Kinematic Control of Redundant Robotic Manipulators

Redundant robotic manipulators, characterised by having more degrees of freedom than strictly necessary to perform a given task, afford enhanced dexterity, improved obstacle avoidance and greater resilience to singular configurations. The kinematic control of such systems involves determining joint trajectories that satisfy primary end‐effector objectives—such as path following or force exertion—while simultaneously resolving secondary goals like joint‐limit avoidance, energy efficiency and singularity robustness. Central to this endeavour is the concept of redundancy resolution, which exploits the null space of the Jacobian matrix to embed secondary tasks without compromising the main task. Modern strategies integrate optimisation techniques, task‐priority frameworks and continuous task transitions to guarantee stability and performance, even in complex unstructured environments. Applications span industrial assembly, medical robotics, space operations and collaborative human–robot interaction, where the ability to negotiate confined workspaces and respond safely to external perturbations is paramount. Recent advances have emphasised hybrid analytical–numerical solutions, energy‐aware control schemes and set‐based task formulations, reflecting the growing demand for manipulators that combine precision, adaptability and safety in real‐world settings.

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Kinematic Control of Redundant Robotic Manipulators publication trend

The graph below shows the total number of articles in kinematic control of redundant robotic manipulators across all publications each year (not limited to Nature Index journals).

Technical terms

Jacobian matrix: A matrix relating joint velocities to end‐effector velocities, fundamental to tasks in velocity and force control.
Null space: The set of joint velocity vectors that produce zero end‐effector motion, used to embed secondary objectives.
Redundancy resolution: The process of selecting a unique joint trajectory from infinitely many solutions, often via optimisation or task‐priority hierarchies.
Manipulability: A quantitative measure of a manipulator’s ability to move or exert forces in different directions, often derived from the Jacobian.
Singularity: A configuration where the Jacobian loses rank, leading to loss of control authority or infinite joint velocities.

References

1. Set-Based Tasks within the Singularity-Robust Multiple Task-Priority Inverse Kinematics Framework: General Formulation, Stability Analysis, and Experimental Results. Frontiers in Robotics and AI (2016).
2. Global Energy-Optimal Redundancy Resolution of Hydraulic Manipulators: Experimental Results for a Forestry Manipulator. Energies (2017).
3. An Efficient and Accurate Inverse Kinematics for 7-DOF Redundant Manipulators Based on a Hybrid of Analytical and Numerical Method. IEEE Access (2020).
4. Precise semi-analytical inverse kinematic solution for 7-DOF offset manipulator with arm angle optimization. Frontiers of Mechanical Engineering (2021).
5. Robot Control near Singularity and Joint Limit Using a Continuous Task Transition Algorithm. International Journal of Advanced Robotic Systems (2013).