IROS2019国际学术会议论文集0860

A Model for Simulating the Robotic Pushing of Dirt* Samuel Rodriguez1and Zixiu Su1and Jiazhen Yu1 AbstractIn this paper we present a model for simulating the pushing of dirt. This is a complex problem requiring the study of the action space for the robot, a deformable model for movable earth, the interaction between the robots pushing surface and the environment, and techniques that will allow this model to simulate such a scenario. We present our novel framework for studying this problem including the grid-based model of the environment, a simplifi ed earth pushing robot model, and action strategies to model the pushing of dirt from one area of the environment to another. I. INTRODUCTION Robotic systems are becoming more and more capable and we are trusting them with more human-like work than ever before. Examples of this are already deployed such as driverless cars, delivery robots, and rescue robots. In this work we will investigate simulating a robotic system for modeling the pushing of dirt. Excavators and bulldozers are common human operated pieces of machinery responsible for moving or gathering dirt from an environment and moving the dirt to some other desired location, usually a dump truck or some designated portion of the environment. By studying a model for the pushing of dirt, it will allow us to study how a machine such as a bulldozer can operate independently in an environment that typically requires a human operator. This would allow construction companies to save the cost of man hours and potentially allow these to be deployed when terraforming in a dangerous or harsh environment. This is a challenging problem to simulate given the dynamic nature of the robot, environment, and the interaction that the robot can have on the model. While planning has been studied in static environments and dynamic environ- ments, this type of planning has been less studied. This is in part due to the complexity of modeling this type of behavior. Indeed complex planning has been studied for deformable models, using deformable roadmaps, allowing the robot to change the environment during planning, and to push rigid objects. However, to the best of our knowledge, this is the only work that attempts to on the fl y develop strategies for a robot to push dirt (interacting/deforming the environment) to achieve the goal of moving terrain to a goal region. Problem Statement: Given a an agent A and a deformable environment mod- eling terrain, fi nd actions for the agent to effectively push *This research supported in part by the Sam Taylor Fellowship Fund 2019. 1Samuel Rodriguez(),ZixiuSu () and Jiazhen Yu () are with the Department of Computer Science, Texas Wesleyan University, Forth Worth, Texas, 76105, USA. (a) Example with surface. (b) Example 3D grid shown. Fig. 1: (a) An example of the agent in the environment on the surface of the grid cells. The surface is shown here. (b) An example 3D grid is shown. Filled cells are fully occupied with a fi ll value = 1. Cells at the top of the grid with 0 fill 1 are drawn partially fi llled. Empty cells are not needed to be displayed. material (portions of the environment) from given start regions Rstartto goal regions Rgoal. We assume an agent can: 1) navigate over the terrain without altering it, 2) push terrain (i.e. grid cells) from its current location on the terrain, and 3) dig into the terrain, altering the height on the terrain and increasing the amount of material it is pushing. We present a complete system for simulating this problem including an environmental model, describing a simplifi ed agent, a push behavior, and scenarios showing the system working and generating physically realistic motions for push- ing terrain. Our main contributions are: Physically realistic and scalable simulation. A deformable environment model. An adaptive push behavior to effectively move the terrain. Agent constraints on environment allowing effective computation of terrain motion. The paper is organized as follows: related work is pre- sented in Sec. II, the dynamic grid model is described in Sec. III, the agent model is presented in Sec. IV, the push 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Macau, China, November 4-8, 2019 978-1-7281-4003-2/19/$31.00 2019 IEEE6949 behavior in Sec. V, and experimental results are shown in Sec. VI. II. RELATEDWORK There are a number of related approaches that we will mention here. These include approaches for planning with manipulating the environment, planning in deformable en- vironments, simulating the pushing or manipulation of dy- namic objects in the environment, and some modelling of fl uid or fracturing of solid models. Robotic excavation has been studied to be able to plan for tasks during the excavation process 1. This work planned for more systematic actions with simple heuristics to determine the stable state of the soil. A robot excavator loading a truck full of dirt was studied in 2. This work used scanning laser rangefi nders to be able to localize the target area of the truck and scripted actions to dig and dump into the truck while avoiding obstacles. This work focused solely on the interaction between the excavator and the truck. A similar problem was studied known as the snowblower problem 3 where the problem is to compute a tour for the snowblower to take to remove snow from a given area with the constraint that as the snowblower passes it will move snow to nearby areas. A physically realistic simulation platform for modelling vehicle interaction in varying environments is studied in 4. These interactions include rigid body interactions and de- formable soil. However, this model is quite computationally complex and does not focus on automated strategies to achieve the movement task. Push interactions between a robot and an object has received a good deal of attention. Some approaches make simplifying assumptions such as modeling the robot or objects as disks 5, 6, 7 or boxes 8, 9. Others focus on a single robot pushing one object 10, 11, 12, 9. Other approaches only model the pushing robot and object as they are in contact reducing the number of DOFs that need to be planned for 13, 7, 6. Some approaches model complex dynamics. A study of motion 11, 12 includes caster wheels on interacting objects. In 14, 11 the goal is to learn from past experience the resulting dynamics, and in 15 the goal is to clear space for a goal placement of an object by using sweeping motions of a manipulator arm. Moreover, uncertainty has been addressed with a POMDP to explore the belief space to generate actions for a disk robot to push a box 9. Planning for deformable environments has been studied producing very interesting and complex motion. Mass-spring systems have been used to model deformable bodies that are then planned for using underlying roadmaps for the environment 16, 17. Tree-based planning was studied in deformable tetrahedral representations of the environment and robot in 18. Planning for a fl exible wire was described in 19 and for linear objects 20. The pushing of movable portions (or agents) in the envi- ronment is also relevant to this work. Shepherding behaviors were presented for a single agent in 21 and for multiple agents 22 push a fl ock of agents through the environment. Sheperheding using deformable shapes to model the fl ock was presented in 23. In 24, a team of agents cooperates to push a set of passive objects including complex interactions between the agents and between the agents and the passive objects being pushed. There has been a number of approaches proposed for modelling complex environmental features such as fl uid. Particle-based fl uids were presented that show high quality results requiring many thousand particles with a number of physically-based constraints applied to them. Examples of the level of detail that these fl uid simulations attempt to support are shown in 25 when they simualte the breaking of waves within a fl uid. Recent work has attempted to improve on the computation time of these complex simulations but maintain visual quality 26. Fracturing of solid models may be considered relevant 27 and shown with physically- realistic results. Sand and soil were modeled in 28 using a voxel based approach and even consided a user guided plane that could manipulate the soil. An adaptive model for soil modeling was presented in 29 that combined mesh and particle based approaches with physically plausible parameters to tune the model. The work we present here takes inspiration from many of these related approaches. We use the idea of agent-based motion with a behavior to interact with a very simplifi ed deformable environment in the form of constraints. These constraints manipulate the environment and allow us to model complex scenarios involving the agent pushing dirt or fi ll in a realistic appearing way. III. SYSTEMOVERVIEW A. Environmental Model This section will detail the underlying grid, grid-cells, and surface that make up the dynamic environment. This environment was modelled is such a way to allow the study of moving terrain. The environment is an L M N, 3-dimensional discretization of grid cells. The environment is bounded by user-defi ned values xmin,xmax,ymin,ymax,zmin,zmax that defi ne the allowable areas for fi ll, dirt, or terrain to be placed. Each grid cell is represented by a center position, pc with ranges of dx, dy, and dz along each axis. dx equals (xmax xmin)/L, dy equals (ymax ymin)/M, and dz equals (zmax zmin)/N. Additionally, each grid cell has a fill value within the range 01. The fi ll value represents how much dirt or terrain exists within each grid cell with a fi ll value of 0 meaning the cell is empty, a fi ll value of 1 being completely full, and a value in between being the proportion of the cell that has dirt in it. An example of the 3D grid is shown in Fig. 1(b). Due to the dynamic nature of the grid, the movement of terrain and constraints imposed on each grid cell is required. Each grid cell has a list of incoming fi ll, , and outgoing, , that describes fi ll that is either coming into or leaving the grid cell after each time 6950 step. Additionally, a list of constraints that exist for a grid cell is also maintained. A surface is created over the top of the fi lled grid cells. The surface is created to represent a smooth terrain. The y- values of the terrain are obtained from the highest grid cell in the grid that is not empty. The y-value obtained at indices i L and k N is the topmost grid cell j M such that y = ymin+ (j + fill) dy. Surface normal values at each i,k pair are averaged over each neighboring normals on the surface. An example of the surface of the 3D grid is shown in Fig. 1(a). B. Environmental Simulation At each step, the environment is updated to allow for the shifting of the dirt. An outline of the updating of the environmental grid is provided in Alg. 1. This grid update step is applied at each step of the simulation and allows us to model shifting terrain based off environmental factors and constraints the agent imposes on the grid. The updating of a grid cells constraints involves ensuring that a constraint exists for a pre-defi ned number of time steps (100 in the simulations shown here) and prevents fi ll from entering a grid cell that currently has a constraint. After a constraint has existed in a grid cell for the determined amount of time, that constraint is removed from the cells set of constraints. Algorithm 1 Grid Update Input: grid representing terrain 1:for gc grid.GetAllGridCells() do 2:gc.UpdateConstraints(); 3:end for 4:for gc grid.GetAllGridCells() do 5:gc.ApplyFillIncoming(); 6:end for 7:for gc grid.GetAllGridCells() do 8:gc.ApplyFillOutgoing(); 9:end for One of the most critical functions in the terrain update is how the terrain will adjust as the simulation progresses. The ApplyFillIncoming function is reponsible for this and outlined in Alg. 2. An illustration of this fi ll transfer process is shown in Fig. 2. The fi rst major step in the algorithm is for the grid cell to accept all of the incoming fi ll that is contained in . This represents fi ll that was passed to this grid cell at a previous step and will result in the current fi ll value potentially increasing above 1 (an issue that will be handled later). The next major step is to send fi ll to the bottom neighbor given that the bottom neighbor (neighbor with a lower y-index value) has space (fi ll reqDiff then 14:.append(gcn) 15:end if 16:end for 17: transferRate = 0.08 # a percentage of fi ll 18:numAvailable = .size() 19:if numAvailable 1 then 20: amtToLose = fi ll transferRate 21:amtToDist = amtToLose / numAvailable 22:for gcn do 23: .append( (gcn, amtToDist ) ) 24:end for 25: fi ll = fi ll - amtToLose 26:else 27:# no outgoing cells 28: if gc is NOT at topmost level AND fi ll 1 then 29: gc.SendFillToNeighborAbove(fi ll) 30:end if 31: fi ll capped off to 1 32:end if agent constraints added to each cell, the dirt or terrain is further adjusted. IV. AGENTMODEL In this section we will detail aspects of the agent model that we use in our system. This include how the agent is modeled, motion that is available to agent, actions that it can take that may infl uence the underlying grid, and a description of the agent constraints. A. Motion We are considering a very basic model for the pushing agent. This consists of a position, orientation, and forward velocity or s = p,velf. The position p is a three dimensional position, x,y,z, on the surface of the terrain. After updating the agents position at each time step, the surface position on the grid is determined and the y value of p is updated. The orientation, , is a single value representing the rotation about the y-axis and velfis a scalar value for the agents forward velocity. The update step for the agent for a time step dt is given as follows: vel = velf cos(),sin() p = p + dt vel ysurf=grid.GetPositionOnSurface(px,py) py= ysurf This allows the modeling of motion on the terrain in a direction given by at a speed of velf. For motion that solely requires the agent to orient toward a target location the value is adjusted toward the desired direction. This aspect will be discuss more in Sec. V. B. Actions We utilize three different actions the agent can be under during navigation. These three actions allow the agent to move over the terrain, dig into the terrain, and push dirt in front of