Alex Elias

I'm a robotics engineer with a Ph.D. (pending conferral) from Rensselaer Polytechnic Institute. My work centers on inverse kinematics, motion planning, and control for robot arms and mobile robots.

I solve real-world problems with math.

Software

IK-Geo

rpiRobotics / ik-geo

Unified inverse kinematics solver using geometric subproblem decomposition. Finds all IK solutions for any 6-DOF or 7-DOF robot arm. Fastest solver in our testing with >40x faster IK for UR5 than IKFast.

Stereographic SEW Angle

rpiRobotics / stereo-sew

Redundancy parameterization and inverse kinematics of 7-DOF arms using stereographic and conventional SEW angles. Stereographic SEW angle enlarges the singularity-free workspace of 7R arms, which is especially useful for teleoperation.

Research

Cuspidality, Redundancy, and Parallel Mechanisms

Spring 2025–Present

Cuspidal robots can switch IK solutions without crossing singularities, so classical path planners may fail. I found new cuspidal robots, proposed planning/optimization methods, and applied cuspidality analysis to 7-DOF arms. I also analyzed the ABB YuMi kinematics and extended IK-Geo for parallel robots.

NASA Goddard On-Orbit Satellite Servicing

Fall 2021–Fall 2024

I designed algorithms for 7-DOF elastic-joint arms to service satellites in orbit, covering compliance control, trajectory tracking, loop stability, optimal control, and dynamics modeling and simulation.

Multi-Robot Systems for Tent Manufacturing

Summer 2020–Spring 2022

I led development of 5 mobile robots (2 custom). We built a wireless teach pendant, implemented QP-based formation control, and achieved ±5 cm UWB+EKF localization to demonstrate heavy fabric/cart transport and collaborative welding.

Robotic Deep Rolling

Summer 2019–Spring 2020

I designed a GUI-based hybrid motion and force controller for deep rolling with an ABB IRB 6640. It generates custom toolpaths, holds ±5% force, uses data-driven robot and compliance models for offline tuning, and was experimentally validated for residual stress.

Publications

IK-Geo: Unified robot inverse kinematics using subproblem decomposition

July 2025

Alexander J. Elias, John T. Wen
Mechanism and Machine Theory vol. 209, 105971

Redundancy parameterization and inverse kinematics of 7-DOF revolute manipulators

December 2024

Alexander J. Elias, John T. Wen
Mechanism and Machine Theory vol. 204, 105824

Path Planning and Optimization for Cuspidal 6R Manipulators

January 2025

Alexander J. Elias, John T. Wen
arXiv:2501.18505.
Accepted for publication in ASME Journal of Mechanisms and Robotics

Redundancy Parameterization of the ABB YuMi Robot Arm

May 2025

Alexander J. Elias, John T. Wen
arXiv:2505.23111