Symbolic derivation of governing equations for dual-arm mobile manipulators used in fruit-picking and the pruning of tall trees

• Motion equations of dual-arm mobile robotic manipulators are derived.
• To avoid Lagrange multipliers, the approach of Gibbs–Appell formulation is applied.
• All mathematical operations are done by only 3 × 3 and 3 × 1 matrices.
• All non-holonomic constraints including no-slipping and no-skidding are considered.
• A recursive formulation is developed to delete the role of manual derivation.

Mobile manipulators with only a single robotic arm have been successfully exploited in many agricultural tasks. The performance of these kinds of robotic systems has been improved by adding another robotic arm. However, for some agricultural applications such as pruning and fruit picking from tall trees, the number of links of each robotic arm should increase so that the arm can reach the target. The increase in the number of links and dynamic interactions between the manipulator and the mobile platform as well as the nonholonomic constraints of the mobile base make the manual derivation of motion equations almost impossible. So, this paper proposes a new solution to the problem of dynamic modeling of wheeled mobile manipulators with dual arms in an automatic and systematic approach. To avoid computing the “Lagrange multipliers” associated with the nonholonomic constraints, the equations of motion are derived according to the recursive Gibbs–Appell formulation. Also all the mathematical operations are performed by 3 × 3 and 3 × 1 matrices which are more efficient compared with the 4 × 4 and 4 × 1 ones. Finally, this method is applied to a mobile manipulator with two robotic arms to demonstrate the ability of the proposed method in deriving the equations of motion for such complex systems.