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Sliding Mode Control of a Redundant Robot Arm in Motion Planning Subject to Joint Space Constraints

Influenced by research in biomechanics engineers attempt to achieve motion flexibility of the robot arm similar to that of a human hand motion. For this purpose the design of modern robot arms most often provides redundant degrees of freedom in executing the assigned tasks in world space. Typical industrial applications of robots involve motion planning subject to constraints in joint space. In the general case additional static constraints in world space can also be mapped into admissible ranges of variation of the joint variables. This paper presents a mathematical model for redundant robot motion control in case of hard constraints on the displacements in the joints. The novelty in this model is the application of sliding mode theory based on the separation of the immutable geometrical artefacts in path planning from the changes in the actual robot motion. This allows to replace the traditionally heavy optimization procedures used with redundant robot arms by computationally efficient and intuitive vector space methods. The sliding mode of control is seamlessly embedded in a uniform kinematic path control algorithm and it is activated only when needed. Unlike existing methods, the sliding mode for motion control in case of constraints on the joint variables can execute concurrently with other forms motion control.