Kinematic control of nonholonomic mobile manipulators in the presence of steering wheels

Abstract

Abstract-We consider the kinematic control problem for nonholonomic mobile manipulators (NMMs) whose base contains steering wheels. For all typical tasks, the steering velocity inputs of such systems do not appear in the differential relationship between the first-order time derivative of the task output and the available NMM inputs. As a consequence, these inputs are not used by velocity-level control laws based on simple (pseudo)inversion of the task Jacobian, leading in general to the impossibility of completing the task. We propose two control solutions to this open problem based on the framework of input-output feedback linearization. First, a static feedback law is presented that defines the unspecified steering velocities via an optimization action in the null space of the task Jacobian. A dynamic feedback law is then proposed based on the input-output differential map obtained by considering the task acceleration. In this case, the velocity of the steering wheels becomes an active input for task execution, together with the manipulator joint accelerations and the driving accelerations of the base. The feasibility and performance of the two kinematic controllers are compared in simulation for a car-like base carrying a planar manipulator.

Modeling and control of a quadrotor UAV with tilting propellers

“…It is interesting to note that this inhomogeneity in the differential levels at which inputs are affecting the output dynamics is not a specificity of the system at hand. As an example, the same structural property is also present in other robotic structures such as mobile manipulators with steering wheels [19] where the role of w α is played by the wheel steering velocities.…”

“…6(a) shows the superimposition of H(w) when including z (red dashed line, case (i)) and not including z (blue solid line, case (ii)). It is clear that, in the latter case, H(w) attains a lower value over time thanks to the optimization action in (19). As a consequence, this results in a lower value for w over time as depicted in Fig.…”

“…II. The aim is twofold: on one side, we want to highlight the tracking capabilities of the proposed controller and the beneficial action of the null-space term (19) in avoiding singularities for matrix A. On the other side, we also want to test the robustness of the controller against all the inertial/gyroscopic effects neglected at the control design stage but included in the quadrotor dynamic model (1)- (3)- (6).…”

“…Each vertex was associated with the Note the large reorientation of the propeller groups in this latter case thanks to the action of the optimization term (19) following desired positions and orientations Figure 8 shows a series of snapshots illustrating the overall motion, while Figs. 9(a-d) show the desired trajectory (p d (t), η d (t)), and the tracking errors (e p (t), e R (t)).…”

Robust control of underactuated wheeled mobile manipulators using GPI disturbance observers

“…Bayle et al [9] [10] solved the kinematic control of mobile manipulators, and avoided singularities and maximized the arm manipulability by using a pseudo-inversion scheme to coordinate the evolution of the mobile platform and the robot arm. De Luca et al [11] studied the kinematic control problem for nonholonomic mobile manipulators in the presence of steering wheels. Liu and Goldenberg [12] used robust damping control (RDC) for the motion control of mobile manipulators with kinematics constraints and in the presence of unknown bounded disturbances.…”