A Task-Driven, Planner-in-the-Loop Computational Design Framework for Modular Manipulators

TL;DR

The paper tackles the challenge of deploying adaptable modular manipulators by unifying motion planning and morphological design. It introduces a planner-in-the-loop framework combining a hierarchical model predictive control (HMPC) trajectory planner with a CMA-ES design optimizer, supported by a sorting-based mapping that converts discrete morphologies into a continuous search space and a bi-branch morphology with an assist branch. A virtual module abstraction (SoM) enables seamless single- and bi-branch configurations, allowing joint optimization of morphology and mounted pose under kinematic, dynamic, and collision constraints. The framework is validated through simulations and hardware experiments across pick-and-place, polishing, and drilling tasks, showing feasible designs with improved manipulability and reduced proximal torque, outperforming a GA baseline. This work advances practical co-design of modular manipulators, enabling task-driven, efficient morphologies without requiring stronger base modules.

Abstract

Modular manipulators composed of pre-manufactured and interchangeable modules offer high adaptability across diverse tasks. However, their deployment requires generating feasible motions while jointly optimizing morphology and mounted pose under kinematic, dynamic, and physical constraints. Moreover, traditional single-branch designs often extend reach by increasing link length, which can easily violate torque limits at the base joint. To address these challenges, we propose a unified task-driven computational framework that integrates trajectory planning across varying morphologies with the co-optimization of morphology and mounted pose. Within this framework, a hierarchical model predictive control (HMPC) strategy is developed to enable motion planning for both redundant and non-redundant manipulators. For design optimization, the CMA-ES is employed to efficiently explore a hybrid search space consisting of discrete morphology configurations and continuous mounted poses. Meanwhile, a virtual module abstraction is introduced to enable bi-branch morphologies, allowing an auxiliary branch to offload torque from the primary branch and extend the achievable workspace without increasing the capacity of individual joint modules. Extensive simulations and hardware experiments on polishing, drilling, and pick-and-place tasks demonstrate the effectiveness of the proposed framework. The results show that: 1) the framework can generate multiple feasible designs that satisfy kinematic and dynamic constraints while avoiding environmental collisions for given tasks; 2) flexible design objectives, such as maximizing manipulability, minimizing joint effort, or reducing the number of modules, can be achieved by customizing the cost functions; and 3) a bi-branch morphology capable of operating in a large workspace can be realized without requiring more powerful basic modules.

Figures (20)

• Figure 1: Concept of a bi-branch modular manipulator consisting of a main branch with an end-effector and an assist branch that is connected via a shared module.
• Figure 2: Schematic of the Computational Design Framework. The manipulation task is defined as a sequence of end-effector trajectories (including position and orientation) in Cartesian space. For the main branch, we employ an HMPC-based planner to compute feasible joint-space trajectories. For the assist branch (in the bi-branch morphology), an additional planning component is introduced to determine the joint movement. With the motion planner in the design loop, the execution performance—measured using designated evaluation metrics—is maximized to refine both the manipulator's morphology and its mounted pose. Note that this framework can automatically select between single-branch and bi-branch morphologies according to the task requirements.
• Figure 3: Comparison of gravitational torque under two different CoM placements. Left scenario: CoMs of both branches lie on opposite sides of the shared module, producing a balancing effect. Right scenario: CoMs are on the same side, leading to increased gravitational torque.
• Figure 4: (Left) The available modules. (Upper right) An example of a bi-branch morphology with its morphology state and modular state representation. (Bottom right) An example of a single-branch morphology with its morphology state representation.
• Figure 5: Tracking-error tolerance profile. The prior value is $\xi / 2 = 0.025$ at the specific waypoint. The blue solid line indicates the posterior mean (set to 0), and the shaded region represents the 95% confidence interval of the posterior tolerance across all time steps.