A Comparison of Damped Least Squares Algorithms for Inverse Kinematics of Robot Manipulators

Vito, Daniele Di; Natale, Ciro; Antonelli, Gianluca

doi:10.1016/j.ifacol.2017.08.1209

Cited by 30 publications

(5 citation statements)

References 16 publications

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“…The weighted control signal in (31) not only allows for energy efficiency and attenuates controller oscillations, but also renders the Hessian matrix positivedefinite. The result is similar to regularization [61], which is used to avoid kinematic singularity. We will verify that the incremental control structure exhibits superior control performance in terms of parameter adjustment.…”

Section: ) Strengths Of Himpcmentioning

confidence: 91%

“…To guarantee tracking accuracy, we need to scale the term τ k+j|k Ri to be roughly the same size to the tracking error term e( x i,k+j+1|k ) Qi . Thus, R i should be tuned manually according to the target trajectory [61], and R i should be readjusted when the reference trajectory changes. This is the main limitation of the regularization method.…”

Section: ) Strengths Of Himpcmentioning

confidence: 99%

See 1 more Smart Citation

Hierarchical Incremental MPC for Redundant Robots: A Robust and Singularity-Free Approach

Wang,

Liu,

Leibold

et al. 2024

IEEE Trans. Robot.

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Section: ) Strengths Of Himpcmentioning

confidence: 91%

Section: ) Strengths Of Himpcmentioning

confidence: 99%

Hierarchical Incremental MPC for Redundant Robots: A Robust and Singularity-Free Approach

Wang,

Liu,

Leibold

et al. 2024

IEEE Trans. Robot.

View full text Add to dashboard Cite

“…For example, the damping factor of the Gaussian distribution with a singularity as the expected value is used so that the damping term is small when it is far away from the singularity and has no significant impact on the entire approximation process. 6,7 The other most commonly used method is to determine the scope of the damping factor by defining a singular region so that the exact solution can be calculated using the normal method without having to solve the approximate value and the error in the non-singular region can be reduced. 8,9 When changing the adaptive damping factor, it is necessary to find an optimal value, which is known as the optimal damping factor and affects the performance and efficiency of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

Singularity avoidance method for dual-arm closed-chain system based on damped least squares

Zhang,

Liu,

Chai

et al. 2023

International Journal of Advanced Robotic Systems

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When two manipulators cooperate to clamp a rigid object, a closed chain with both ends fixed is formed. The singularity of a single manipulator causes the closed chain to be at a singularity, which results in uncertainty in the velocity mapping between the terminal and joint space. This study proposes a closed-chain singularity processing method for dual-arm collaboration, adopting the Jacobian pseudoinverse method based on damped least squares to obtain an approximate solution. During the solution process, the adaptive damping factor is improved by cubic polynomials, and the optimal damping factor is determined by quadratic sequence programming. Furthermore, this study analyzes the kinematic constraints of the closed-chain system and constructs a closed-chain Jacobian to judge whether the system is in a singular region. Finally, the effectiveness of the proposed method is verified through simulations.

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“…However, the GPM may lead to joint singularity or joint position limits while avoiding obstacles; thus the manipulator will fail to track the desired trajectory. The damped least-squares method (DLS) [ 10 ] and weighted least-norm methods (WLN) [ 11 ] are introduced to solve the problem. Combined with DSL and WLN, Zhang [ 12 ] presented an improved weighted gradient projection method (IWGPM), in which the manipulator can handle joint singularity and joint position limits, but it increases the tracking error.…”

Section: Introductionmentioning

confidence: 99%

Reinforcement Learning-Based Reactive Obstacle Avoidance Method for Redundant Manipulators

Shen

Jia

Huang

et al. 2022

Entropy

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Redundant manipulators are widely used in fields such as human-robot collaboration due to their good flexibility. To ensure efficiency and safety, the manipulator is required to avoid obstacles while tracking a desired trajectory in many tasks. Conventional methods for obstacle avoidance of redundant manipulators may encounter joint singularity or exceed joint position limits while tracking the desired trajectory. By integrating deep reinforcement learning into the gradient projection method, a reactive obstacle avoidance method for redundant manipulators is proposed. We establish a general DRL framework for obstacle avoidance, and then a reinforcement learning agent is applied to learn motion in the null space of the redundant manipulator Jacobian matrix. The reward function of reinforcement learning is redesigned to handle multiple constraints automatically. Specifically, the manipulability index is introduced into the reward function, and thus the manipulator can maintain high manipulability to avoid joint singularity while executing tasks. To show the effectiveness of the proposed method, the simulation of 4 degrees of planar manipulator freedom is given. Compared with the gradient projection method, the proposed method outperforms in a success rate of obstacles avoidance, average manipulability, and time efficiency.

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A Comparison of Damped Least Squares Algorithms for Inverse Kinematics of Robot Manipulators

Cited by 30 publications

References 16 publications

Hierarchical Incremental MPC for Redundant Robots: A Robust and Singularity-Free Approach

Hierarchical Incremental MPC for Redundant Robots: A Robust and Singularity-Free Approach

Singularity avoidance method for dual-arm closed-chain system based on damped least squares

Reinforcement Learning-Based Reactive Obstacle Avoidance Method for Redundant Manipulators

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