Adaptive, Constraint-Aware Inverse Kinematics for Efficient Robotic Manipulator Control

Robotic arm motion planning and Inverse Kinematics (IK) represent critical components in enabling robots to perform sophisticated tasks in complex and dynamic environments. Traditional robotic control approaches typically rely on extensive manual programming and deterministic solvers, resulting in limited adaptability, high expert dependency, and challenges in real-time responsiveness and robustness.

This thesis addresses these limitations by proposing an integrated adaptive approach that enhances robotic motion planning by improving the interaction between motion planners and IK solvers. The research develops an advanced Dynamically Weighted Damped Least Squares Inverse Kinematics (DLS-IK) method combined with learned motion representations through Probabilistic Movement Primitives (ProMPs). The approach leverages probabilistic modelling and adaptive weighting strategies to dynamically adjust task constraints and improve motion feasibility, effectively handling singularities, joint limitations, and environmental uncertainties.

Three primary contributions are presented. First, the thesis investigates environmental factors influencing robotic motion planning, offering comprehensive analyses of workspace characteristics and comparative studies of prominent robotic arms. Second, it presents an enhanced DLS-IK method that integrates velocity damping control and joint constraint adherence, significantly improving trajectory accuracy and stability near singularities. Third, it introduces an Adaptive Weighted and Regularised Optimisation for Efficient Inverse Kinematics (AWARE-IK) integrated with DLS-IK, enabling robust, adaptive trajectory generation that efficiently manages conflicting kinematic objectives, such as end-effector accuracy, joint-limit avoidance, and singularity regularisation, within a unified multi-objective optimisation framework.

Evaluations across diverse and cluttered environments demonstrate that the proposed adaptive framework significantly outperforms existing methods regarding task generalisation, computational efficiency, and resilience to environmental complexity. By bridging learning-based methods with optimisation-based IK solutions, this thesis contributes substantially towards practical, reliable robotic manipulation for real-world applications.