# Contingent Task and Motion Planning under Uncertainty for Human-Robot Interactions
## 8 Empirical Results and Discussion  
This section describes some manipulation problem solved using the proposed framework, and the implementation issues. The mobile robot considered is _TIAGo_. It has 7 degrees of freedom arm, equipped with a gripper, mounted on a mobile platform through a lift torso. The executive simulated result of the manipulation problem represented in Figure 4, called _Problem-1_, is shown in Figure 6. For the domain of the problem, a number of actions is considered for the robot being _transit_, _transfer_, _open_, and _push_ along with some actions for an operator that are _humanTransfer_ and _humanOpen_. Actions are selected according to the planning mechanism in terms of symbolic and geometric reasoning. We assume that the values of the uncertainty information are provided in run-time in simulation. Therefore, the executive plan is provided below:  
_Executive Plan:_ { _Transit-B_, _CheckContainer-Box1-Open (False)_, _HumanOpen-Box1_, _Transfer-B-Box1_, _Transit-A_, _SenseColor-A-Red (True)_, _Transfer-A-RedTray_ }  
The states represented in the figure are classified as follows:  
1. is the initial belief state of the robot and environment. 2. is the state where the robot applies _transit_ action to reach cylinder B. 3. is the state where the sensing action _CheckContainer-Box1-Open_ showed that Box 1 is currently closed. 4. is the state where the _HumanOpen_ action is executed as the robot is not capable enough to open the box. 5. is the state where the robot places cylinder B within box 1. 6. is the state where the robot transits to cylinder A. 7. is the state where the sensing action _SenseColor-A-Red_ showed that the cylinder is actually red. 8. is the state where the robot moves its base and the arm configuration to place cylinder A over the red tray. In addition, the proposal has been evaluated for other cluttered problems where the robot needs to sort objects according to the colors. Regarding the action domain, Robot actions are _transit_ and _transfer_, and the action template _humanTransfer_ is considered for an operator. The problem represented in Figure 7, called _Problem-2_, shows the initial and goal states of manipulation where the green and red objects must be located on the green and red regions respectively. The red object is not initially located on the table. The pink region is considered on the robot workspace where an operator can transfer objects. The planning uncertainties are the color of the green object which could be actually green or red and the location of the red object which could be on the robot table or in the human workspace. Therefore, the _humanTransfer_ action is applied to transfer the object to the robot workspace as the robot is not allowed to move to the human workspace. The final executable plan would be to transfer the green object to the target placement region by the robot. It then looks for the red object and figures out the object is not located on the table and asks an operator to transfer the object. The _humanTransfer_ action is selected in the conditional plan, so the requested object is transferred to the robot workspace. The operator updates the robot knowledge through the robot system terminal. The robot is aware that the human action has been successfully performed, and afterwards it travels to grasp the object. Eventually, the robot transfers the object to the target region. The proposed approach has been tested for similar problems by increasing the number of objects and varying color and/or location uncertainties. The problems performance are represented in Table 1 in terms of conditional and executive plan length, and moreover planning time. _Problems-3_ includes a cluttered problem where there are nine objects and three of them need to be sorted. Similar uncertainty of _Problem-2_ is considered regarding the color and location of objects.