Virtual links and virtual joints can be appended to the kinematic chain of a robot arm to assist in modelling and control of certain tasks. Activities such as spray painting, sand blasting, or scanning with a laser or camera can be enhanced by modelling the fluid stream, light beam, or field of view using a virtual link. Virtual joints can be used to allow movement in semi-redundant degrees of freedom of the task space. This can can be exploited to optimize the control of the real robot. A prudent choice is to minimize the effort required by the manipulator to execute the task. This often requires the inversion of the inertia matrix. However, virtual links have no inertia so the inverse does not exist. This paper first explores methods of adding virtual mass or modifying the inertia matrix to allow inversion and the consequences. Then an optimal control problem is proposed that minimizes kinetic energy in the real manipulator and maximizes use of the virtual joints. In doing so, we only need the real inertia matrix which is always invertible. The method is validated in a case study for high pressure water blasting. It is shown to reduce the dynamic torque norm compared to a minimum velocity controller.

This article proposes a predictive end-effector control method for manipulators operating on mobile platforms subjected to unwanted base motion. Time series is used to forecast the base motion using historical state information. Then, a trajectory specified in the inertial frame is transformed to a predicted trajectory with respect to the manipulator. By tracking this transformed trajectory, the manipulator negates the base motion. A model-predictive control problem is formulated via quadratic programming (QP) to track said trajectory over the prediction horizon. Only the first control action in the control sequence is constrained by kinematic feasibility. In this manner, QP can be swiftly solved with linear inequality constraints. It is shown that the actual joint trajectory executed by the manipulator is always kinematically feasible. Moreover, tracking error can still be reduced despite future predicted control actions being infeasible. The method is validated through both simulation and experiment. The proposed method can reduce pose error by over 60% compared to a proportional–integral feedback controller.

Autonomous Underwater Vehicle-Manipulator Systems (AUVMS) operating in shallow waters or near-surface environments may be exposed to wave disturbances which will cause undesired motion of the end effector. This paper presents a method to maneuver the manipulator joints and counteract undesired motion of the vehicle body, in order to maintain a steady end-effector position in the inertial frame. An Autoregressive (AR) model is used to predict vehicle motion, and then combined with Model Predictive Control (MPC) to optimize joint motion. Simulation was conducted using real data to verify the efficacy of this method.