## 5 Simulation Results and Validation  
The SNOPT [35] was used to solve the optimization problem with the sequential quadratic programming algorithm. SNOPT has four solvers; the solver NPOPT was used in this study to solve the dense nonlinear optimization problem [35]. By following the flowchart in Figure 3, the simulation results were obtained by solving the subtask-based optimization problem based on the input data from experiments (mean values from all subjects). Figure 4 shows the resulting optimal delivery motion snapshots. Figure 5 shows the comparison of the joint angle profiles from the subtask-based optimization formulation with the experimental results. The joint torque profiles are shown in Figure 6. Table 2 lists the total number of design variables, constraints, and Central Processing Unit (CPU) times for the subtask-based approach. A laptop computer with an Intel(R) Core(TM) i5-1035G4 [EMAIL_ADDRESS] GHz and 8 GB RAM was used to solve the optimization problem. Table 3 lists the root-mean-square-error (RMSE) and Pearson's correlation coefficient (r) for comparing the predicted and experimental joint angle profiles.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Lift/Unload** & **Carry** & **Transition** \\ \hline
1. Joint angle limits Equation (10) & \(\surd\) & \(\surd\) & \(\surd\) \\
2. Joint torque limits Equation (11) & \(\surd\) & \(\surd\) & \(\surd\) \\
3. Foot contacting position Equation (12) & \(\surd\) & \(\surd\) & \(\surd\) \\
4. Foot ground penetration Equation (13) & \(\surd\) & \(\surd\) & \(\surd\) \\
5. Dynamic balance Equation (14) & \(\surd\) & \(\surd\) & \(\surd\) \\
6. Body collision avoidance Equation (15) & \(\surd\) & \(\surd\) & \(\surd\) \\
7. Boundary conditions from experiments Equation (16) & \(\surd\) & & \\
8. Knee flexion Equation (17) & & \(\surd\) & \(\surd\) \\
9. Upper body constraints for carrying Equation (18) & & \(\surd\) & \\
10. Upper body continuity conditions and lower body & & \(\surd\) & \\ symmetric conditions Equations (19)–(21) & & & \\
11. Boundary conditions from other subtasks Equation (22) & & & \(\surd\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Constraints for subtasks.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Subtask-Based Approach**} \\ \cline{2-7}  & **Lift** & **Transition 1** & **Carry** & **Transition 2** & **Unload** \\ \hline Number of design variables & 56 & 86 & 86 & 86 & 56 \\ Number of control points for each DOF & 4 & 6 & 6 & 6 & 4 \\ Number of constraints & 217 & 526 & 783 & 526 & 217 \\ CPU time (s) & 0.99 & 0.62 & 2.39 & 0.79 & 1.92 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Optimization information for subtask-based approach.  
Figure 4: Predicted optimal delivery motion snapshots for a 10.16 Kg box.  
Figure 5: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **Spine** & **Shoulder** & **Elbow** & **Right Hip** & **Right Knee** \\ \hline \multirow{3}{*}{Subtask-based method} & RMSE & 13.02 & 14.00 & 14.86 & 14.50 & 17.05 \\  & & (4.68) & (5.86) & (5.93) & (2.17) & (3.86) \\ \cline{2-7}  & & 0.90 & 0.90 & 0.68 & 0.81 & 0.73 \\ \cline{2-7}  & r & (0.06) & (0.07) & (0.41) & (0.10) & (0.12) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Root-mean-square-error (RMSE) and Pearson correlation coefficient (r) averaged across 18 subjects; values are represented as mean (standard deviation).  
Figure 5: Joint angle profiles for deliver motion: (**a**) spine, (**b**) shoulder, (**c**) elbow, (**d**) right hip, and (**e**) right knee.