configuration and \({}^{H}_{L}T\) can be calculated using Equation (1) conducted by the HHH experiments. Finally, the \(\frac{L}{T}T\) can be computed using the following equation:  
\[\frac{L}{T}T=\left(\begin{subarray}{c}{}^{H}_{L}T\\ \end{subarray}\right)^{-1}\cdot\left(\begin{subarray}{c}{}^{C}_{H}T\\ \end{subarray}\right)^{-1}\cdot\left(\begin{subarray}{c}{}^{R}_{C}T\\ \end{subarray}\right)^{-1}\cdot\left(\begin{subarray}{c}{}^{R}_{A}T\\ \end{subarray}\right)^{-1}\cdot\frac{R}{A}T\cdot\frac{A}{T}T \tag{15}\]  
The transformation matrix of the [L] frame relative to the [R] can be expressed by Equation (16).  
\[\frac{R}{L}T=\frac{R}{A}T\cdot\frac{A}{T}T\cdot\left(\begin{subarray}{c}{}^{L} _{T}T\\ \end{subarray}\right)^{-1} \tag{16}\]  
The relationship is subsequently implemented on the real-time hybrid PID position and impedance control of the robot compliant motions in HRH.