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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2018-03-16</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001652522</rptOwnerCik>
            <rptOwnerName>Hudson Executive Capital LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>570 LEXINGTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>35TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001700567</rptOwnerCik>
            <rptOwnerName>HEC Management GP LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>570 LEXINGTON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>35TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11336154</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Series A Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.25</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2018-03-16</value>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10800000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Warrant</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.40</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2018-09-16</value>
            </exerciseDate>
            <expirationDate>
                <value>2028-03-16</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4725000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">In addition to Hudson Executive Capital LP, a Delaware limited partnership (&quot;Hudson Executive&quot;), this Form 3 is being filed jointly by HEC Management GP LLC, a Delaware limited liability company (&quot;Management GP&quot; and, together with Hudson Executive, the &quot;Reporting Persons&quot;), which has the same business address as Hudson Executive and may be deemed to have a pecuniary interest in the securities beneficially reported on this Form 3 (the &quot;Subject Securities&quot;).</footnote>
        <footnote id="F2">Hudson Executive, as the investment adviser to certain affiliated investment funds, may be deemed to be the beneficial owner of the Subject Securities for purposes of Rule 16a 1(a) under the Securities Exchange Act of 1934. Management GP, as the general partner of Hudson Executive, may be deemed to be the beneficial owner of the Subject Securities for purposes of Rule 16a-1(a).</footnote>
        <footnote id="F3">Each of the Reporting Persons disclaims any beneficial ownership of any of the Subject Securities, except to the extent of any pecuniary interest therein.</footnote>
        <footnote id="F4">The preferred stock is perpetual and therefore has no expiration date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>HUDSON EXECUTIVE CAPITAL LP, By: HEC Management GP, its general partner, By: /s/ Douglas L. Braunstein, Name: Douglas L. Braunstein, Title: Managing Member</signatureName>
        <signatureDate>2018-03-20</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>HEC MANAGEMENT GP, By: /s/ Douglas L. Braunstein, Name: Douglas L. Braunstein, Title: Managing Member</signatureName>
        <signatureDate>2018-03-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
