Motion Planning for Minimally Actuated Serial Robots

TL;DR

This work tackles motion planning for Minimally Actuated Serial Robots (MASR) by introducing MASR-RRT*, a tailored sampling-based planner that uses a data-driven inverse-kinematics NN (IK-NN) to compute low-cost configurations and guide exploration toward the goal. IK-NN is trained in an unsupervised fashion from forward-kinematics data and includes a regularizer that biases solutions toward minimal traverse time for both joints and the Mobile Actuator (MA). The MASR-RRT* framework achieves faster convergence and better path quality than standard RRT*, and is validated through extensive simulations and real-robot demonstrations, including obstacle avoidance and balloon grasp tasks. The approach enables efficient, real-time planning for MASR in confined environments and lays groundwork for extending to 3D planning and sensor-driven autonomy.

Abstract

Modern manipulators are acclaimed for their precision but often struggle to operate in confined spaces. This limitation has driven the development of hyper-redundant and continuum robots. While these present unique advantages, they face challenges in, for instance, weight, mechanical complexity, modeling and costs. The Minimally Actuated Serial Robot (MASR) has been proposed as a light-weight, low-cost and simpler alternative where passive joints are actuated with a Mobile Actuator (MA) moving along the arm. Yet, Inverse Kinematics (IK) and a general motion planning algorithm for the MASR have not be addressed. In this letter, we propose the MASR-RRT* motion planning algorithm specifically developed for the unique kinematics of MASR. The main component of the algorithm is a data-based model for solving the IK problem while considering minimal traverse of the MA. The model is trained solely using the forward kinematics of the MASR and does not require real data. With the model as a local-connection mechanism, MASR-RRT* minimizes a cost function expressing the action time. In a comprehensive analysis, we show that MASR-RRT* is superior in performance to the straight-forward implementation of the standard RRT*. Experiments on a real robot in different environments with obstacles validate the proposed algorithm.

Figures (10)

• Figure 1: The Minimally actuated serial robot (MASR) with its serial design and a Mobile Actuator (MA), moving from an initial straight configuration to grasping a balloon near obstacles (see video).
• Figure 2: (a) MASR components, serial arm and mobile actuator (MA) with its mechanisms. (b) A schematic diagram showing a typical $5$R MASR configuration $\mathbf{q}$, with an example of how $j_{d}$ and $d_{link}$ are derived from $d$ (i.e., $d=r_3+d_{link}=l_1+l_2+d_{link}$).
• Figure 3: (a) Example of an environment containing two polygonal obstacles with typical configurations $\mathbf{q}_{k}, \mathbf{q}_{k+1}$. Fictitious margins, each of width $0.5w$, are added around obstacles. Here, $w$ is the actual links' width. Therefore, treating the arm as a series of lines and using a simple collision checker function is sufficient. (b) An illustration of the process of exerting an action $\mathbf{a}_k$ by the motion convention. Each step is numbered. The length to be moved will be $D_\mathbf{a}=d_{link}+2l_1+l_2$. (c) OnGoal function illustration. Given a goal $\mathbf{x}_{goal}$, the second rectangle, $R_2$, satisfies $R_2\cap \mathbf{x}_{goal}\neq\emptyset$. (d) Then, function GoalFix updates the new configuration $\mathbf{q}_{k+1}=\mathbf{q}_{goal}$ (red) and discards the old configuration $\mathbf{q}_{k+1}$ (green).
• Figure 4: (a) An example of redundancy in 3R MASR due to the additional MA DoF $d$ whereas the conventional 2D serial arm with $d=l$ has one solution on the last link tip. Here, the green configuration has a smaller overall action time than the red configuration since only the first joint must be actuated from the grey configuration. (b) The model architecture for training the IK-NN including a FK module. (c) Example of weights assigned to the joints of a 5R MASR by initial configuration $\mathbf{q}_c = (\mathbf{0}^T, 1.5l)^T$ and estimated configuration $\tilde{\mathbf{q}}=(\alpha, 2\alpha, -3\alpha, -3\alpha, 2\alpha, 2.5l)^T$ for $\mathcal{L}_{reg}$ calculation.
• Figure 5: Success rate and cost value for 300 random environments, with regard to the number of planning iterations $N_c$ and probability $p_c$.