Whole-Body Ergodic Exploration with a Manipulator Using Diffusion

TL;DR

This letter introduces an approach that decomposes the whole-body of a robotic manipulator into multiple kinematically constrained agents and generates control actions by calculating a consensus among the agents using the non-stationary heat equation.

Abstract

This paper presents a whole-body robot control method for exploring and probing a given region of interest. The ergodic control formalism behind such an exploration behavior consists of matching the time-averaged statistics of a robot trajectory with the spatial statistics of the target distribution. Most existing ergodic control approaches assume the robots/sensors as individual point agents moving in space. We introduce an approach that decomposes the whole-body of a robotic manipulator into multiple kinematically constrained agents. Then, we generate control actions by calculating a consensus among the agents. To do so, we use an ergodic control formulation called heat equation-driven area coverage (HEDAC) and slow the diffusion using the non-stationary heat equation. Our approach extends HEDAC to applications where robots have multiple sensors on the whole-body (such as tactile skin) and use all sensors to optimally explore the given region. We show that our approach increases the exploration performance in terms of ergodicity and scales well to real-world problems. We compare our method in kinematic simulations with the state-of-the-art and demonstrate the applicability of an online exploration task with a 7-axis Franka Emika robot. Additional material available at https://sites.google.com/view/w-ee-d/

Figures (8)

• Figure 1: Whole-body exploration of a target distribution using the last three links of the robot manipulator. In kinematic simulation, the exploration target is given in red. In the real-world experiment, the robot explores the cube region in dashed lines to localize a target object (a tennis ball whose location is unknown). Blue, turquoise, and purple spheres are the virtual agents constrained to the $5$-th, $6$-th, and $7$-th links, respectively. The green and yellow arrows show the net virtual force and torque acting on each link's center of mass calculated by our agent weighing strategy. We further weigh the net wrenches acting on the active link to obtain the consensus control action for the robot.
• Figure 2: The HEDAC ivicErgodicityBasedCooperativeMultiagent2017 method computes the potential field $u(\bm{x},t)$ that guides the agents for ergodic exploration. The time-averaged coverage of the agent(s) $c(\bm{x},t)$ at time $t$ is subtracted from the target distribution $p(\bm{x})$ and positive values corresponding to unexplored regions are squared and used as the virtual heat source $s(\bm{x},t)$. The diffusion (heat) equation \ref{['eq:heat']} is then used for diffusing the potential field and propagating information of unexplored regions to the agents.
• Figure 3: Comparison of uniform and local temperature weighting. The green square is the exploration target and small arrows show the temperature gradient. Blue dots and arrows show active agents and the force exerted on each agent after weighting.
• Figure 4: Planar exploration using different configurations. The black shape is the target distribution, and the colored lines are agent trajectories, where the blue dashed lines correspond to the agent's path at the tip of the last link. We show the configuration of the planar manipulator at equally spaced timesteps. Red is the start configuration, and the transparency decreases as time increases.
• Figure 5: Coverage performance given by the normalized ergodic metric for different virtual agent configurations. Target distributions for the coverage task are given on the top right.