ABSTRACT
Motion planning of mobile manipulators is concerned with obtaining open
loop controls that steer the system from an initial configuration to a final
one, without violating nonholonomic constraints or collision avoidance con-
straints. Moving mobile manipulator systems presents many unique problems
that are due to the coupling of holonomic manipulators with nonholonomic
platforms. The path planning for a mobile manipulator accomplishing a se-
quence of coordination and manipulation tasks is formulated in [121] as a
nonlinear optimization problem with state boundary equality constraints and
a general cost function, which was solved using a stochastic algorithm of a
simulated annealing. Motion planning of mobile manipulators to execute mul-
of Mobile
tiple tasks consisting of a sequence of pre-specified trajectory in a fixed world
frame [122] is formulated as a global optimization problem and simultaneously
obtains the motion trajectory set and commutation configurations. A general
approach based on the calculus of variations was proposed for motion planning
for nonholonomic cooperating mobile robots to obtain optimal trajectories and
optimal actuator forces/torques in the presence of obstacles [123] such that
geometric constraints, kinematic constraints, and dynamic constraints can be
easily incorporated into the planning scheme. Navigating a mobile manipula-
tor among obstacles had been studied in [124] by simultaneously considering
the obstacle avoidance and the coordination. The developed control allows the
system to retain optimal or sub-optimal configurations while the manipulator
avoids obstacles using potential functions. In approach, it was assumed that
only the manipulator may encounter the obstacle, while in the same study
[125], the obstacle avoidance by the entire mobile manipulator system was
considered and the proposed nonholonomic motion planner is based on a dis-
continuous feedback law under the influence of a potential field. Motion plan-
ning applicable to handling deformable material by multiple nonholonomic
mobile manipulators was described in the obstacles environment [126], which
is based on a new class of nonsmooth Lyapunov functions and an extension
of the navigation function. The dipolar inverse Lyapunov functions and po-
tential field technique using diffeomorphic transformations were introduced
for nonholonomic control. The standard definition of manipulability was gen-
eralized to the case of mobile manipulators in [63], and the optimization of
criteria inherited from manipulability considerations was given to generate the
controls of the system when its end effector motion was imposed. Path plan-
ning of nonholonomic mobile platforms with manipulators in the presence
of obstacles was developed in [127], which employs smooth and continuous
functions such as polynomials and is based on mapping the nonholonomic
constraint to a space where it can be satisfied trivially. Motion planning for a
mobile manipulator with end-effector along a given path was developed by the
randomized generation of configurations that are compatible with the end ef-
fector path constraint [128]. A modular fuzzy navigation method and a robust
control in unstructured environments were developed for the navigation and
control of mobile manipulators by using fuzzy reactive motion planning and
robust adaptive control [129]. The probabilistic road map and the fuzzy reac-
tive planner based on elastic band for the vehicle platform to avoid unknown
static/dynamic obstacles are also presented [129].
