inverse 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.

To address the lack of unified, flexible, and real-time inverse dynamics (ID) computation across simulation and real-robot deployments, this paper introduces a lightweight, robot-agnostic ID software library built natively for ROS 2. Methodologically, it employs an abstract interface layer to decouple underlying dynamics engines (KDL/Pinocchio) and hardware specifics, integrates DDS natively for deterministic real-time communication, and supports URDF parsing and cross-platform deployment. Its key contributions include: (i) the first ROS 2-native, extensible ID module architecture enabling seamless integration across simulation and physical robots (UR10, Franka), and (ii) experimental validation demonstrating sub-millisecond latency, high computational accuracy, and robust runtime stability. The implementation is open-source and officially integrated into the ROS 2 GBP ecosystem.

This paper addresses high-precision path following for autonomous mobile robots, including fixed-wing UAVs. Methodologically, it introduces a novel paradigm that extends inverse kinematics principles to guidance vector field (GVF) design: a geometric error signal is derived from an implicit path representation (zero-level set), mapped via inverse kinematics to construct the GVF, and integrated with nonlinear feedback linearization and feedforward control to achieve error dynamics linearization and transient response shaping. Key contributions include: (i) the first theoretical linkage between inverse kinematics and GVF design; (ii) explicit accommodation of constant-speed unicycle dynamics—beyond the conventional single-integrator assumption; (iii) rigorous proof of global asymptotic convergence; and (iv) experimental validation on a fixed-wing UAV, demonstrating centimeter-level 2D path tracking accuracy and tunable transient performance.

Robot path planning and trajectory optimization are commonly formulated as optimal control problems (OCPs), yet designing appropriate trade-offs among multi-objective cost components remains challenging, and resulting solutions often lack interpretability—leading to inefficient debugging. Method: We propose the first direction-corrected cost consistency analysis framework, integrating sensitivity analysis, gradient direction projection, and expert-feedback-driven iterative reweighting optimization. Contribution/Results: This approach enables interpretable diagnostic analysis of cost components and automated weight tuning, shifting from conventional trial-and-error to goal-directed correction. It significantly improves solution rationality and task success rates while supporting adaptive objective function reconstruction with low cost and minimal samples.

This work addresses the challenge of long-horizon robotic manipulation planning, which is hindered by the nonlinear contact dynamics and combinatorial complexity of multi-contact modes, leading to rapidly escalating computational costs over extended time horizons. The paper introduces, for the first time, a spectral decomposition of the inverse dynamics equations into trajectory generation, enabling efficient approximation of an object’s reachable set through orthogonal trajectory components. This approach preserves dynamic feasibility while substantially improving exploration efficiency. Integrated with search-based planners such as RRT, the proposed method generates 45-second manipulation plans encompassing more than ten distinct contact modes within 15 seconds, thereby achieving real-time, long-horizon planning for highly complex tasks.

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.

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.

Conventional robotic systems rely on fixed kinematic models, limiting their ability to generalize across tools of variable lengths. Method: We propose an extended inverse kinematics (IK) framework that explicitly incorporates variable-length tool modeling, unifying tool selection, grasp pose planning, orientation optimization, and precise manipulation. Our approach integrates simulation-driven trajectory generation, reinforcement learning–based policy training, and sim-to-real transfer techniques—marking the first IK formulation to explicitly embed dynamic tool length as a learnable parameter. Contribution/Results: The framework enables seamless multi-tool switching and cross-task skill transfer. Experiments demonstrate sub-centimeter positioning accuracy (<1 cm) in real-world settings and an average 8 cm error in simulation, with consistent performance across two distinct tool lengths. This significantly enhances generalization and robustness in tool manipulation tasks.

This study addresses the trajectory planning challenge for redundant robotic arms equipped with coupled-finger grippers in laboratory automation, where high-dimensional configuration spaces and task-constraint coupling impede conventional approaches. We propose an autonomous manipulation framework integrating visual perception with multimodal motion planning. Collision-free trajectories are generated using RRT*, while an accurate forward kinematic model is established via screw theory. Three inverse kinematics solvers—Jacobian transpose (JT), pseudoinverse (PI), and damped least squares (DLS)—are systematically compared. Innovatively, manipulability analysis and joint-space Jacobian computation are introduced to quantitatively evaluate trajectory smoothness, positional accuracy (RMSE), and higher-order motion continuity. Results demonstrate that DLS significantly enhances motion stability and end-effector precision, achieving superior robustness and adaptability in complex experimental environments. This work provides an efficient, reliable control strategy for autonomous robotic manipulation under stringent operational constraints.

This work addresses the challenge of degraded task performance in torque-controlled redundant robots under joint limit constraints, where conventional inverse kinematics formulations often fail to ensure feasibility and compatibility with downstream torque controllers. To overcome this, the paper proposes a convex quadratic programming-based inverse kinematics framework that outputs joint velocities while jointly optimizing task tracking accuracy, joint limit admissibility, and redundancy resolution. A novel controller-compatibility objective is introduced, incorporating actuator torque capacity weighting and command continuity. Feasibility with respect to joint limits is enforced via control-barrier-function-inspired constraints at the reference level, and slack variables are employed to handle task equation violations gracefully. Experimental validation on a seven-degree-of-freedom upper-limb exoskeleton demonstrates significant reductions in joint-limit impacts, bounded and admissible velocity outputs, and improved task tracking performance—all without requiring modifications to the downstream torque controller.