advanced lecture 11 6

Multi-Robot Coordination Using a Market-based Approach: 

Multi-Robot Coordination Using a Market-based Approach Gabe Reinstein and Austin Wang 6.834J November 6, 2002

Outline: 

Outline Why multiple robots? Design requirements Other approaches The market-based approach Example: Multi-robot exploration

Source Papers: 

Source Papers Dias, M. B. and Stentz, A. 2001. A Market Approach to Multirobot Coordination. Technical Report, CMU-RI-TR-01-26, Robotics Institute, Carnegie Mellon University. Explains idea of market-based approach Zlot, R. et al. 2002. Multi-Robot Exploration Controlled by a Market Economy. IEEE. Describes a particular implementation of this idea: mapping and exploration with multiple robots

Why Multiple Robots?: 

Why Multiple Robots? Some tasks require a team Robotic soccer Some tasks can be decomposed and divided for efficiency Mapping a large area Many specialists preferable to one generalist Increase robustness with redundancy Teams of robots allow for more varied and creative solutions

A Few Multi-robot Scenarios: 

A Few Multi-robot Scenarios Automated warehouse management Planetary exploration and colonization Automatic construction Robotic cleanup of hazardous sites Agriculture

Outline: 

Outline Why multiple robots? Design requirements Other approaches The market-based approach Example: Multi-robot exploration

A Good Multi-robot System Is:: 

A Good Multi-robot System Is: Robust: no single point of failure Optimized, even under dynamic conditions Quick to respond to changes Able to deal with imperfect communication Able to allocate limited resources Heterogeneous and able to make use of different robot skills

Outline: 

Outline Why multiple robots? Design requirements Other approaches The market-based approach Example: Multi-robot exploration

Basic Approaches: 

Basic Approaches Centralized Attempting optimal plans Distributed Every man for himself Market-based

Centralized Approaches: 

Centralized Approaches Robot team treated as a single “system” with many degrees of freedom A single robot or computer is the “leader” Leader plans optimal actions for group Group members send information to leader and carry out actions

Centralized Methods: Pros: 

Centralized Methods: Pros Leader can take all relevant information into account In theory, coordination can be perfect: Optimal plans possible!

Centralized Methods: Cons: 

Centralized Methods: Cons Computationally hard Intractable for more than a few robots Makes unrealistic assumptions: All relevant info can be transmitted to leader This info doesn’t change during plan construction Result: response sluggish or inaccurate Vulnerable to malfunction of leader Heavy communication load

Distributed Approaches: 

Distributed Approaches Planning responsibility spread over team Each robot basically independent Robots use locally observable information to make their plans

Distributed Methods: Pros: 

Distributed Methods: Pros Fast response to dynamic conditions Little or no communication required Little computation required Smooth response to environmental changes Very robust No single point of failure

Distributed Methods: Cons: 

Distributed Methods: Cons Not all problems can be decomposed well Plans based only on local information Result: solutions are often highly sub-optimal

Outline: 

Outline Why multiple robots? Design requirements Other approaches The market-based approach Example: Multi-robot exploration

Market-based Approach:The Basic Idea: 

Market-based Approach: The Basic Idea Based on the economic model of a free market Each robot seeks to maximize individual “profit” Robots can negotiate and bid for tasks Individual profit helps the common good Decisions are made locally but effects approach optimality Preserves advantages of distributed approach

Analogy To Real Economy: 

Analogy To Real Economy Robots must be self-interested Sometimes robots cooperate, sometimes they compete Individuals reap benefits of their good decisions, suffer consequences of bad ones Just like a real market economy, the result is global efficiency

The Market Mechanism In Detail: Background: 

The Market Mechanism In Detail: Background Consider: A team of robots assembled to perform a particular set of tasks Each robot is a self-interested agent The team of robots is an economy The goal is to complete the tasks while minimizing overall costs

How Do We Determine Profit?: 

How Do We Determine Profit? Profit = Revenue – Cost Team revenue is sum of individual revenues, and team cost is sum of individual costs Costs and revenues set up per application Maximizing individual profits must move team towards globally optimal solution Robots that produce well at low cost receive a larger share of the overall profit

Examples: 

Examples Cost functions may be complex Based on distance traveled Based on time taken Some function of fuel expended, CPU cycles, etc. Revenue based on completion of tasks Reaching a goal location Moving an object Etc.

Prices and Bidding: 

Prices and Bidding Robots can receive revenue from other robots in exchange for goods or services Example: haulage robot If robots can produce more profit together than apart, they should deal with each other If one is good at finding objects and another is good at transporting them, they can both gain

No Communication: 

No Communication

Subcontracting a Task: 

Subcontracting a Task

How Are Prices Determined?: 

How Are Prices Determined? Bidding Robots negotiate until price is mutually beneficial Note: this moves global solution towards optimum Robots can negotiate several deals at once Deals can potentially be multi-party Prices determined by supply and demand Example: If there are a lot of haulers, they won’t be able to command a high price This helps distribute robots among “occupations”

Competition vs. Coordination: 

Competition vs. Coordination Complementary robots will cooperate A grasper and a transporter could offer a combined “pick up and place” service Similar robots will compete This drives prices down This isn’t always true: Subgroups of robots could compete Similar robots could agree to segment the market Several grasping robots might coordinate to move a heavy objects

Leaders: 

Leaders A robot can offer its services as a leader A leader investigates plans for other robots If it finds a way for other robots to coordinate to maximize profit: Uses this profit to bid for the services of the robots Keeps some profit for itself Note that this introduces a notion of centralization Difficult for more than a few robots

Why Is This Good?: 

Why Is This Good? Robust to changing conditions Not hierarchical If a robot breaks, tasks can be re-bid to others Distributed nature allows for quick response Only local communication necessary Efficient resource utilization and role adoption Advantages of distributed system with optimality approaching centralized system

Outline: 

Outline Why multiple robots? Design requirements Other approaches The market-based approach Example: Multi-robot exploration

Multi-Robot Exploration: 

Multi-Robot Exploration Goal: explore and map unknown environment Environment may be hostile and uncertain Communication may be difficult Multiple robots: Cover more territory more quickly Robust if some robots fail Attempt to minimize repeated coverage Key: coordination Maximize information gain, reduce total costs

Previous Work: 

Previous Work Balch and Arkin: communication unnecessary if robots leave physical trace behind Latimer: can provably cover a region with minimal repeated coverage Very high communication requirement Fails if one robot fails Simmons: frontier-based search with bidding Central agent greedily assigns tasks Suboptimal, centralized, high communication Yamauchi: group frontier-based search Highly distributed: local maps and local frontier lists Coordination is limited, repeated coverage possible

Architecture of the Market Approach: 

Architecture of the Market Approach World is represented as a grid Squares are unknown (0), occupied (+), or empty (-) Goals are squares in the grid for a robot to explore Goal points to visit are the main commodity exchanged in market For any goal square in the grid: Cost based on distance traveled to reach goal Revenue based on information gained by reaching goal R = (# of unknown cells near goal) x (weighting factor) Team profit = sum of individual profits When individual robots maximize profit, the whole team gains

Example World: 

Example World

Exploration Algorithm: 

Exploration Algorithm Algorithm for each robot: Generate goals (based on goal selection strategy) If OpExec (human operator) is reachable, check with OpExec to make sure goals are new to colony Rank goals greedily based on expected profit Try to auction off goals to each reachable robot If a bid is worth more than you would profit from reaching the goal yourself (plus a markup), sell it

Exploration Algorithm: 

Exploration Algorithm Once all auctions are closed, explore highest-profit goal Upon reaching goal, generate new goal points Maximum # of goal points is limited Repeat this algorithm until map is complete

Bidding Example: 

Bidding Example R1 auctions goal to R2

Expected vs. Real: 

Expected vs. Real Robots make decisions based on expected profit Expected cost and revenue based on current map Actual profit may be different Unforeseen obstacles may increase cost Once real costs exceed expected costs by some margin, abandon goal Don’t get stuck trying for unreachable goals

Goal Selection Strategies: 

Goal Selection Strategies Possible strategies: Randomly select points, discard if already visited Greedy exploration: Choose goal point in closest unexplored region Space division by quadtree

Benefit of Prices: 

Benefit of Prices Low-bandwidth mechanisms for communicating aggregate information Unlike other systems, map info doesn’t need to be communicated repeatedly for coordination

Information Sharing: 

Information Sharing If an auctioneer tries to auction a goal point already covered by a bidder: Bidder tells auctioneer to update map Removes goal point Robots can sell map information to each other Price negotiated based on information gained Reduces overlapping exploration When needed, OpExec sends a map request to all reachable robots Robots respond by sending current maps OpExec combines the maps by adding up cell values

Experimental Setup: 

Experimental Setup 4 or 5 robots Equipped with fiber optic gyroscopes 16 ultrasonic sensors

Experimental Setup: 

Experimental Setup Three test environments Large room cluttered with obstacles Outdoor patio, with open areas as well as walls and tables Large conference room with tables and 100 people wandering around Took between 5 and 10 minutes to map areas

Experimental Results: 

Experimental Results

Experimental Results: 

Experimental Results

Experimental Results: 

Experimental Results Successfully mapped regions Performance metric (exploration efficiency): Area covered / distance traveled [m2 / m] Market architecture improved efficiency over no communication by a factor of 3.4

Conclusion: 

Conclusion Market-based approach for multi-robot coordination is promising Robustness and quickness of distributed system Approaches optimality of centralized system Low communication requirements Probably not perfect Cost heuristics can be inaccurate Much of this approach is still speculative Some pieces, such as leaders, may be too hard to do