<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-06-22</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001528557</issuerCik>
        <issuerName>Corindus Vascular Robotics, Inc.</issuerName>
        <issuerTradingSymbol>CVRS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000313216</rptOwnerCik>
            <rptOwnerName>KONINKLIJKE PHILIPS NV</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>PHILIPS CENTER, AMSTELPLEIN 2, 1096 BC</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>AMSTERDAM</rptOwnerCity>
            <rptOwnerState>P7</rptOwnerState>
            <rptOwnerZipCode></rptOwnerZipCode>
            <rptOwnerStateDescription>NETHERLANDS</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.0001 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2019-05-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>27649</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>2.17</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>26449007</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.0001 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2019-10-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
                <footnoteId id="F6"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>26449007</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>4.28</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-qualified stock option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.68</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-10-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
                <footnoteId id="F7"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>17857</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>2.60</value>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F7"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>17857</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The common stock represents shares issuable upon vesting of restricted stock units (&quot;RSUs&quot;) granted to Nathan Harrington in his capacity as a director of the Issuer as part of his 2019 annual equity award. The RSUs provide for vesting in quarterly installments on August 3, 2019, November 3, 2019, February 3, 2020 and May 3, 2020, subject to Mr. Harrington's continuous service with the Issuer</footnote>
        <footnote id="F2">Includes shares of common stock related to RSUs granted to Mr. Harrington in his capacity as a director of the Issuer as part of his 2017 and 2018 annual equity awards.</footnote>
        <footnote id="F3">These securities were held directly by Mr. Harrington, an employee of the reporting person, as compensation for his service as a director of the Issuer. Pursuant to Mr. Harrington's arrangement with the reporting person as his employer, any compensation received by Mr. Harrington during his service as a director of the Issuer was for the benefit of the reporting person and, as such, Mr. Harrington transferred his securities to the reporting person for no consideration.</footnote>
        <footnote id="F4">Pursuant to the Agreement and Plan of Merger, dated as of August 7, 2019 (the &quot;Merger Agreement&quot;), by and among the Issuer, Siemens Medical Solutions USA, Inc., a Delaware corporation (&quot;SMS USA&quot;) and Corpus Merger, Inc., a Delaware corporation and a wholly owned subsidiary of SMS USA, Merger Sub was merged with and into the Issuer (the &quot;Merger&quot;), with the Issuer continuing as the surviving corporation and a wholly owned subsidiary of SMS USA.</footnote>
        <footnote id="F5">Pursuant to the Merger Agreement, at the effective time of the Merger, each share of Issuer common stock, par value $0.0001, was cancelled and converted into the right to receive an amount in cash equal to $4.28, without interest and less any applicable withholding taxes.</footnote>
        <footnote id="F6">Pursuant to the Merger Agreement, at the effective time of the Merger, each RSU, whether vested or unvested, was cancelled and converted into the right to receive a cash payment (without interest and less any applicable withholding taxes) equal to the product of (i) $4.28 and (ii) the number of shares of Issuer common stock underlying the award as of the effective time of the Merger.</footnote>
        <footnote id="F7">Pursuant to the Merger Agreement, at the effective time of the Merger, each option to purchase Issuer common stock, whether vested or unvested, was cancelled and converted into the right to receive a cash payment (without interest and less any applicable withholding taxes) equal to the product of (i) the excess, if any, of $4.28 over the per share exercise price of such option, and (ii) the number of shares of Issuer common stock subject to such option as of the effective time of the Merger. Options having an exercise price per share equal to or exceeding $4.28 were cancelled without payment.</footnote>
    </footnotes>

    <remarks>Mr. Harrington is an employee of the reporting person and served as a director of the Issuer until the consummation of the transaction contemplated by the Merger Agreement. As a result, during Mr. Harrington's tenure as a director of the Issuer, the reporting person may have been deemed a director by deputization for the purposes of Section 16 of the Securities Exchange Act of 1934, as amended.</remarks>

    <ownerSignature>
        <signatureName>/s/ Abhijit Bhattacharya, Chief Financial Officer</signatureName>
        <signatureDate>2019-10-31</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Marnix van Ginneken, Chief Legal Officer</signatureName>
        <signatureDate>2019-10-31</signatureDate>
    </ownerSignature>
</ownershipDocument>
