# Optimal Collision-Free Grip Planning for Biped Climbing Robots in Complex Truss Environment
## 5 Gait Interpreter
## Nomenclature

\(\Gamma\): set of all feasible routes

\(\Gamma_{i}\): \(i\)-th feasible route, \(\Gamma_{i}=\left\{\mathfrak{M},{}^{W}R,\mathfrak{R}_{t}\right\}\)

\(\mathfrak{M}\): member sequence along the route

\(\mathfrak{M}_{j}\): \(j\)-th member

\(\mathfrak{R}\): operational region \(\mathfrak{R}=\left\{\mathfrak{R}_{o},\mathfrak{R}_{t},\mathfrak{R}_{init}\right\}\), each inclusive of the takeoff segement and the landing segement

\(\mathfrak{R}_{t}\): operational region for transiting between adjacent members

\(\mathfrak{R}_{o}\): operational region for negotiating obstacle members

\(\mathfrak{R}_{init}\): operational region representing starting point and destination

\({}^{W}R\): set of gripping orientations corresponding to member sequence \(\mathfrak{M}\)

\({}^{W}R_{j}\): gripping orientation on the \(j\)-th member

\({}^{W}P_{0},{}^{W}P_{dir},L_{mem},r_{mem}\): reference point, direction unit vector, length and radius of the \(j\)-th member

\(t\): a scale to specify the gripping position on the \(j\)-th member

\({}^{W}Truss\): truss environment

\({}^{j}x_{k}\): \(k\)-th gripping position in the takeoff segment \([i\underline{x}_{k},i\ \overline{x}_{k}]\) on the \(j\)-th member

\({}^{j}y_{k}\): \(k\)-th gripping position in the landing segment \([i\underline{y}_{k},i\ \overline{y}_{k}]\) on the \(j\)-th member

\({}^{j}\mathcal{O}\): obstacles when moving on the \(j\)-th member

\(\mathbb{S}_{or}\left(G_{or},C_{or}\right)\): grips in the operational regions

\(G_{or}\): a grip in the operational region, inclusive of gripping position and orientation

\(C_{or}\): a configuration corresponding to \(G_{or}\)

\(\mathbb{S}\left(G,C\right)\): entire grip sequence

\({}^{P}R_{rp}\): key point for negotiating an obstacle member, \(\mathbf{P}_{kp}=[x_{kp},y_{kp},z_{kp}]\)

\(\eta\): robot plane

\(\Delta\): the cuboid space where collision may happen, for moving on a member

\(\Omega\): the sphere space where collision may happen, for transiting

\(l_{cub},w_{cub}.h_{cub}\): length, width and height of the cuboid space

\(l_{safe}\): a pre-defined safe distance to facilitate the gripping and grip-releasing operations

\({}^{j}N_{min}\): minimum number of climbing steps when passing the \(j\)-th member

\({}^{j}N_{k}\): minimum number of climbing steps from the \(k\)-th landing segment to the \((k+1)\)-th takeoff segment

\(S_{0},S_{1}\): minimum and maximum step lengths of the inchworm-like gait

\(S_{2},S_{3}\): minimum and maximum step lengths of the flipping-over gait and

\(\text{swinging-around gait}\): maximum step length of the hybrid gait

\(\mathcal{R}\): robot

## References

* [PERSON] et al. (1994) [PERSON]; [PERSON]; [PERSON]; [PERSON] Mobility and Manipulation of a Light-weight Space Robot. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Munich, Germany, 12-16 September 1994; pp. 11-19. * [PERSON] et al. (2000) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] A Climbing Autonomous Robot for Inspection Applications in 3D Complex Environments. _Robotica_**2000**, _18_, 287-297. [CrossRef]
* [PERSON] et al. (2007) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Self-assembling Mobile Linkages. _IEEE Robot. Autom. Mag._**2007**, _14_, 45-55. [CrossRef]
* [PERSON] et al. (2008) [PERSON]; [PERSON]; [PERSON]; [PERSON]. 3 DCLIMBER: A Climbing Robot for Inspection of 3D Human Made Structures. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Nice, France, 22-26 September 2008; pp. 4130-4135. * [PERSON] and [PERSON] (2011) [PERSON]; [PERSON] [PERSON] 3 DCLIMBER: Climbing and Manipulation over 3D Structures. _Mechatronics_**2011**, _21_, 48-62. [CrossRef]
* [PERSON] et al. (2005) [PERSON]; [PERSON]; [PERSON]; [PERSON] A Hybrid Pole Climbing and Manipulating Robot with Minimum DOFs for Construction and Service Applications. _Ind. Robot. Int. J._**2005**, _32_, 171-178. [CrossRef]
* [PERSON] and [PERSON] (2011) [PERSON]; [PERSON] A Flexible Tree Climbing Robot: Treebot--Design and Implementation.