# US 10,442,081 B2 · Device and method for estimating possible existence region of specific state quantity of mobile robot

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- Number: US 10,442,081 B2
- Document ID: US10442081B2
- Status: Granted
- Kind: B2
- Application number: 15/632,729
- Filed: 2017-06-26
- Published: 2018-01-04
- Granted: 2019-10-15
- Earliest claimed: 2016-06-29
- Assignees: Honda Motor Co., Ltd.; The University of Tokyo
- Applicants: Honda Motor Co., Ltd.; The University of Tokyo
- Inventors: Masao Kanazawa; Yoshiki Kanemoto; Shunichi Nozawa; Yohei Kakiuchi; Kei Okada; Masayuki Inaba
- Web page: https://patentgrep.com/patent/US10442081B2

## CPC

- B25J 9/1664: {characterised by motion, path, trajectory planning}
- B62D 57/024: specially adapted for moving on inclined or vertical surfaces (endless-track vehicles for ascending or descending stairs B62D55/075; hand-carts with provision for travelling up or down stairs B62B5/02)
- B62D 57/032: with alternately or sequentially lifted supporting base and legs; with alternately or sequentially lifted feet or skid (B62D57/024 takes precedence)
- B62D 57/02: with ground-engaging propulsion means, e.g. walking members
- B25J: MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES ({manipulators specially adapted for use in surgery A61B34/70; manipulators used in cleaning hollow articles B08B9/04}; manipulators associated with rolling mills B21B39/20; manipulators associated with forging machines B21J13/10; {manipulators associated with picking-up and placing mechanisms B23P19/007}; means for holding wheels or parts thereof B60B30/00; {vehicles with ground-engaging propulsion means, e.g. walking members B62D57/02, B62D57/032; devices for picking-up and depositing articles or materials between conveyors B65G47/90, B65G47/91; manipulators with gripping or holding means for transferring packages B65H67/065}; cranes B66C; {manipulators used in the protection or supervision of pipe-line installations F17D5/00; walking equipment adapted for nuclear steam-generators F22B37/006}; manipulators specially adapted for, or associated with, nuclear reactors G21C; {apparatus used for handling wafers during manufacture or treatment of semiconductor H10P72/50})
- B62D: MOTOR VEHICLES; TRAILERS (steering, or guiding on a desired track, of agricultural machines or implements A01B69/00; wheels, castors, axles, increasing wheel adhesion B60B; vehicle tyres, tyre inflation or tyre changing B60C; connections between vehicles of a train or the like B60D; vehicles for use on rail and road, amphibious or convertible vehicles B60F; suspension arrangements B60G; heating, cooling, ventilating or other air treating devices B60H; windows, windscreens, non-fixed roofs, doors or similar devices, protective coverings for vehicles not in use B60J; propulsion plant arrangements, auxiliary drives, transmissions, controls, instrumentation or dashboards B60K; electric equipment or propulsion of electrically-propelled vehicles B60L; power supply for electrically-propelled vehicles B60M; passenger accommodation not otherwise provided for B60N; adaptations for load transportation or to carry special loads or objects B60P; arrangement of signalling or lighting devices, the mounting or supporting thereof or circuits therefor, for vehicles in general B60Q; vehicles, vehicle fittings or vehicle parts not otherwise provided for B60R; servicing, cleaning, repairing, supporting, lifting, or manoeuvring, not otherwise provided for, B60S; brake arrangements, brake control systems or parts thereof B60T; air-cushion vehicles B60V; motor-cycles, accessories therefor B62J, B62K; testing of vehicles G01M)

## Abstract

An arithmetic processing unit 40 estimates a possible existence region of a specific state quantity by performing polyhedron projection processing for finding a projection region obtained by projecting a convex polyhedron to a subspace representing the specific state quantity, where the convex polyhedron is within a space configured with the contact reaction forces of a plurality of contacting portions (13, 23) of a mobile robot 1 and the specific state quantity as variable components and where the convex polyhedron is specified by a mechanical relation between the contact reaction forces and the specific state quantity and by a linear inequality representing a contact reaction force constraint condition.

## Claims

### Claim 1

A device for estimating a possible existence region of a specific state quantity of a mobile robot which moves by a motion of repeating an air movement and a contact with an external object following the air movement of each of a plurality of contacting portions, wherein the possible existence region is intended for a value of a specific state quantity composed of one or more state quantities among a position of an overall center-of-gravity of the mobile robot, a translational motion state quantity of the overall center of gravity, and a rotational motion state quantity about the overall center of gravity, and wherein the possible existence region is able to satisfy a contact reaction force constraint condition which is a constraint condition related to contact reaction forces acting on the respective contacting portions,
wherein:
the device includes at least one processor configured to function as a polyhedron projection processing section which performs one of multi parametric linear programming processing and processing of repeating linear programming processing more than once, as polyhedron projection processing for finding a projection region obtained by projecting a convex polyhedron to a subspace representing the specific state quantity among variable components, where the convex polyhedron is within a space configured with the contact reaction forces of the plurality of contacting portions and the specific state quantity as the variable components and where the convex polyhedron is specified by a mechanical relation between the contact reaction forces and the specific state quantity and by a linear inequality representing a contact reaction force constraint condition, and the device is configured to output the projection region found by the polyhedron projection processing as an estimated region of the possible existence region,
the specific state quantity includes two state quantities s(1) and s(2); and
the polyhedron projection processing section is configured to perform the following processes 1 to 4 as the polyhedron projection processing:
process 1: find an upper limit value and a lower limit value of the state quantity s(1) able to satisfy the mechanical relation and the contact reaction force constraint condition by the linear programming processing;
process 2: set a plurality of representative values with the upper limit value and the lower limit value of the state quantity s(1) included in a range between the upper limit value and the lower limit value;
process 3: find an upper limit value and a lower limit value of the state quantity s(2) able to satisfy the mechanical relation and the contact reaction force constraint condition by the linear programming processing for all representative values of the state quantity s(1) on the assumption that the value of the state quantity s(1) coincides with one of the plurality of representative values set in the process 2; and
process 4: find a region obtained by convex hull of a plurality of points specified by all respective representative values of the state quantity s(1) and by the upper limit value and the lower limit value of the state quantity s(2) for each representative value of the state quantity s(1) as the projection region.

### Claim 2

A device for estimating a possible existence region of a specific state quantity of a mobile robot which moves by a motion of repeating an air movement and a contact with an external object following the air movement of each of a plurality of contacting portions, wherein the possible existence region is intended for a value of a specific state quantity composed of one or more state quantities among a position of an overall center-of-gravity of the mobile robot, a translational motion state quantity of the overall center of gravity, and a rotational motion state quantity about the overall center of gravity, and wherein the possible existence region is able to satisfy a contact reaction force constraint condition which is a constraint condition related to contact reaction forces acting on the respective contacting portions,
wherein:
the device includes at least one processor configured to function as a polyhedron projection processing section which performs one of multi parametric linear programming processing and processing of repeating linear programming processing more than once, as polyhedron projection processing for finding a projection region obtained by projecting a convex polyhedron to a subspace representing the specific state quantity among variable components, where the convex polyhedron is within a space configured with the contact reaction forces of the plurality of contacting portions and the specific state quantity as the variable components and where the convex polyhedron is specified by a mechanical relation between the contact reaction forces and the specific state quantity and by a linear inequality representing a contact reaction force constraint condition, and the device is configured to output the projection region found by the polyhedron projection processing as an estimated region of the possible existence region,
the specific state quantity includes three or more state quantities s(i) (i=1, 2, . . . , and N); and
the polyhedron projection processing section is configured to perform the following processes 11 to 18 as the polyhedron projection processing:
process 11: find an upper limit value and a lower limit value of the state quantity s(1) able to satisfy the mechanical relation and the contact reaction force constraint condition by the linear programming processing;
process 12: set a plurality of representative values with the upper limit value and the lower limit value of the state quantity s(1) included in a range between the upper limit value and the lower limit value;
process 13: find an upper limit value and a lower limit value of the state quantity s(2) able to satisfy the mechanical relation and the contact reaction force constraint condition by the linear programming processing for all representative values of the state quantity s(1) on the assumption that the value of the state quantity s(1) coincides with one of the plurality of representative values set in the process 12;
process 14: set a plurality of representative points, including respective apexes of a two-dimensional convex hull region, within the two-dimensional convex hull region which is obtained by convex hull of a plurality of points specified by all respective representative values of the state quantity s(1) and by the upper limit value and the lower limit value of the state quantity (2) for each representative value of the state quantity s(1) in a two-dimensional space with the state quantities s(1) and s(2) as variable components;
process 15: find an upper limit value and a lower limit value of the state quantity s(k) able to satisfy the mechanical relation and the contact reaction force constraint condition by the linear programming processing for all representative points set within a (k−1)-dimensional convex hull region, on the assumption that each of the values of (k−1) (k: 3 or greater integer) state quantities s(1), . . . , and s(k−1), among N state quantities s(i) (i=1, 2, . . . , and N), coincides with the value at one set representative point within the (k−1)-dimensional convex hull region;
process 16: if k<N, set a plurality of representative points, including respective apexes of a k-dimensional convex hull region, within the k-dimensional convex hull region which is obtained by convex hull of a plurality of points specified by a group of values of s(1), . . . , and s(k−1) corresponding to all respective representative points set within the (k−1)-dimensional convex hull region and by the upper limit value and the lower limit value of a state quantity s(k) for each of the representative points in a k-dimensional space with k state quantities s(1), . . . , and s(k) as variable components;
process 17: repeat the processes 15 and 16 until the process 15 when k=N is completed and, upon the completion of the process 15 when k=N, proceed to process 18; and
process 18: find, as the polyhedron projection region, an N-dimensional convex hull region obtained by convex hull of a plurality of points specified by a group of values of s(1), . . . , and s(N−1) corresponding to all respective representative points set within an (N−1)-dimensional convex hull region and by the upper limit value and the lower limit value of a state quantity s(N) for each of the representative points in an N-dimensional space with N state quantities s(i) (i=1, 2, . . . , and N) as variable components.