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+method%252C+which+considers+chance+constraints+on+system+states.+The+proposed+belief-space+stochastic+MPPI+(BSS-MPPI)+applies+Monte-Carlo+sampling+to+evaluate+state+distributions+resulting+from+underlying+systematic+disturbances%252C+and+utilizes+a+Control+Barrier+Function+(CBF)+inspired+heuristic+in+belief+space+to+fulfill+the+specified+chance+constraints.+Compared+to+several+previous+stochastic+predictive+control+methods%252C+our+approach+applies+to+general+nonlinear+dynamics+without+requiring+the+computationally+expensive+system+linearization+step.+Moreover%252C+the+BSS-MPPI+controller+can+solve+optimization+problems+without+limiting+the+form+of+the+objective+function+and+chance+constraints.+By+multi-threading+the+sampling+process+using+a+GPU%252C+we+can+achieve+fast+real-time+planning+for+time-+and+safety-critical+tasks+such+as+autonomous+racing.+Our+results+on+a+realistic+race-car+simulation+study+show+significant+reductions+in+constraint+violation+compared+to+some+of+the+prior+MPPI+approaches%252C+while+being+comparable+in+computation+times.&cdnurl=https%3a%2f%2fth.bing.com%2fth%2fid%2fR.89c791e5fc9897c0b37672503cb94b7f%3frik%3d1DRQtBkhHXQH0Q%26pid%3dImgRaw%26r%3d0&exph=630&expw=1200&q=Chance+Model+Example&FORM=IRPRST&ck=24902972F24236CD6B89DBFCC73B7DF3&selectedIndex=9&itb=0)
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