Obstacle-aware inverse kinematics of variable-length continuum robots via teaching–learning-based optimization with experimental validation

Abstract Continuum robots offer high dexterity and compliance, which makes them attractive for tasks in confined, hazardous, and hard-to-reach environments. Despite this potential, inverse kinematics (IK) for multi-section continuum robots remains challenging due to strong nonlinearities and redundancy, and the problem becomes more demanding when each section can actively change its backbone length. This paper addresses obstacle-aware IK for a cable-driven variable-length continuum robot by formulating IK as a constrained optimization problem built on a constant-curvature forward kinematic model. A teaching–learning-based optimization (TLBO) algorithm is adopted to search for section bending angles, orientation angles, and section lengths that minimize end-effector tracking error while avoiding static obstacles through a capsule-based penalty constraint handling strategy that accounts for the robot’s physical radial dimension. The approach is evaluated through multiple three-dimensional MATLAB simulations, including linear and circular trajectory tracking with and without obstacle avoidance, and is benchmarked against particle swarm optimization (PSO), a real-coded genetic algorithm (GA), and differential evolution (DE) over 30 independent runs. Statistical analysis shows that TLBO achieves the best or near-best tracking accuracy (mean error $$7.84\times 10^{-5}$$ mm, best $$4.95\times 10^{-7}$$ mm) while requiring no algorithm-specific tuning parameters. The method is further validated experimentally on a Continuum Bionic Handling Assistant (CBHA) platform by comparing the IK-derived cable-length profiles with potentiometer-based measurements. The results demonstrate accurate trajectory tracking in simulation and good agreement with experimental cable-length measurements, supporting the feasibility of TLBO for constrained IK of variable-length continuum robots.