{"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":44823,"title":"Relative points in 2D: problem 1","description":"The 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T. A landmark point is described by a 2x1 coordinate vector P with respect to the world coordinate frame. What is the coordinate of the landmark with respect to the robot?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; 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: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 8px; transform-origin: 383.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T. A landmark point is described by a 2x1 coordinate vector P with respect to the world coordinate frame. What is the coordinate of the landmark with respect to the robot?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function PB = user_function(T, P)\r\n  % Input:  T a 3x3 homogeneous transformation matrix\r\n  %         P a 2x1 vector representing the coordinate of a point\r\n  % Output: PB a 2x1 vector representing the coordinate of a point\r\n  PB = ;\r\nend","test_suite":"%%\r\nth = 2*pi*rand;\r\nt = rand(2,1)*20-10;\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nT = [R t; 0 0 1];\r\nP = rand(2,1)*20-10;\r\n\r\nPB = user_function(T, P);\r\n\r\nassert(all(size(PB) == [2 1]), 'The point should be described by a 2x1 vector')\r\nassert(isreal(PB), 'The point should be described by a vector of real, not complex, numbers');\r\nPBref = R'*P - R'*t;\r\nassert( all(abs(PB-PBref) \u003c 0.001), 'The relative coordinates are not correct')\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":13332,"edited_by":223089,"edited_at":"2023-04-16T17:43:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":111,"test_suite_updated_at":"2023-04-15T16:49:35.000Z","rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-10T01:14:43.000Z","updated_at":"2026-05-24T22:50:28.000Z","published_at":"2020-03-14T23:40:51.000Z","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\u003eThe 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T. A landmark point is described by a 2x1 coordinate vector P with respect to the world coordinate frame. What is the coordinate of the landmark with respect to the robot?\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":44831,"title":"Composing relative poses 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. \r\n\r\nThere is a playing field with a reference frame denoted by {F}.  The rigid-body displacement from {O} to {F} is given by the homogenous transformation |TF| .\r\n\r\nThere 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.  The rigid-body displacement displacement of {B} relative to {F} is given by the homogenous transformation |TB| .\r\n\r\nThe robot carries a laser scanner which reports the range and bearing of landmarks with respect to its coordinate frame {S} with zero bearing angle corresponding to its x-axis.  The scanner is displaced from the centre of the robot and the displacement of frame {S} relative to {B} is given by the homogenous transformation |TS| .\r\n\r\nThere is a landmark with position described by a coordinate vector P with respect to the world coordinate frame {O}.\r\n\r\nWhat is the range and bearing of the landmark as observed by the laser scanner?","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.\u003c/p\u003e\u003cp\u003eThere is a playing field with a reference frame denoted by {F}.  The rigid-body displacement from {O} to {F} is given by the homogenous transformation \u003ctt\u003eTF\u003c/tt\u003e .\u003c/p\u003e\u003cp\u003eThere 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.  The rigid-body displacement displacement of {B} relative to {F} is given by the homogenous transformation \u003ctt\u003eTB\u003c/tt\u003e .\u003c/p\u003e\u003cp\u003eThe robot carries a laser scanner which reports the range and bearing of landmarks with respect to its coordinate frame {S} with zero bearing angle corresponding to its x-axis.  The scanner is displaced from the centre of the robot and the displacement of frame {S} relative to {B} is given by the homogenous transformation \u003ctt\u003eTS\u003c/tt\u003e .\u003c/p\u003e\u003cp\u003eThere is a landmark with position described by a coordinate vector P with respect to the world coordinate frame {O}.\u003c/p\u003e\u003cp\u003eWhat is the range and bearing of the landmark as observed by the laser scanner?\u003c/p\u003e","function_template":"function [bearing, range] = user_function(TF, TB, TS, P)\r\n  % Input:  TF a 3x3 homogeneous transformation matrix\r\n  %         TB a 3x3 homogeneous transformation matrix\r\n  %         TS a 3x3 homogeneous transformation matrix\r\n  %         P a 2x1 vector representing the coordinate of a point\r\n  % Output: bearing, a scalar angle\r\n  %         range, a scalar distance\r\n  bearing = ;\r\n  range = ;\r\nend","test_suite":"th = 2*pi*rand - pi;\r\nt = rand(2,1)*60-30;\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nTF = [R t; 0 0 1];\r\n\r\nth = 2*pi*rand - pi;\r\nt = rand(2,1)*20-10;\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nTB = [R t; 0 0 1];\r\n\r\nth = 30*pi/180;\r\nt = [0.5; -0.3];\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nTS = [R t; 0 0 1];\r\n\r\nP = rand(2,1) * 500 - 250;\r\n\r\nPref = inv(TF * TB * TS) * [P; 1];\r\n[bearingRef,rangeRef] = cart2pol( Pref(1), Pref(2) );\r\n\r\n[bearing, range] = user_function(TF, TB, TS, P);\r\n\r\n%%\r\nassert(isscalar(bearing) \u0026 isreal(bearing), 'Bearing angle must be a real scalar')\r\n%%\r\nassert(isscalar(range) \u0026 isreal(range), 'Range must be a real scalar')\r\n%%\r\nassert(abs(bearing-bearingRef) \u003c 0.001, 'Bearing angle is not correct')\r\n%%\r\nassert(abs(range-rangeRef) \u003c 0.001, 'Range is not correct')\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":"2019-01-10T10:52:52.000Z","rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-10T10:46:31.000Z","updated_at":"2026-05-24T23:09:10.000Z","published_at":"2019-01-10T10:52:52.000Z","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.\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\u003eThere is a playing field with a reference frame denoted by {F}. The rigid-body displacement from {O} to {F} is given by the homogenous transformation\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\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\u003eThere 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. The rigid-body displacement displacement of {B} relative to {F} is given by the homogenous transformation\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\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\u003eThe robot carries a laser scanner which reports the range and bearing of landmarks with respect to its coordinate frame {S} with zero bearing angle corresponding to its x-axis. The scanner is displaced from the centre of the robot and the displacement of frame {S} relative to {B} is given by the homogenous transformation\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\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\u003eThere is a landmark with position described by a coordinate vector P with respect to the world coordinate frame {O}.\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\u003eWhat is the range and bearing of the landmark as observed by the laser scanner?\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":44823,"title":"Relative points in 2D: problem 1","description":"The 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T. A landmark point is described by a 2x1 coordinate vector P with respect to the world coordinate frame. What is the coordinate of the landmark with respect to the robot?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; 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: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 8px; transform-origin: 383.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T. A landmark point is described by a 2x1 coordinate vector P with respect to the world coordinate frame. What is the coordinate of the landmark with respect to the robot?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function PB = user_function(T, P)\r\n  % Input:  T a 3x3 homogeneous transformation matrix\r\n  %         P a 2x1 vector representing the coordinate of a point\r\n  % Output: PB a 2x1 vector representing the coordinate of a point\r\n  PB = ;\r\nend","test_suite":"%%\r\nth = 2*pi*rand;\r\nt = rand(2,1)*20-10;\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nT = [R t; 0 0 1];\r\nP = rand(2,1)*20-10;\r\n\r\nPB = user_function(T, P);\r\n\r\nassert(all(size(PB) == [2 1]), 'The point should be described by a 2x1 vector')\r\nassert(isreal(PB), 'The point should be described by a vector of real, not complex, numbers');\r\nPBref = R'*P - R'*t;\r\nassert( all(abs(PB-PBref) \u003c 0.001), 'The relative coordinates are not correct')\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":13332,"edited_by":223089,"edited_at":"2023-04-16T17:43:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":111,"test_suite_updated_at":"2023-04-15T16:49:35.000Z","rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-10T01:14:43.000Z","updated_at":"2026-05-24T22:50:28.000Z","published_at":"2020-03-14T23:40:51.000Z","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\u003eThe 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T. 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The rigid-body displacement from {O} to {F} is given by the homogenous transformation |TF| .\r\n\r\nThere 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.  The rigid-body displacement displacement of {B} relative to {F} is given by the homogenous transformation |TB| .\r\n\r\nThe robot carries a laser scanner which reports the range and bearing of landmarks with respect to its coordinate frame {S} with zero bearing angle corresponding to its x-axis.  The scanner is displaced from the centre of the robot and the displacement of frame {S} relative to {B} is given by the homogenous transformation |TS| .\r\n\r\nThere is a landmark with position described by a coordinate vector P with respect to the world coordinate frame {O}.\r\n\r\nWhat is the range and bearing of the landmark as observed by the laser scanner?","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.\u003c/p\u003e\u003cp\u003eThere is a playing field with a reference frame denoted by {F}.  The rigid-body displacement from {O} to {F} is given by the homogenous transformation \u003ctt\u003eTF\u003c/tt\u003e .\u003c/p\u003e\u003cp\u003eThere 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.  The rigid-body displacement displacement of {B} relative to {F} is given by the homogenous transformation \u003ctt\u003eTB\u003c/tt\u003e .\u003c/p\u003e\u003cp\u003eThe robot carries a laser scanner which reports the range and bearing of landmarks with respect to its coordinate frame {S} with zero bearing angle corresponding to its x-axis.  The scanner is displaced from the centre of the robot and the displacement of frame {S} relative to {B} is given by the homogenous transformation \u003ctt\u003eTS\u003c/tt\u003e .\u003c/p\u003e\u003cp\u003eThere is a landmark with position described by a coordinate vector P with respect to the world coordinate frame {O}.\u003c/p\u003e\u003cp\u003eWhat is the range and bearing of the landmark as observed by the laser scanner?\u003c/p\u003e","function_template":"function [bearing, range] = user_function(TF, TB, TS, P)\r\n  % Input:  TF a 3x3 homogeneous transformation matrix\r\n  %         TB a 3x3 homogeneous transformation matrix\r\n  %         TS a 3x3 homogeneous transformation matrix\r\n  %         P a 2x1 vector representing the coordinate of a point\r\n  % Output: bearing, a scalar angle\r\n  %         range, a scalar distance\r\n  bearing = ;\r\n  range = ;\r\nend","test_suite":"th = 2*pi*rand - pi;\r\nt = rand(2,1)*60-30;\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nTF = [R t; 0 0 1];\r\n\r\nth = 2*pi*rand - pi;\r\nt = rand(2,1)*20-10;\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nTB = [R t; 0 0 1];\r\n\r\nth = 30*pi/180;\r\nt = [0.5; -0.3];\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nTS = [R t; 0 0 1];\r\n\r\nP = rand(2,1) * 500 - 250;\r\n\r\nPref = inv(TF * TB * TS) * [P; 1];\r\n[bearingRef,rangeRef] = cart2pol( Pref(1), Pref(2) );\r\n\r\n[bearing, range] = user_function(TF, TB, TS, P);\r\n\r\n%%\r\nassert(isscalar(bearing) \u0026 isreal(bearing), 'Bearing angle must be a real scalar')\r\n%%\r\nassert(isscalar(range) \u0026 isreal(range), 'Range must be a real scalar')\r\n%%\r\nassert(abs(bearing-bearingRef) \u003c 0.001, 'Bearing angle is not correct')\r\n%%\r\nassert(abs(range-rangeRef) \u003c 0.001, 'Range is not correct')\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":"2019-01-10T10:52:52.000Z","rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-10T10:46:31.000Z","updated_at":"2026-05-24T23:09:10.000Z","published_at":"2019-01-10T10:52:52.000Z","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.\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\u003eThere is a playing field with a reference frame denoted by {F}. The rigid-body displacement from {O} to {F} is given by the homogenous transformation\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\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\u003eThere 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. The rigid-body displacement displacement of {B} relative to {F} is given by the homogenous transformation\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\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\u003eThe robot carries a laser scanner which reports the range and bearing of landmarks with respect to its coordinate frame {S} with zero bearing angle corresponding to its x-axis. The scanner is displaced from the centre of the robot and the displacement of frame {S} relative to {B} is given by the homogenous transformation\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\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\u003eThere is a landmark with position described by a coordinate vector P with respect to the world coordinate frame {O}.\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\u003eWhat is the range and bearing of the landmark as observed by the laser scanner?\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:\"homogenous transformation\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}