Due to the complexity in unstructured environments (e.g., rescue response and forestry logging), more hydraulic manipulators are equipped with redundant joints to improve their motion flexibility. In addition to considering joint limit constraint and maneuverability optimization like electrically driven manipulators, hydraulic manipulators have to consider flow optimization aiming at energy saving and flow anti-saturation for redundancy resolution, since multiple joints are supplied by one pump. Ortiz Morales et al. addressed the joint-limited minimum-time redundancy resolution of hydraulic manipulators. Löfgren studied redundancy resolution which maximizes load capacity. Beiner et al.&nbsp;proposed a pseudo-inverse method for redundancy resolution to minimize the cylinder velocity norm. But none of them are optimized for flow consumption. Nurmi et al. derived an algorithm using dynamic programming for global energy optimization of a redundant manipulator, but it cannot be used for real-time control due to its time-consuming calculations. Cheng et al. used the gradient projection method (GPM) with the system flow as the objective function for redundancy resolution and obtained a solution with less flow consumption without affecting the task. However, it has the problem of excessive acceleration at joint limit positions.Therefore, this paper proposes a redundancy resolution method combining the gradient projection method with a weighted Jacobian matrix (GPM-WJM). The solution consists of two parts: special solution (the weighted least-norm solution) and general solution (the projection of the optimization index in the null space of the weighted task Jacobian matrix). When the operator or computer gives the desired endpoint velocity, the algorithm will adjust the weight matrix according to the joint limit avoidance index, so that the manipulator can meet the joint limit constraint while tracking the command velocity. Then the gradients of demand flow and manipulability optimization are projected to the null space of the weighted task Jacobian matrix, to reduce the system flow demand and increase the dexterity without affecting the velocity tracking and joint limit avoidance tasks. Since the weighted least squares method uses the Lagrange multiplier method to solve the joint velocity, its first goal is to achieve the velocity tracking task (minimize the tracking error), and its second goal is to meet the joint limit task (minimize the weighted velocity norm). Therefore, the GPM-WJM can achieve three task priority divisions on a manipulator with only one degree of redundancy, so that the manipulator can meet the joint limit constraints while performing velocity tracking tasks and make full use of redundancy to optimize performance without affecting the basic tasks.To verify the effectiveness of the GPM-WJM, a 3-DOF hydraulic manipulator simulation model is established in Matlab/Simulink environment. Two existing redundancy resolution algorithms, the GPM and weighted least-norm method (WLNM) are taken as comparisons respectively to complete the task of drawing a circle on the yoz plane. The endpoint trajectories, system flow, and joint position of each simulation are recorded. The simulation results show that the endpoint trajectories of the three algorithms are identical. The average system flow (ASF) rates are 12.15L/min (WLNM), 10.63L/min (GPM), and 10.88L/min (GPM-WJM), respectively. Their maximum system flow rates are 19.59L/min, 22.39L/min, and 18.78L/min, respectively. Their maximum accelerations are 33.65°/s2, 343.8°/s2, and 68.35°/s2, respectively. The result shows that compared with WLNM, the ASF of GPM is reduced by 10.45%, and the ASF of GPM-WJM is reduced by 12.5%. Although the flow optimization effect of GPM-WJM is reduced compared with GPM, the maximum flow and maximum acceleration of GPM-WJM are also reduced. That is, the flow fluctuation of GPM-WJM is smaller and its joint movement is more stable, which will help improve the position accuracy of the manipulator in practice. In addition, GPM-WJM can realize real-time calculation within 10 ms with a common computer configuration. Therefore, the proposed method can meet the constraints of joint limit without affecting the endpoint trajectory, and utilize the remaining redundancy to optimize the flow consumption and manipulability.

Real-Time Flow Optimization of Hydraulic Manipulator with One Degree of Redundancy Considering Joint Limit Constraint

Paper Proceedings: https://asmedigitalcollection.asme.org/FPST/FPMC2021/volume/85239

2021 ASME/BATH Symposium on Fluid Power and Motion Control (FPMC2021)

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