Sub-optimal trajectory planning for mobile manipulators

Abstract

SUMMARYThis paper presents a method of planning a sub-optimal trajectory for a mobile manipulator subject to mechanical and control constraints. The path of the end-effector is defined as a curve that can be parameterised by any scaling parameter—the reference trajectory of a mobile platform is not needed. Constraints connected with the existence of mechanical limits for a given manipulator configuration, collision avoidance conditions and control constraints are considered. Nonholonomic constraints in a Pfaffian form are explicitly incorporated to the control algorithm. To avoid manipulator singularities, the motion of the robot is planned in order to maximise the manipulability measure.

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

“…As it has been shown in [23], the full rank of the matrix J R depends on the rank of the Jacobian matrix of a holonomic manipulator, a full rank of this matrix is a consequence of maximising the manipulability measure (9). The results of simulations presented in Section 4 show that the application of the proposed method leads to an increase of the holonomic manipulability measure during the task accomplishment.…”

“…It is based on the trajectory planning methods for mobile manipulators tracking an end-effector path described in [22,23].…”

“…For this purpose, the task of searching minimum of the performance index (10) with constraints (3) and (4) should to be solved. Following the method presented in the work [24] for stationary manipulators, the necessary conditions for minimum of function (10) with equality constraints (3) and (4) have been derived for a mobile manipulator in [23] and they take the following form:…”

“…In order to find a point-to-point trajectory of the mobile manipulator, based on the solution presented in [23] and using the transversality conditions (11), the mapping E (q,q) is introduced:…”

Planning of Collision-Free Trajectory for Mobile Manipulators

“…The approach is to use penalty functions (interior or exterior), presented in Fiacco and McCormic (1968), Findeisen et al (1977), which cause the inequality constraints to be satisfied, but the performance index (9) to be somewhat increased. The approach presented herein is the explication of the trajectory planning method described in Galicki (1998), Pająk and Galicki (1999), Pająk and Galicki (2000), Pająk and Pająk (2009).…”