Mechanic Modeling and Nonlinear Optimal Control of Actively Articulated Suspension of Mobile Heavy-Duty Manipulators

Abstract

This paper presents the analytic modeling of mobile heavy-duty manipulators with actively articulated suspension and its optimal control to maximize its static and dynamic stabilization. By adopting the screw theory formalism, we consider the suspension mechanism as a rigid multibody composed of two closed kinematic chains. This mechanical modeling allows us to compute the spatial inertial parameters of the whole platform as a function of the suspension's linear actuators through the articulated-body inertia method. Our solution enhances the computation accuracy of the wheels' reaction normal forces by providing an exact solution for the center of mass and inertia tensor of the mobile manipulator. Moreover, these inertial parameters and the normal forces are used to define metrics of both static and dynamic stability of the mobile manipulator and formulate a nonlinear programming problem that optimizes such metrics to generate an optimal stability motion that prevents the platform's overturning, such optimal position of the actuator is tracked with a state-feedback hydraulic valve control. We demonstrate our method's efficiency in terms of C++ computational speed, accuracy and performance improvement by simulating a 7 degrees-of-freedom heavy-duty parallel-serial mobile manipulator with four wheels and actively articulated suspension.

Figures (11)

• Figure 1: Heavy-duty mobile manipulator. This consists of a heavy-duty parallel-serial manipulator mounted on top of a wheeled mobile platform with actively articulated suspension powered by linear actuators.
• Figure 2: Graphical representation of the topological structure.
• Figure 3: Snapshots of the mobile platform with articulated suspension. From left to right, the side view, top view, and chassis with wheels. The inertial reference frame of the world is represented by $\Sigma_{w}$ and the chassis reference frame by $\Sigma_{c}$. The manipulator reference frame $\Sigma_{m}$ and the base frame $\Sigma_{fb}$ are fixed to the base rigid body in red. The wheels' reference frames are depicted by $\Sigma_{wFR}$, $\Sigma_{wFL}$, $\Sigma_{wRR}$, and $\Sigma_{wRL}$.
• Figure 4: Geometry of the articulated suspension with linear actuator. This one-DOF closed kinematic chain can be locally analyzed in $SE(2)$, i.e. plane $x \!\cdot\! z$, and it is articulated by three passive rotational joints placed at reference frames $\Sigma_{\!B1}$, $\Sigma_{\!B3}$ and $\Sigma_{\!Tc}$, and a linearly actuated one at $\Sigma_{\!B4}$ which is powered by a hydraulic valve system.
• Figure 5: Wheels normal forces. Simscape is used as ground truth while variable and fixed inertial-parameters analytic solutions are depicted.