{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44820,"title":"Relative pose in 2D: problem 2","description":"We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\r\nWith respect to the robot's coordinate frame, the world frame origin is at a distance of 67.2m in the x-direction and 32.4m in the y-direction, and at a bearing angle of 42 degrees.\r\nWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eWe consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWith respect to the robot's coordinate frame\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, the world frame origin is at a distance of 67.2m in the x-direction and 32.4m in the y-direction, and at a bearing angle of 42 degrees.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = your_fcn_name()\r\n  % return a 3x3 matrix describing the robot's pose\r\n  T = [];\r\nend","test_suite":"%%\r\nT = your_fcn_name;\r\nassert(all(size(T)==3), 'The matrix must be 3x3');\r\nassert(isreal(T), 'The matrix must be real, not complex');\r\n\r\n%% bottom row\r\nT = your_fcn_name;\r\nassert(isequal(T(3,:), [0 0 1]), 'The bottom row of the homogeneous transformation matrix is not correct')\r\n\r\n%% x coordinate\r\nT = your_fcn_name;\r\nassert(abs(T(1,3)+71.619164)\u003c1e-4, 'The representation of the x-coordinate is not correct')\r\n\r\n%% y coordinate\r\nT = your_fcn_name;\r\nassert(abs(T(2,3)-20.88768)\u003c1e-4, 'The representation of the y-coordinate is not correct')\r\n\r\n%% valid rotation matrix\r\nT = your_fcn_name;\r\nR = T(1:2,1:2);\r\nassert( abs(det(R)-1) \u003c 0.01, 'The determinant of the rotation submatrix is not correct')\r\n\r\n%% correct rotation matrix\r\nT = your_fcn_name;\r\nR = T(1:2,1:2);\r\nassert( abs(atan2d(R(2,1), R(1,1)) + 42) \u003c 0.1, 'The rotation matrix is not correct, check your calculation of the heading SSW and whether you are using radians or degrees')\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":13332,"edited_by":26769,"edited_at":"2022-04-12T14:43:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":111,"test_suite_updated_at":"2022-04-12T14:43:28.000Z","rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-06T08:01:07.000Z","updated_at":"2026-05-24T22:49:57.000Z","published_at":"2019-01-06T08:10:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWith respect to the robot's coordinate frame\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the world frame origin is at a distance of 67.2m in the x-direction and 32.4m in the y-direction, and at a bearing angle of 42 degrees.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44819,"title":"Relative pose in 2D: problem 1","description":"We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north.  There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\r\n\r\n*With respect to the world frame origin* , the robot's centre is at a distance of 123m in the x-direction and -74.6m in the y-direction.  The car's heading angle is exactly SSW.\r\n\r\nWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.*","description_html":"\u003cp\u003eWe consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north.  There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\u003c/p\u003e\u003cp\u003e\u003cb\u003eWith respect to the world frame origin\u003c/b\u003e , the robot's centre is at a distance of 123m in the x-direction and -74.6m in the y-direction.  The car's heading angle is exactly SSW.\u003c/p\u003e\u003cp\u003eWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.*\u003c/p\u003e","function_template":"function T = user_function()\r\n  % return a 3x3 matrix describing the pose\r\n  T = [];\r\nend","test_suite":"%%\r\nT = user_function\r\n\r\nassert(all(size(T)==3), 'The matrix must be 3x3');\r\nassert(isreal(T), 'The matrix must be real, not complex');\r\n\r\n%% bottom row\r\nT = user_function\r\nassert(isequal(T(3,:), [0 0 1]), 'The bottom row of the homogeneous transformation matrix is not correct')\r\n\r\n%% x coordinate\r\nT = user_function\r\nassert(isequal(T(1,3),123), 'The representation of the x-coordinate is not correct')\r\n\r\n%% y coordinate\r\nT = user_function\r\nassert(isequal(T(2,3),-74.6), 'The representation of the y-coordinate is not correct')\r\n\r\n%% valid rotation matrix\r\nT = user_function\r\nR = T(1:2,1:2);\r\nassert( abs(det(R)-1) \u003c 0.01, 'The determinant of the rotation submatrix is not correct')\r\n\r\n%% correct rotation matrix\r\nT = user_function\r\nR = T(1:2,1:2);\r\nassert( abs(atan2d(R(2,1), R(1,1)) + 112.5) \u003c 0.1, 'The rotation matrix is not correct, check your calculation of the heading SSW and whether you are using radians or degrees')","published":true,"deleted":false,"likes_count":3,"comments_count":7,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":176,"test_suite_updated_at":"2019-01-20T07:53:15.000Z","rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-06T07:56:12.000Z","updated_at":"2026-05-24T22:49:29.000Z","published_at":"2019-01-06T08:55:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWith respect to the world frame origin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e , the robot's centre is at a distance of 123m in the x-direction and -74.6m in the y-direction. The car's heading angle is exactly SSW.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"problems":[{"id":44820,"title":"Relative pose in 2D: problem 2","description":"We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\r\nWith respect to the robot's coordinate frame, the world frame origin is at a distance of 67.2m in the x-direction and 32.4m in the y-direction, and at a bearing angle of 42 degrees.\r\nWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eWe consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWith respect to the robot's coordinate frame\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, the world frame origin is at a distance of 67.2m in the x-direction and 32.4m in the y-direction, and at a bearing angle of 42 degrees.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = your_fcn_name()\r\n  % return a 3x3 matrix describing the robot's pose\r\n  T = [];\r\nend","test_suite":"%%\r\nT = your_fcn_name;\r\nassert(all(size(T)==3), 'The matrix must be 3x3');\r\nassert(isreal(T), 'The matrix must be real, not complex');\r\n\r\n%% bottom row\r\nT = your_fcn_name;\r\nassert(isequal(T(3,:), [0 0 1]), 'The bottom row of the homogeneous transformation matrix is not correct')\r\n\r\n%% x coordinate\r\nT = your_fcn_name;\r\nassert(abs(T(1,3)+71.619164)\u003c1e-4, 'The representation of the x-coordinate is not correct')\r\n\r\n%% y coordinate\r\nT = your_fcn_name;\r\nassert(abs(T(2,3)-20.88768)\u003c1e-4, 'The representation of the y-coordinate is not correct')\r\n\r\n%% valid rotation matrix\r\nT = your_fcn_name;\r\nR = T(1:2,1:2);\r\nassert( abs(det(R)-1) \u003c 0.01, 'The determinant of the rotation submatrix is not correct')\r\n\r\n%% correct rotation matrix\r\nT = your_fcn_name;\r\nR = T(1:2,1:2);\r\nassert( abs(atan2d(R(2,1), R(1,1)) + 42) \u003c 0.1, 'The rotation matrix is not correct, check your calculation of the heading SSW and whether you are using radians or degrees')\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":13332,"edited_by":26769,"edited_at":"2022-04-12T14:43:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":111,"test_suite_updated_at":"2022-04-12T14:43:28.000Z","rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-06T08:01:07.000Z","updated_at":"2026-05-24T22:49:57.000Z","published_at":"2019-01-06T08:10:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWith respect to the robot's coordinate frame\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the world frame origin is at a distance of 67.2m in the x-direction and 32.4m in the y-direction, and at a bearing angle of 42 degrees.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44819,"title":"Relative pose in 2D: problem 1","description":"We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north.  There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\r\n\r\n*With respect to the world frame origin* , the robot's centre is at a distance of 123m in the x-direction and -74.6m in the y-direction.  The car's heading angle is exactly SSW.\r\n\r\nWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.*","description_html":"\u003cp\u003eWe consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north.  There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\u003c/p\u003e\u003cp\u003e\u003cb\u003eWith respect to the world frame origin\u003c/b\u003e , the robot's centre is at a distance of 123m in the x-direction and -74.6m in the y-direction.  The car's heading angle is exactly SSW.\u003c/p\u003e\u003cp\u003eWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.*\u003c/p\u003e","function_template":"function T = user_function()\r\n  % return a 3x3 matrix describing the pose\r\n  T = [];\r\nend","test_suite":"%%\r\nT = user_function\r\n\r\nassert(all(size(T)==3), 'The matrix must be 3x3');\r\nassert(isreal(T), 'The matrix must be real, not complex');\r\n\r\n%% bottom row\r\nT = user_function\r\nassert(isequal(T(3,:), [0 0 1]), 'The bottom row of the homogeneous transformation matrix is not correct')\r\n\r\n%% x coordinate\r\nT = user_function\r\nassert(isequal(T(1,3),123), 'The representation of the x-coordinate is not correct')\r\n\r\n%% y coordinate\r\nT = user_function\r\nassert(isequal(T(2,3),-74.6), 'The representation of the y-coordinate is not correct')\r\n\r\n%% valid rotation matrix\r\nT = user_function\r\nR = T(1:2,1:2);\r\nassert( abs(det(R)-1) \u003c 0.01, 'The determinant of the rotation submatrix is not correct')\r\n\r\n%% correct rotation matrix\r\nT = user_function\r\nR = T(1:2,1:2);\r\nassert( abs(atan2d(R(2,1), R(1,1)) + 112.5) \u003c 0.1, 'The rotation matrix is not correct, check your calculation of the heading SSW and whether you are using radians or degrees')","published":true,"deleted":false,"likes_count":3,"comments_count":7,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":176,"test_suite_updated_at":"2019-01-20T07:53:15.000Z","rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-06T07:56:12.000Z","updated_at":"2026-05-24T22:49:29.000Z","published_at":"2019-01-06T08:55:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWith respect to the world frame origin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e , the robot's centre is at a distance of 123m in the x-direction and -74.6m in the y-direction. The car's heading angle is exactly SSW.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a 3x3 matrix homogeneous transformation matrix that expresses the pose of the robot frame {B} with respect to the world frame {O}.*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"errors":[],"facets":[[{"value":"Fundamentals of robotics: 2D problems","count":2,"selected":false}],[{"value":"medium","count":2,"selected":false}]],"term":"tag:\"orientation\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}