Robotics

Built-in Activity and Movement Planning (TAMP) in robotics


Within the earlier publish, we launched process planning in robotics. This discipline broadly includes a set of planning methods which can be domain-independent: That’s, we are able to design a website which describes the world at some (sometimes excessive) degree of abstraction, utilizing some modeling language like PDDL. Nevertheless, the planning algorithms themselves will be utilized to any area that may be modeled in that language, and critically, to unravel any legitimate downside specification inside that area.

The important thing takeaway of the final publish was that process planning is finally search. These search issues are sometimes difficult and develop exponentially with the scale of the issue, so it’s no shock that process planning is commonly symbolic: There are comparatively few attainable actions to select from, with a comparatively small set of finite parameters. In any other case, search is prohibitively costly even within the face of intelligent algorithms and heuristics.

Bridging the hole between this summary planning area and the true world, which we deeply care about in robotics, is difficult. In our instance of a cell robotic navigating a family surroundings, this may look as follows: On condition that we all know two rooms are related, a plan that takes our robotic from room A to room B is assured to execute efficiently. After all, this isn’t essentially true. We’d give you a wonderfully legitimate summary plan, however then fail to generate a dynamically possible movement plan by a slender hallway, or fail to execute a wonderfully legitimate movement plan on our actual robotic {hardware}.

That is the place Activity and Movement Planning (TAMP) is available in. What if our planner spends extra effort deliberating about extra concrete points of a plan earlier than executing it? This presents a key tradeoff in additional up-front computation, however a decrease threat of failing at runtime. On this publish we’ll discover a couple of issues that differentiate TAMP from “plain” process planning, and dive into some detailed examples with the pyrobosim and PDDLStream software program instruments.

Some motivating examples

Earlier than we formalize TAMP additional, let’s take into account some tough examples you may encounter with purely symbolic planning in robotics functions.

On this first instance, our objective is to select up an apple. In purely symbolic planning the place all actions have the identical value, there is no such thing as a distinction in navigating to table0 and table1, each of which have apples. Nevertheless, you’ll discover that table0 is in an unreachable location. Moreover, if we determine to embed navigation actions with a heuristic value corresponding to straight-line distance from the place to begin, our heuristic under will favor table0 as a result of it’s nearer to the robotic’s beginning place than table1.

It wouldn’t be till we attempt to refine our plan — for instance, utilizing a movement planner to seek for a legitimate path to table0 within the unreachable room — that we’d fail, must replace our planning area to someway flag that main_room and unreachable are disconnected, after which replan with this new data.

Pathological process planning instance for goal-directed navigation.
Each table0 and table1 can result in fixing the objective specification of holding an apple, however table0 is totally unreachable.

On this second instance, we wish to place a banana on a desk. As with the earlier instance, we might select to put this object on both desk0 or desk1. Nevertheless, within the absence of extra data — and particularly if we proceed to deal with close by areas as decrease value — we could plan to put banana0 on desk0 and fail to execute at runtime due to the opposite obstacles.

Right here, some various options would come with putting banana0 on desk1, or transferring one of many different objects (water0 or water1) out of the way in which to allow banana0 to suit on desk0. Both approach, we want some notion of collision checking to allow our planner to get rid of the seemingly optimum, however in follow infeasible, plan of merely putting the thing on desk0.

Pathological process planning instance for object manipulation.
Inserting banana0 on both desk0 or desk1 will fulfill the objective, however desk0 has different objects that will result in collisions. So, banana0 should both positioned on desk1, or the objects have to be rearranged and/or moved elsewhere to permit banana0 to suit on desk0.

In each instances, what we’re lacking from our purely symbolic process planner is the flexibility to contemplate the feasibility of summary actions earlier than spitting out a plan and hoping for the very best. Particularly for embodied brokers corresponding to robots, which transfer within the bodily world, symbolic plans have to be made concrete by movement planning. As seen in these two examples, what if our process planner additionally required the existence of a selected path to maneuver between two areas, or a selected pose for putting objects in a cluttered area?

What’s Activity and Movement Planning?

In our examples, the core situation is that if our process planning area is just too summary, a seemingly legitimate plan is more likely to fail down the road after we name a totally decoupled movement planner to strive execute some portion of that plan. So, process and movement planning is precisely as its identify states — collectively occupied with duties and movement in a single planner. As Garrett et al. put it of their 2020 survey paper, “TAMP really lies between discrete “high-level” process planning and steady “low-level” movement planning”.

Nevertheless, there’s no free lunch. When contemplating all of the wonderful particulars up entrance in deliberative planning, search turns into costly in a short time. In symbolic planning, an motion could have a discrete, finite listing of attainable targets (let’s say someplace round 5-10), so it might be cheap to exhaustively search over these and discover the one parameter that’s optimum in accordance with our mannequin. Once we begin occupied with detailed movement plans which have a steady parameter area spanning infinite attainable options, this turns into intractable. So, a number of approaches to TAMP will apply sampling-based methods to make planning work in steady motion areas.

One other approach to make sure TAMP is sensible is to leverage hierarchy. One widespread method for breaking down symbolic planning into manageable items is Hierarchical Activity Networks (HTNs). In these 2012 lecture slides, Nilufer Onder mentions “It could be a waste of time to assemble plans from particular person operators. Utilizing the built-in hierarchy helps escape from exponential explosion.” An instance of hierarchical planning is proven within the diagram under. Utilizing this diagram, you possibly can discover the advantages of hierarchy; for instance, this planner would by no means must even take into account tips on how to open a door if the summary plan didn’t require happening the hallway.

An instance of hierarchical planning for a robotic, the place high-level, or summary, plans for a robotic might be refined into lower-level, or concrete, actions.
Supply: Automated Planning and Performing (2016)

Hierarchical planning is nice in that it helps prune infeasible plans earlier than spending time producing detailed, low-level plans. Nevertheless, on this area the legendary downward refinement property is commonly cited. To straight quote the 1991 paper by Bacchus and Yang, this property states that “given {that a} concrete-level answer exists, each summary answer will be refined to a concrete-level answer with out backtracking throughout summary ranges”. This isn’t all the time (and I might argue not often) achievable in robotics, so backtracking in hierarchical planning is essentially unavoidable.

To this finish, one other technique behind TAMP has to do with dedication in sampling parameters throughout search. Within the literature, you will note many equal phrases thrown round, however I discover the primary distinction is between the next methods:

  • Early-commitment (or binding) methods will pattern motion parameters from steady area earlier than search, successfully changing the issue to a purely discrete process planning downside.
  • Least-commitment (or optimistic) methods will as an alternative give you a purely symbolic plan skeleton. If that skeleton is possible, then the mandatory parameter placeholders are crammed by sampling.

Flowcharts representing two excessive sorts of sampling-based TAMP.
*H-CSP = hybrid constraint satisfaction downside
Supply: Garrett et al. (2020), Built-in Activity and Movement Planning

Each methods have benefits and drawbacks, and in follow trendy TAMP strategies will mix them not directly that works for the sorts of planning domains and issues being thought-about. Additionally, observe that within the diagram above each methods have a loop again to the start when an answer isn’t discovered; so backtracking stays an unavoidable a part of planning.

One key paper that demonstrated the stability of symbolic search and sampling was Sampling-based Movement and Symbolic Motion Planner (SMAP) by Plaku and Hager in 2010. Across the similar time, in 2011, Leslie Kaelbling and Tomás Lozano-Pérez offered Hierarchical Planning within the Now (HPN), which mixed hierarchy and sampling-based methods for TAMP. Nevertheless, the authors themselves admitted the sampling half left one thing to be desired. There’s a nice quote on this paper which foreshadows a few of the different work that will come out of their lab:

“As a result of our domains are infinite, we can not take into account all instantiations of the operations. Our present implementation of suggesters solely considers a small variety of attainable instantiations of the operations. We might recuperate the comparatively weak properties of probabilistic completeness by having the suggesters be mills of an infinite stream of samples, and managing the search as a non-deterministic program over these streams.”

– Leslie pack kaelbling and Tomás Lozano-Pérez (2011), Hierarchical planning within the now.

Instantly following this quote is the work their scholar Caelan Garrett took on — first within the creation of STRIPStream in 2017 after which PDDLStream in 2018. The astute reader can have seen that PDDLStream is the precise software program utilized in these weblog posts, so take this “literature evaluation” with this bias in thoughts, and maintain studying if you wish to be taught extra about TAMP with this particular software.

If you wish to know extra about TAMP normally, I’ll refer you to 2 current survey papers that I discovered helpful:

Cell robotic instance, revisited

As an instance the advantages of built-in TAMP, we’ll proceed the identical cell robotics instance from the earlier publish. On this downside,

  • The robotic’s objective is to put the apple on the desk.
  • Navigation now requires arising with a objective pose (which is a steady parameter), as effectively the precise path from begin to objective. For this instance, we’re utilizing a Quickly-exploring Random Tree (RRT), however you would swap for another path-finding algorithm.
  • Inserting an object now requires sampling a legitimate pose that’s inside the location floor polygon and doesn’t collide with different objects on that floor.

As you learn the next listing explaining this downside, be sure to scroll by the slideshow under to get a visible illustration.

STEP 1: Wanting on the state of the world, you possibly can see how a purely symbolic process planner would output a comparatively easy plan: choose the apple, transfer to the desk, and place the apple on the desk. Within the context of TAMP, this now represents a plan skeleton which a number of parameters which can be but to be crammed — particularly,

  • ?pt is the pose of the robotic when navigating to the desk
  • ?path is the precise output of our movement planner to get to ?pt
  • ?pa-1 is the brand new pose of the apple when positioned on the desk (which follows from its preliminary pose ?pa-0)


STEP 2
: To make the issue slightly easier, we made it such that each location has a discrete, finite set of attainable navigation areas comparable to the perimeters of its polygon. So wanting on the desk location, you see there are 4 attainable navigation poses pt-T, pt-B, pt-L, and pt-R comparable to the highest, backside, left, and proper sides, respectively. Since this set of areas is comparatively small, we are able to pattern these parameters up entrance (or eagerly) firstly of search.

STEP 3: Our transfer motion can now have totally different instantiations for the objective pose ?pt which can be enumerated throughout search. That is in distinction with the ?path argument, which should be sampled by calling our RRT planner. We don’t wish to do that eagerly as a result of the area of paths is steady, so we favor to defer sampling of this parameter. If our motion has a value related to the size of a path, we might think about that the lowest-cost motion can be to navigate to the left facet of the desk (pt-L), and a few randomly sampled path (path42) could describe how we get there.

STEP 4: Subsequent comes the place motion, which now should embrace a legitimate collision-free pose for the apple on the desk. Due to how we arrange our downside, our robotic can not discover a legitimate placement pose when approaching from the left facet of the desk. So, we should backtrack.

STEP 5: After backtracking, we have to discover an alternate navigation pose for the desk (?pt). Given the environment, the one different possible location is the underside facet of the desk (pt-b), because the partitions block the robotic from the highest and proper sides and it might be not possible to discover a legitimate path with our RRT. Nevertheless, when the robotic is on the backside facet of the desk, it could actually additionally pattern a legitimate placement pose! In our instance, the placeholder ?pa-1 is due to this fact glad with some randomly sampled pose pa29.

STEP 6: … And there you could have it! A sound plan that defines a sequence of symbolic actions (choose, transfer, place) together with the mandatory navigation pose, path to that pose, and placement location for the apple. It’s not optimum, however it’s probabilistically full!

(1/6) By being optimistic about all the continual parameters associated to movement, we are able to attain a possible objective state with relative ease.

(2/6) For the reason that navigation poses across the desk and the desk are finite, we are able to pattern them eagerly; that’s, we enumerate all choices up entrance in planning.

(3/6) As soon as we decide to a navigation pose across the desk, we are able to proceed filling in our plan by sampling a possible trajectory from the robotic’s present pose to the goal pose on the desk.

(4/6) Subsequent, we have to pattern a placement pose for the apple. Suppose on this case we fail to pattern a collision-free answer primarily based on the robotic’s present location.

(5/6) This implies we have to backtrack and take into account a unique navigation pose, thereby a unique movement plan to this new pose.

(6/6) From this new pose, though the trajectory is longer and due to this fact higher-cost, we are able to pattern a legitimate placement pose for the apple and eventually full our process and movement plan.

Now, suppose we alter the environment such that we are able to solely method the desk from the left facet, so there is no such thing as a approach to straight discover a legitimate placement pose for the apple. Utilizing the identical planner, we must always finally converge on a process and movement plan that rearranges the objects world — that’s, it requires transferring one of many different objects on the desk to make room for the apple.

Implementing TAMP with PDDLStream

We are going to now revisit our pathological examples from the start of this publish. To do that, we’ll use PDDLStream for planning and pyrobosim as a easy simulation platform. For fast background on PDDLStream, you might consult with this video.

The important thing thought behind PDDLStream is that it extends PDDL with a notion of streams (bear in mind the sooner quote from the Hierarchical Planning within the Now paper?). Streams are generic, user-defined Python features that pattern steady parameters corresponding to a legitimate pattern certifies that stream and offers any vital predicates that (often) act as preconditions for actions. Additionally, PDDLStream has an adaptive method that balances exploration (looking for discrete process plans) vs. exploitation (sampling to fill in steady parameters).

Objective-directed navigation

We will use PDDLStream to reinforce our transfer motion such that it contains metric particulars in regards to the world. As we noticed in our illustrative instance, we now should issue within the begin and objective pose of our robotic, in addition to a concrete path between these poses.

As further preconditions for this motion, we should be sure that:

  • The navigation pose is legitimate given the goal location (NavPose)
  • There should be a legitimate path from the begin to objective pose (Movement)

Moreover, we’re capable of now use extra practical prices for our motion by calculating the precise size of our path produced by the RRT! The separate file describing the streams for this motion could look as follows. Right here, the s-navpose stream certifies the NavPose predicate and the s-motion stream certifies the Movement predicate.

The Python implementations for these features would then look one thing like this. Discover that the get_nav_poses perform returns a finite set of poses, so the output is an easy Python listing. However, sample_motion can constantly spit out paths from our RRT, and it applied as a generator:

Placing this new area and streams collectively, we are able to remedy our first pathological instance from the introduction. Within the plan under, the robotic will compute a path to the farther away, however reachable room to select up an apple and fulfill the objective.

Object manipulation

Equally, we are able to lengthen our place motion to now embrace the precise poses of objects on the earth. Particularly,

  • The ?placepose argument defines the goal pose of the thing.
  • The Placeable predicate is licensed by a s-place stream.
  • The IsCollisionFree predicate is definitely a derived predicate that checks particular person collisions between the goal object and all different objects at that location.
  • Every particular person collision examine is set by the CollisionFree predicate, which is licensed by a t-collision-free steam.

The Python implementation for sampling placement poses and checking for collisions could look as follows. Right here, sample_place_pose is our generator for placement poses, whereas test_collision_free is an easy Boolean (true/false) examine.

By increasing our area to cause in regards to the feasibility of object placement, we are able to equally remedy the second pathological instance from the introduction. Within the first video, we’ve got an alternate location desk1 the place the robotic can place the banana and fulfill the objective.

Within the second video, we take away the choice desk1. The identical process and movement planner then produces an answer that includes choosing up one of many objects on desk0 to make room to later place the banana there.

You possibly can think about extending this to a extra practical system — that’s, one that’s not a degree robotic and has an precise manipulator — that equally checks the feasibility of a movement plan for choosing and putting objects. Whereas it wasn’t the primary focus of the work, our Lively Studying of Summary Plan Feasibility work did precisely this with PDDLStream. Particularly, we used RRTs to pattern configuration-space paths for a Franka Emika Panda arm and doing collision-checking utilizing a surrogate mannequin in PyBullet!

Conclusion

On this publish we launched the overall idea of process and movement planning (TAMP). In concept, it’s nice to deliberate extra — that’s, actually suppose extra in regards to the feasibility of plans all the way down to the metric degree — however with that comes extra planning complexity. Nevertheless, this will repay in that it reduces the chance of failing in the midst of executing a plan and having to cease and replan.

We launched 3 basic rules that may make TAMP work in follow:

  • Hierarchy, to find out the feasibility of summary plans earlier than planning at a decrease degree of refinement.
  • Steady parameter areas, and methods like sampling to make this tractable.
  • Least-commitment methods, to give you symbolic plan skeletons earlier than spending time with costly sampling of parameters.

We then dug into PDDLStream as one software for TAMP, which doesn’t do a lot in the way in which of hierarchy, however actually tackles steady parameter areas and least-commitment methods for parameter binding. We went by a couple of examples utilizing pyrobosim, however you possibly can entry the complete set of examples within the pyrobosim documentation for TAMP.

The PDDLStream repository has many extra examples which you could try. And, in fact, there are various different process and movement planners on the market that concentrate on various things — corresponding to hierarchy with out steady parameters, or factoring in different widespread goals corresponding to temporal points and useful resource consumption.

Hope you could have loved these posts! If the instruments proven right here provide you with any cool concepts, I might love to listen to about them, so be happy to succeed in out.


You possibly can learn the unique article at Roboticseabass.com.


Sebastian Castro
is a Senior Robotics Engineer at PickNik.

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