Modular Kinematic Reduction of Closed-Chain Mechanisms Using Path Assembly and Defect Homotopy

Underground mining robots are increasingly modeled for planning, operator training, and digital-twin workflows, where reliable actuator-level kinematics is needed to reduce hazardous in situ trials. Unlike typical open-chain industrial manipulators, representative mining machines are often linear-actuator-driven closed-chain mechanisms with planar four-bar linkages, making reusable kinematic modeling and real-time FK/IK solving challenging. We present \textit{\hl{MineRobot}}, an actuator-centered framework for modeling and solving the kinematics of this representative mechanism class. MineRobot introduces the Mining Robot Description Format (MRDF), a domain-specific representation that parameterizes mining-robot kinematics with native semantics for actuators and loop closures. It then contracts planar four-bar substructures into generalized joints and extracts, for each actuator, an Independent Topologically Equivalent Path (ITEP) classified into four canonical types. Based on this decomposition, per-type solvers are composed into a sequential forward-kinematics (FK) pipeline, while inverse kinematics (IK) is formulated as a bound-constrained actuator-length optimization solved by a Gauss--Seidel-style update scheme. By converting coupled closed-chain kinematics into small topology-aware solves, MineRobot reduces robot-specific hand derivations and supports efficient repeated FK/IK computation without treating each query as a full coupled constraint-solving problem. Experiments on representative underground mining robots demonstrate real-time FK performance and robust IK convergence within the tested operating ranges, supporting the use of MineRobot as an actuator-centered kinematic layer for planning, training, and digital-twin workflows.

Self-motion manifold (SMM) characterizes the geometric structure of the infinite inverse kinematic solutions set of a redundant manipulator at a fixed end-effector pose, and its efficient recovery underpins feasible and global optimal motion planning. Existing methods such as null-space continuation and learning-based methods are formulated around the assumption that an SMM is a curve, and do not extend to higher redundancy orders. We instead adopt a probabilistic view: SMMs are the support of the conditional posterior over configurations given a target pose, so that recovering it reduces to sampling from a learned distribution and separating its disjoint components by clustering. The formulation is independent of the manifold dimension and requires no architectural change as the redundancy order grows. In this work, we demonstrate that our method can approximate 1-D SMMs with performance comparable to the latest null-space continuation and learning-based approach, and that it is the first method capable of approximating highly redundant 4-D SMMs in a 7R manipulator for position tasks. Project website: \href{https://github.com/accuracy-maker/high-dimenstional-self-motion-manifold-approximation}{https://github.com/accuracy-maker/high-dimenstional-self-motion-manifold-approximation}

We present the PccDiffuser, a conditional diffusion framework for continuum robots that learns a multimodal distribution over complete configuration-space paths and samples multiple candidate solutions in parallel, which are subsequently converted into an executable trajectory by time allocation considering actuator constraints. Under the piecewise constant-curvature model, we use exponential co-ordinates to describe the robot kinematics, and use graph neural network to encode a variable number of environment obstacles. Analytical differential kinematics is incorporated in the denoising process to improve terminal accuracy and whole-body clearance. On a mixed test set comprising workspace with zero to four obstacles, PccDiffuser achieved a success rate of 91%. Compared with existing sampling- and optimisation-based benchmarks, it delivered both a higher success rate and greater computational efficiency, with the latter advantage becoming more substantial when sampling more candidate solutions. Experiments on a three-section tendon-driven continuum robot further demonstrate consecutive planning, multi-solution planning, and whole-body obstacle avoidance.