arXiv subjects

Liangting Wu

Publications and source records attributed to Liangting Wu.

4 recordsLinked to original sources

arXiv2026

IKSPARK: Obstacle-Aware Inverse Kinematics via Convex Optimization

Inverse kinematics (IK) is central to robot control and motion planning, yet its nonlinear kinematic mapping makes it inherently nonconvex and particularly challenging under complex constraints. We present IKSPARK (Inverse Kinematics using Semidefinite Programming And RanK minimization), an obstacle-aware IK solver for robots with diverse morphologies, including open and closed kinematic chains with spherical, revolute, and prismatic joints. Our formulation expresses IK as a semidefinite programming (SDP) problem with additional rank-1 constraints on symmetric matrices with fixed traces. IKSPARK first solves the relaxed SDP, whose infeasibility certifies infeasibility of the original IK problem, and then recovers a rank-1 solution using iterative rank-minimization methods with proven local convergence. Obstacle avoidance is handled through a convexified formulation of mixed-integer constraints. Extensive experiments show that IKSPARK computes highly accurate solutions across various kinematic structures and constrained environments without post-processing. In obstacle-rich settings, especially fixed workcell environments, IKSPARK achieves substantially higher success rates than traditional nonlinear optimization methods.

cs.RO↗

arXiv2025

Certifiably Optimal Estimation and Calibration in Robotics via Trace-Constrained Semi-Definite Programming

Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them to rank-1 matrices, a condition that can be challenging to achieve. In this work, we focus on trace-constrained SDPs (TCSDPs), where the decision variables are Positive Semi-Definite (PSD) matrices with fixed trace values. We show that the latter can be used to design a gradient-based refinement procedure that projects relaxed SDP solutions toward rank-1, low-cost candidates. We also provide fixed-trace SDP relaxations for common robotic quantities, such as rotations and translations, and a modular virtual robot abstraction that simplifies modeling across different problem settings. We demonstrate that our trace-constrained SDP framework can be applied to many robotics tasks, and we showcase its effectiveness through simulations in Perspective-n-Point (PnP) estimation, hand-eye calibration, and dual-robot system calibration.

cs.RO↗

arXiv2024

Inverse Kinematics with Vision-Based Constraints

This paper introduces the Visual Inverse Kinematics problem (VIK) to fill the gap between robot Inverse Kinematics (IK) and visual servo control. Different from the IK problem, the VIK problem seeks to find robot configurations subject to vision-based constraints, in addition to kinematic constraints. In this work, we develop a formulation of the VIK problem with a Field of View (FoV) constraint, enforcing the visibility of an object from a camera on the robot. Our proposed solution is based on the idea of adding a virtual kinematic chain connecting the physical robot and the object; the FoV constraint is then equivalent to a joint angle kinematic constraint. Along the way, we introduce multiple vision-based cost functions to fulfill different objectives. We solve this formulation of the VIK problem using a method that involves a semidefinite program (SDP) constraint followed by a rank minimization algorithm. The performance of this method for solving the VIK problem is validated through simulations.

cs.RO↗

arXiv2024

Learning deep Koopman operators with convex stability constraints

In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization problems. More specifically, we tackle the problem of imposing asymptotic stability to a Koopman matrix learned from data during iterative gradient descent optimization processes. We show that this sufficient condition can be decoupled by rows of the system matrix, and propose a control barrier function-based projected gradient descent to enforce gradual evolution towards the stability set by running an optimization-in-the-loop during the iterative learning process. We compare the performance of our algorithm with other two recent approaches in the literature, and show that we get close to state-of-the-art performance while providing the added flexibility of allowing the optimization problem to be further customized for specific applications.

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