AWS CDKでStepFunctionsを実行するApiGatewayを構築

import * as cdk from 'aws-cdk-lib/core';
import * as apigw from 'aws-cdk-lib/aws-apigateway';
import * as iam from 'aws-cdk-lib/aws-iam';


export class ApigatewayCdkStack extends cdk.Stack {
  constructor(scope: cdk.App, id: string, props?: cdk.StackProps) {
    super(scope, id, props);
    
    // 既存のステートマシンのARNを指定
    const stateMachineArn = 'arn:aws:states:ap-northeast-1:XXXXXXXX:stateMachine:JankenStateMachine';

    // API Gatewayを作成
    const api = new apigw.RestApi(this, 'CdkTestApi', {
      restApiName: 'CdkTestApi',
      description: 'CDK Test',
      endpointConfiguration: {
          types: [apigw.EndpointType.REGIONAL], //エンドポイントタイプ設定
      },
    });

    // API Gatewayにリソース作成
    const startExecutionResource = api.root.addResource(
        'startExecution'
    );
    // リソースにメソッドを追加
    startExecutionResource.addMethod('POST', new apigw.AwsIntegration({
      service: 'states',
      action: 'StartSyncExecution', //同時実行なのでStartSyncExecutionを設定
      options: {
        //実行ロール設定（ここで新規ポリシー、新規ロールを作成している)
        credentialsRole: new iam.Role(this, 'StatesExecutionRole', {
          assumedBy: new iam.ServicePrincipal('apigateway.amazonaws.com'),
          inlinePolicies: {
            StatesExecutionPolicy: new iam.PolicyDocument({
              statements: [
                new iam.PolicyStatement({
                  actions: ['states:StartSyncExecution'], //ここもStartSyncExecutionを設定
                  resources: [stateMachineArn],
                }),
              ],
            }),
          },
        }),	
        //リクエスト本文の簡素化のための設定をする
        requestTemplates: {
          'application/json': `{
            "stateMachineArn": "${stateMachineArn}",
            "input": "$util.escapeJavaScript($input.json('$'))"
          }`,
        },
        //レスポンスの設定、
        //正常終了の場合はレスポンスのマッピングテンプレートに
　　　　 //本文の簡素化のための設定をする
        integrationResponses: [
          {
            statusCode: '200',
            responseTemplates: {
              'application/json': `$util.parseJson($input.json('$.output'))`,
            },
          },
          {
            selectionPattern: '4\\d{2}',
            statusCode: '400',
            responseTemplates: {
              'application/json': `$input.path('$.errorMessage')`,
            },
          },
          {
            selectionPattern: '5\\d{2}',
            statusCode: '500',
            responseTemplates: {
              'application/json': `$input.path('$.errorMessage')`,
            },
          },
        ],
      },
    }), {
      methodResponses: [
        { statusCode: '200' },
        { statusCode: '400' },
        { statusCode: '500' },
      ],

    });
  }
}