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.

This paper develops a stochastic programming framework for multi-agent systems where task decomposition, assignment, and scheduling problems are simultaneously optimized. The framework can be applied to heterogeneous mobile robot teams with distributed sub-tasks. Examples include pandemic robotic service coordination, explore and rescue, and delivery systems with heterogeneous vehicles. Due to their inherent flexibility and robustness, multi-agent systems are applied in a growing range of real-world problems that involve heterogeneous tasks and uncertain information. Most previous works assume one fixed way to decompose a task into roles that can later be assigned to the agents. This assumption is not valid for a complex task where the roles can vary and multiple decomposition structures exist. Meanwhile, it is unclear how uncertainties in task requirements and agent capabilities can be systematically quantified and optimized under a multi-agent system setting. A representation for complex tasks is proposed: agent capabilities are represented as a vector of random distributions, and task requirements are verified by a generalizable binary function. The conditional value at risk (CVaR) is chosen as a metric in the objective function to generate robust plans. An efficient algorithm is described to solve the model, and the whole framework is evaluated in two different practical test cases: capture-the-flag and robotic service coordination during a pandemic (e.g., COVID-19). Results demonstrate that the framework is generalizable, scalable up to 140 agents and 40 tasks for the example test cases, and provides low-cost plans that ensure a high probability of success.