The aim of this paper is the formulation and numerical solution for finding the maximum dynamic load of mobile manipulators for a given two-end-point task. In fixed-base classical robots, the maximum allowable load is limited mainly by their joint actuator capacity constraints. However, besides actuator capacity constraints, kinematic redundancy and nonholonomic constraints should be considered for finding maximum dynamic payload of mobile manipulators, both of which arise from base mobility. The extended Jacobian matrix concept is used to solve the redundancy resolution and non-holonomic constraints. The problem is formulated as a trajectory optimisation problem, which fundamentally is a constrained nonlinear optimisation problem. Then, the iterative linear programming (ILP) method is utilised to solve the optimisation problem. Finally, by a numerical example involving a two-link manipulator mounted on a differentially driven wheeled base, use of the method is presented and the results are discussed.
SUMMARYThis paper presents a new formulation as well as numerical solution for the problem of finding a point-to-point trajectory with maximum load carrying capacities for flexible manipulators. For rigid manipulators, the major limiting factor in determining the maximum allowable load (mass and mass moment of inertia) is the joint actuator capacity, while the flexibility exhibited by light weight robots or by robots operating at a higher speed dictates the need for an additional constraint to be imposed for situations where precision tracking is required, that is, the allowable deformation at the end effector. The Lagrangian assumed mode method was used to model the manipulator and load dynamics, including both joint and deflection motions. An Iterative Linear Programming (ILP) method is then used to determine the maximum allowable load of elastic robot subject to both constraints, while a general computational procedure for the multiple-link case given arbitrary trajectories is presented in detail. Symbolic derivation and simulation by using a PC-based symbolic language MATHEMATICA庐 was carried out for a two-link planer robot and the results further confirm the necessity of the dual constraints.Rough joint flexibility is the dominant source of compliance in today's commercial robots in future robots containing light weight flexible arms link flexibility may become most important. Hence this paper stresses link flexibility rather than joint flexibility.
A computational technique for obtaining the maximum load-carrying capacity of robotic manipulators with joint elasticity is described while different base positions are considered. The maximum load-carrying capacity which can be achieved by a robotic manipulator during a given trajectory is limited by a number of factors. Probably the most important factors are the actuator limitations, joint elasticity (transmissions, reducers and servo drive system) and relative configuration of the robot with respect to its base. Therefore, both actuator torque capacity constraint considering typical torque-speed characteristics of DC motors and trajectory accuracy constraints considering a series of spherical bounds centred at each desired trajectory are applied as the main constraints. For the desired trajectory of load, different base locations are considered. It is seen that the load-carrying capacity at different base positions is different due to distinct dynamic effects of links and load motions on joint actuators. Then, a general computational algorithm for a multi-link case on a given trajectory and different base location is laid out in detail. Finally, two numerical examples involving a two-link manipulator and a PUMA robot using the method are presented. The obtained results illustrate the effect of base location, dual actuator torque and end effector precision constraints on load-carrying capacity on a given trajectory.
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