Point-to-Point Collision-Free Trajectory Planning for Mobile Manipulators

Abstract

The collision-free trajectory planning method subject to control constraints for mobile manipulators is presented. The robot task is to move from the current configuration to a given final position in the workspace. The motions are planned in order to maximise an instantaneous manipulability measure to avoid manipulator singularities. Inequality constraints on state variables i.e. collision avoidance conditions and mechanical constraints are taken into consideration. The collision avoidance is accomplished by local perturbation of the mobile manipulator motion in the obstacles neighbourhood. The fulfilment of mechanical constraints is ensured by using a penalty function approach. The proposed method guarantees satisfying control limitations resulting from capabilities of robot actuators by applying the trajectory scaling approach. Nonholonomic constraints in a Pfaffian form are explicitly incorporated into the control algorithm. A computer example involving a mobile manipulator consisting of nonholonomic platform (2,0) class and 3DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.

Tracking the Kinematically Optimal Trajectories by Mobile Manipulators

“…In the further analysis, useful properties of both dynamic equations (5) and kinematic mapping (10) are summarised that will be applied while designing the controller. In the case of revolute kinematic pairs of the holonomic manipulator, the following inequalities hold true:…”

“…The first approach is the extended or augmented task space formulation (including also input-output linearization techniques) of the inverse kinematics problem showed in works [2][3][4][5][6][7][8][9][10][11][12][13][14]. Extending the dimension of the task space by incorporating as many additional constraints as the degree of the redundancy is the essence of it.…”

“…The control formulations based on the augmented task space technique have some disadvantages. The controllers proposed in [2][3][4][5][6][7][8][9][10][11] require inverse of the extended Jacobian matrix that can potentially consist of algorithmic and/or kinematic singularities [15] and as a consequence, can produce the control inputs to become unbounded even though the mobile manipulator is not in a singular configuration. Rigorous definitions of singularity for mobile manipulators have been proposed in works [46,47], which introduce the traditional concept of singularity built on the definition of the extended Jacobian and the concepts of posture and configuration singularity.…”

“…Moreover, the dimensionality of the inverse kinematics problem associated with an extended Jacobian increases. Furthermore, control algorithms from [2][3][4][5][6][7][8][9][10][11] require full knowledge of the dynamic equations. The controllers offered in [12][13][14] need the knowledge of both holonomic end-effector and platform desired trajectories and are not optimal in any sense.…”

Real-Time Trajectory Generation Methods for Cooperating Mobile Manipulators Subject to State and Control Constraints

“…The proposed solutions are the development of the method discussed in [21] and shows that an approach for a single mobile manipulator can be easily adopted to the cooperative task of two mobile robots. In the first method, the trajectory generation problem is solved by using the leader-follower conception.…”