Optimal Design of Continuum Robots with Reachability Constraints

TL;DR

The paper tackles optimal design of multi-joint continuum robots under reachability constraints by combining fast forward-kinematics reachability assessment with torque-aware inverse-kinematics refinement, and a derivative-free Estimation of Distribution Algorithm (EDA) to search the design space. The method employs a penalty-based fitness that enforces reachability on a discretized workspace and models promising designs with univariate normal distributions, iteratively sampling new designs. Compared to a genetic algorithm, the EDA yields 4–15% lower objective values across three applications (mobile platform, deep-sea mining, and car-panel welding), demonstrating superior efficiency in reaching feasible, low-cost designs. The approach promises substantial reductions in design time (2–4 hours versus weeks) and is extensible to additional performance criteria and more complex robots.

Abstract

While multi-joint continuum robots are highly dexterous and flexible, designing an optimal robot can be challenging due to its kinematics involving curvatures. Hence, the current work presents a computational method developed to find optimal designs of continuum robots given reachability constraints. First, we leverage both forward and inverse kinematic computations to perform reachability analysis in an efficient yet accurate manner. While implementing inverse kinematics, we also integrate torque minimization at joints such that robot configurations with the minimum actuator torque required to reach a given workspace could be found. Lastly, we apply an estimation of distribution algorithm (EDA) to find optimal robot dimensions while considering reachability, where the objective function could be the total length of the robot or the actuator torque required to operate the robot. Through three application problems, we show that the EDA is superior to a genetic algorithm (GA) in finding better solutions within a given number of iterations, as the objective values of the best solutions found by the EDA are 4-15\% lower than those found by the GA.

Figures (5)

• Figure 1: A three-joint spatial continuum robot. Each joint consists of a base, top and spine. The spine can bend continuously along its length about two orthogonal axes.
• Figure 2: Simplistic representation of a three-joint continuum robot with the proposed parametrization. (a) The tangent vector at the base defines the direction towards which the first joint is pointing at, and the normal vector determines the bending plane of that joint. (b) The tip of each joint coincides with the bottom of the subsequent joint. (c) $\theta$ of each joint is defined as the rotation of $\vec{\tilde{n}}$ about that joint's tangent $\vec{t}$ leading to $\vec{n}$ determining the bending plane of that joint. (d) Given each joint's radius $R$ and $\theta$, the robot can be fully configured in space.
• Figure 3: The robot's location/orientation and the workspaces that must be reached for each application problem. For (a) and (b), the end-effector must reach the entire workspace volumes while for (c), it must reach a series of points along the periphery of the car panel.
• Figure 4: Reachability analysis performed using the hybrid approach. (a) First, the reachability is estimated using forward kinematics with randomly generated configurations. (b) Then, inverse kinematics is used to check the reachability of those points not reached during the forward kinematics simulation. Dark blue boxes indicate the points deemed unreachable within the workspace by the forward kinematics simulation. Red boxes indicate the missed points confirmed as reachable by the inverse kinematics simulation.
• Figure 5: Summary of optimization results for the application problems. Reported in the y-axis are the objective values of the best feasible solution at each iteration, averaged from 20 runs for each algorithm. The algorithms with "select" notation indicate the usage of select generation. In all cases, the final objective values are significantly lower for the EDA compared to the GA.