robot kinematics

This work proposes a novel framework for inverse kinematics (IK) optimization that addresses the high failure rates commonly caused by the nonlinear relationship between joint variables and end-effector poses, as well as non-convex constraints such as obstacle avoidance. By introducing analytical IK solutions as a change of variables within the optimization process, the method uniquely combines the precision of analytical approaches with the flexibility of numerical optimization, substantially simplifying the problem structure. Evaluated across three mainstream optimizers, the approach demonstrates significantly higher success rates than conventional optimization techniques and baseline methods in complex tasks—including obstacle avoidance, grasp selection, and humanoid robot stability—thereby achieving an effective unification of analytical and optimization-based IK strategies.

This work addresses the challenge of globally characterizing the geometric structure of solution manifolds in redundant robotic tasks, which exhibit non-uniqueness and form continuous manifolds in configuration space. Existing approaches struggle to capture these structures comprehensively. The paper proposes a representation-centric implicit modeling paradigm that constructs a scalar field over the configuration space, whose zero-level set precisely coincides with the task-induced solution manifold. By integrating Jacobian-guided neighborhood sampling with implicit neural representations, the method learns a signed distance field of the solution manifold, enabling globally consistent and continuous modeling under arbitrary task mappings—a capability demonstrated for the first time. Experiments on a planar three-link robot and a seven-degree-of-freedom Franka manipulator validate the approach’s ability to accurately reconstruct solution manifolds and generalize across varying task parameters.

This work addresses the challenges posed by singular configurations in inverse kinematics for serial manipulators—such as loss of task-space mobility, unbounded joint velocities, and solver divergence—by proposing a unified framework that integrates Jacobian regularization, Riemannian manipulability tracking, constrained optimization, and data-driven techniques. It establishes, for the first time, a systematic taxonomy bridging classical robust inverse kinematics and learning-based approaches, categorizing existing methods according to the geometric structures they preserve and the nature of their robustness guarantees, whether formal or empirical. Evaluation of twelve solvers on the Franka Panda platform demonstrates that purely learning-based methods exhibit high failure rates, whereas hybrid architectures employing classical methods for refinement achieve significantly higher success rates of 98.6%–100%, thereby validating the efficacy and superiority of the proposed framework.

Analytical inverse kinematics (IK) solutions for robotic manipulators have long suffered from reliance on manual derivation, numerical ill-conditioning, and inefficiency of symbolic computation. Method: This paper proposes a fully automated analytical IK generation framework. It re-models the kinematic chain based on geometric relationships among joint axes (e.g., intersecting or parallel), systematically classifies subproblems for structural decomposition, and integrates geometric modeling, kinematic classification, and subproblem mapping to build a high-performance C++ core engine with a Python interface. Contribution/Results: The method enables one-click analytical IK generation, achieving derivation speeds orders of magnitude faster than conventional symbolic tools (e.g., Maple or Mathematica). Online IK evaluation incurs sub-millisecond latency (<1 ms) and demonstrates superior accuracy and computational efficiency compared to state-of-the-art baselines such as IKFast.

This work addresses the inefficiency and numerical instability of existing trajectory optimization methods, which typically rely on numerical or automatic differentiation to compute Jacobians of high-order time derivatives—such as jerk and rate of force change—while neglecting the structural properties of multibody systems. The authors propose a novel analytical framework that explicitly models physical quantities and their higher-order derivatives by leveraging the inherent structure of multibody dynamics. For the first time, they derive structured Jacobian matrices with respect to generalized coordinates and their higher-order time derivatives. By integrating analytical differentiation with multibody dynamics, the method enables efficient and scalable forward and inverse optimization. It significantly improves computational efficiency and numerical stability compared to conventional approaches and demonstrates success in accurately recovering cost function weights from motion data in inverse optimization tasks.

This study addresses the challenge of dynamic modeling for mechanisms with variable topology, particularly when constraints such as joint locking, static friction, or ideal contact lead to abrupt changes in degrees of freedom. To ensure physically consistent and continuous dynamic behavior during topological transitions, the work proposes a set of physically coherent switching conditions. Building upon this foundation, two nonsmooth dynamics frameworks are developed: one based on redundant coordinates employing projected equations of motion, and another using minimal coordinates formulated via Voronets equations. The computational characteristics of both approaches are systematically compared. The proposed methodology is successfully validated on a planar 3R mechanism and a 6-DOF industrial manipulator under joint-locking scenarios, significantly enhancing the accuracy and feasibility of forward dynamics simulations for complex systems with varying topology.

This work addresses the challenges of kinematic redundancy and task-space decoupling in serial manipulators performing low-degree-of-freedom tasks. To overcome these issues, the authors propose a geometrically defined screw projector that directly decomposes the end-effector twist into task-relevant and redundant components, thereby establishing a compact inverse kinematics framework. Unlike conventional approaches relying on Jacobian null-space projection, this method leverages geometric screw decomposition to intuitively separate motions inside and outside the task space, offering a unified treatment of both kinematic and task redundancy. Experimental results demonstrate that the proposed approach enables efficient, intuitive, and natural motion control while effectively managing redundancy.