This paper addresses a constrained motion planning problem for mobile manipulators. The constraints are included into the system model by means of a sort of penalty function, and then processed in accordance with the endogenous configuration space approach. Main novelty of this paper lies in deriving a constrained Jacobian motion planning algorithm with the following features: inequality constraints are included into an extended kinematics model using a smooth approximation of the plus function, the model is then regularized against singularities, and the resulting imbalance in error equations is handled as a perturbation of an exponentially stable linear dynamic system. The operation of the constrained motion planning algorithm is illustrated by a motion planning problem of a mobile manipulator with bounds imposed on a platform variable. Performance of the algorithm is tested by computer simulations.