Inverse Kinematic Analysis of a Redundant Hybrid Climbing Robot

This paper presents the complete inverse kinematic analysis of a novel redundant truss-climbing robot with 10 degrees of freedom. The robot is bipedal and has a hybrid serial-parallel architecture, where each leg consists of two parallel mechanisms connected in series. By separating the equation for inverse kinematics into two parts - with each part associated with a different leg - an analytic solution to the inverse kinematics is derived. In the obtained solution, all the joint coordinates are calculated in terms of four or five decision variables (depending on the desired orientation) whose values can be freely decided due to the redundancy of the robot. Next, the constrained inverse kinematic problem is also solved, which consists of finding the values of the decision variables that yield a desired position and orientation satisfying the joint limits. Taking the joint limits into consideration, it is shown that all the feasible solutions that yield a given desired position and orientation can be represented as 2D and 3D sets in the space of the decision variables. These sets provide a compact and complete solution to the inverse kinematics, with applications for motion planning.