Lie Theory Based Optimization for Unified State Planning of Mobile Manipulators

TL;DR

An approach using Lie theory to find the inverse kinematic constraints by converting the kinematic model, created using screw coordinates, between its Lie group and vector representation between its Lie group and vector representation is proposed.

Abstract

Mobile manipulators are finding use in numerous practical applications. The current issues with mobile manipulation are the large state space owing to the mobile base and the challenge of modeling high degree of freedom systems. It is critical to devise fast and accurate algorithms that generate smooth motion plans for such mobile manipulators. Existing techniques attempt to solve this problem but focus on separating the motion of the base and manipulator. We propose an approach using Lie theory to find the inverse kinematic constraints by converting the kinematic model, created using screw coordinates, between its Lie group and vector representation. An optimization function is devised to solve for the desired joint states of the entire mobile manipulator. This allows the motion of the mobile base and manipulator to be planned and applied in unison resulting in a smooth and accurate motion plan. The performance of the proposed state planner is validated on simulated mobile manipulators in an analytical experiment. Our solver is available with further derivations and results at https://github.com/peleito/slithers.

Figures (9)

• Figure 1: Pictorial representation of using Lie theory to move across the Lie group using the corresponding Lie algebra. The motion in between each point on the Lie group ($[P_{n}]$) can be represented as a motion on the corresponding Lie algebra ($[P_{n}]^{\wedge}$).
• Figure 2: The framework of the proposed method takes in a set of desired end effector poses, computes the desired state based on an objective function and executes the motion to achieve the desired states.
• Figure 3: Mobile manipulators consisting of a six degree of freedom industrial robotic manipulator mounted on a non-holonomic mobile platform (left) and holonomic mobile platform (right).
• Figure 4: Test paths used for the simulated experiment with the colored axes representing the desired pose of the end effector. The red, blue, and green axes represent the x, y, and z axes, respectively.
• Figure 5: The error of the end effector on each of the different paths for both the position and orientation when using a non-holonomic and holonomic mobile platform.