Modern robots are required to operate in complex environments and perform diverse tasks, resulting in redundant degrees of freedom (DoF) for flexibility. However, managing redundancy is challenging due to the high-dimensional and non-convex nature of robotic kinematics. When executing complex tracking tasks, redundant robots must handle non-convex constraints while maintaining many objectives, such as balancing and obstacle avoidance. This paper models the pathwise inverse kinematics of redundant mechanisms as a multi-objective nonlinear optimization problem. We propose an efficient gradient-free optimization method named MoeIK, which demonstrates strong multi-objective balance, rapid global convergence, and adaptability. Our approach enhances the method by integrating relaxation dominance, adaptive interval search strategies, and a restart strategy, significantly improving performance in overcoming many-objective optimization challenges. We compared MoeIK with RelaxedIK, Trac-IK, and BioIK across multiple trajectories on various redundant robots, and the experimental results demonstrate that our algorithm exhibits better multi-objective balance capabilities and supports real-time computation.

Energy sharing among modular robots enables sustainable operation of the system by maintaining energy balance among the modules. In this paper, we propose a novel energy sharing mechanism for FreeSN, a modular self-reconfigurable robot consisting of node and strut modules. Utilizing the feature that our modules are connected in a face-to-face manner, our method successfully establishes an energy sharing channel at almost any point on a sphere by placing transmission intermediaries at the interfacing face between modules, which is facilitated by the combination of brush contact and shell decomposition. Such mechanism also allows the utilization of the node module’s inner space for extra energy storage. A prototype of this energy sharing system has been implemented on FreeSN and rigorously tested. Our findings indicate that energy sharing is reliably established between modules; for strut modules positioned randomly on a node module’s surface, the probability of forming a valid connection is 56.6%. With orientation adjustment, a connection is achievable at nearly any position on the sphere, barring a few exceptional points. As a result, the operational endurance of the strut modules, which provide all the driving forces in the system, is markedly enhanced. This technique also holds potential for broader application across other freeform robotic platforms that incorporate conductive spherical surfaces for sliding connections.

The redundant manipulators' analytical solutions can be obtained by the parameterization method. Multiple parameterized joints and their corresponding parametric representations exist for a redundant manipulator. However, how to select the optimal parameterized joints has yet to be well-addressed. This paper delves into the mechanism of the parameterization method and proposes a method to select the optimal parametric representations to improve the motion planning performance of manipulators. We tested the proposed method on an 8-degree-of-freedom (DOF) manipulator. First, all feasible parametric representations are derived, followed by an approach to obtain solution manifolds. We then introduce a metric called the “feasible rate,” which characterizes the percentage of the solution manifold in the joint space. This metric is used to rapidly assess the influence of different parameterized joints on the manipulator's motion planning performance. To verify the proposed method's correctness, we evaluated the performance of different representations with the MOEA/D algorithm in solving the same path optimization problems based on the algorithm running time and overall motion magnitude of the manipulator. Our simulation results demonstrate that different selections of parameterized joints affect the motion planning performance, and the performance planned by the optimal parametric representation is up to four times greater than that of the worst one.

In this paper, a new method is proposed to solve the inverse kinematics problem of redundant manipulators. This method demonstrates superior performance on continuous motion by combining interval search genetic algorithm based on trajectory which we propose with parametric joint angle method. In this method, population continuity strategy is utilized to improve search speed and reduce evolutionary generation, interval search strategy is introduced to enhance the search ability and overcome the influence of singularity, and reference point strategy is used to avoid sudden changes of joint variables. By introducing those three strategies, this method is especially suitable for redundant manipulators that perform continuous motion. It can not only obtain solutions of inverse kinematics quickly, but also ensure the motion continuity of manipulator and accuracy of the end effector. Moreover, this algorithm can also perform multi-objective tasks by adjusting the fitness function. Finally, this algorithm is applied to an 8 degree of freedom tunnel shotcrete robot. Field experiments and data analysis show that the algorithm can solve the problem quickly in industrial field, and ensure the motion continuity and accuracy.