An Optimization-Based Inverse Kinematics Solver for Continuum Manipulators in Intricate Environments

Abstract

Continuum manipulators have gained significant attention as a promising alternative to rigid manipulators, offering notable advantages in terms of flexibility and adaptability within intricate workspace. However, the broader application of high degree-of-freedom (DoF) continuum manipulators in intricate environments with multiple obstacles necessitates the development of an efficient inverse kinematics (IK) solver specifically tailored for such scenarios. Existing IK methods face challenges in terms of computational cost and solution guarantees for high DoF continuum manipulators, particularly within intricate workspace that obstacle avoidance is needed. To address these challenges, we have developed a novel IK solver for continuum manipulators that incorporates obstacle avoidance and other constraints like length, orientation, etc., in intricate environments, drawing inspiration from optimization-based path planning methods. Through simulations, our proposed method showcases superior flexibility, efficiency with increasing DoF, and robust performance within highly unstructured workspace, achieved with acceptable latency.

Figures (6)

• Figure 1: A) Rational Bézier representation of a single circular arc. B) A 2 segments piece-wise arc spline with $G^1$ continuity.
• Figure 2: Cost function for obstacles with relate to distance between current position and the nearest obstacle.
• Figure 3: A sketch for obstacle avoidance. Blue points represent the path points, which are also the end points of each arc segment. Blue vectors are generated by the optimization-based path planning algorithm, aiming to guide the overall path towards lower potential positions in the obstacle-related artificial potential field. The red points are samples taken from the piece-wise arcs, representing the continuum robot body. The red vectors depict the gradients calculated using a numerical method to move the piece-wise arcs away from obstacles during optimization.
• Figure 4: The result of the four settings by the IK solver introduced in this paper. The piece-wise arcs represent the configuration of the continuum robot calculated by our IK solver, under four different settings of end position and orientation.
• Figure 5: Upper figures depict the continuum robot successfully navigating various intricate environments filled with sphere obstacles. The red piece-wise arcs with blue end points represent the continuum robot configuration calculated by our IK solver, and the blue lines represent the path to be tracked. The lower plots provide a visual representation of the corresponding time consumption. The x-axis represents the path point index, while the y-axis indicates the time consumption for each path point, measured in milliseconds.