1. Introduction
Spatial trusses consisting of members are widely used in the construction of roofs, towers, bridges, and the like. However, so far truss-associated routine tasks such as construction, painting, inspection, maintenance, and so on rely highly on manual labor. These routine tasks are usually high-rise and high-intensity, signifying a great risk to workers’ safety. Thus, a kind of biped climbing robot has been designed as an ideal assistant or substitute for human workers carrying out these tasks. Typical representatives of BiCRs include SM2 [
1], ROMA [
2], Shady3D [
3], 3DCLIMBER [
4,
5], PoleClimbingRobot [
6] and Treebot [
7]. These BiCRs generally comprise of an arm-like serial body for locomotion and grippers at both ends for attachment. Thanks to their biped climbing patterns, BiCRs can agilely move in complex 3D truss environments. Motivated by these characteristics, we also developed a biped climbing robot [
8], named Climbot as shown in
Figure 1. For the system implementation details and the climbing performance of Climbot, refer to [
9].
To complete a given task, for example inspecting the connection reliability of truss joints, BiCRs must be capable of motion planning. Basically, the motion planning of BiCRs consists of grip planning and single-step motion planning [
10]. In the grip planning procedure, a list of discrete grip locations, following which robots can navigate from the starting point to the destination, is determined. While in the single-step motion planning procedure, the shifting motion between adjacent grips is generated. It should be noted that not only the grips but also the single-step shifting motion must be free of collision. In this paper, we focus on the study of collision-free grip planning, assuming the truss environment is known or captured with integrated sensors such as in [
11].
Figuring out the grip sequences in a 3D truss environment is challenging for BiCRs. Besides the demand for collision avoidance, grips must satisfy the robot kinematic constraints for continuous cycles of climbing from the point of view of reachability. Furthermore, grips should contribute to the formation of a reasonable combination of various gaits with corresponding step lengths, to save the climbing time and energy.
The grip sequences to BiCRs are like the footprint sequences to humanoid robots. Therefore, we can learn from the foot placement problem of humanoid robots that has been addressed in the literature. There are two families of approaches for solving the humanoid robot foot placement problem, which is based on discrete search and continuous optimization, respectively. The discrete search methods normally require a pre-generated set of potential footprints before planning. Then classical methods, such as
and RRT, are commonly used for searching. Based on the terrain map and a discrete set of footstep placement positions, Kuffner [
12,
13] presented a global dynamic programming approach using greedy heuristics to plan safe navigation strategies for biped robots moving in obstacle-cluttered environments. Chestnutt et al. [
14,
15] used an
search algorithm to generate a sequence of collision-free footstep locations to reach a given goal state. A tiered planning strategy was introduced in [
16] that split the planner into three layers to traverse different terrain types. Ayaz et al. [
17,
18] presented a global reactive footstep planning strategy based upon a humanistic approach, in which a heuristic cost based on the complexity of stepping motion was used to assign foot placements and an exhaustive search was employed to identify the best path. These approaches can easily handle obstacle avoidance but introduce the trade-off between computational efficiency and solution precision. The continuous optimization approaches operate directly on the poses of the footsteps as continuous decision variables. Thus, it can make up for the precision deficiency of the discrete search methods. In [
19,
20], the authors presented a novel footstep optimization method with mixed-integer convex constraints that could solve the problem to its global optimum. However, the generation of each reachable region deeply relied on the position of the previous step, increasing the time consumption. In addition, adjusting the parameters to approximate the reachable regions was always difficult and thus reduced the planning accuracy. Guan et al. [
21,
22] built global optimization models with non-linear constraints to find the maximum heights of the obstacles that can be overcome. The results were then used as a priori knowledge and a database for surmounting obstacles. However, they focused on how to stride across one obstacle only, but not generating the nearby footprint sequences. Please note that these footstep planning methods for humanoid robots are always applied in 2D or 2.5D environments, which differs from the grip planning for BiCRs in complex 3D truss environments.
To the best of our knowledge, the collision-free grip planning problem has rarely been studied in the literature. Balaguer et al. [
2,
23] treated the BiCRs’ climbing path planning as a TSP-like problem. They modeled the environment as a graph with two categories of primitives. They then proposed a heuristic algorithm to solve the climbing path, along which the robot visited all beam faces without repetition. Detweiler et al. [
24] presented a path planning algorithm to optimize the locomotion sequences for the Shady3D robot. A set of potential gripping points was first dispersed in the truss environment up to a certain density. Then the shortest locomotion sequence represented with gripping points was computed with the Dijkstra’s distance. Based on the framework of conventional genetic algorithm, Chung et al. [
25] adopted the concept of genetic modification to design a new genetic operator. They used this method to solve the climbing path with the minimum energy demand. However, these methods all suffer limitations from spending long planning time, ignoring specific transition movement, and not thinking about obstacle avoidance. Lam et al. [
7] discretized the tree surface into finite grasp points, then used a dynamic programming algorithm to identify the global path and adopted a motion planning algorithm to generate the single-step climbing motion. Therefore, this method was only applicable to BiCRs climbing on the object surface with non-enclosure grippers. It can only obtain a near-optimal solution. Zhu et al. [
26] presented two optimal strategies to select a collision-free grip from its potential region based on three criteria step by step. However, this method lacks global guidance in searching, and hence, is inefficient most of the time.
For BiCRs rapidly generating optimal collision-free grips, we have proposed a novel framework, which further subdivides the grip generation procedure into three steps:
- (1)
quick determination of all feasible climbing routes in global, outputting member sequence and corresponding grip orientation and operational regions for transition;
- (2)
optimal arrangement of collision-free grips on the operational regions on each member along each feasible climbing route;
- (3)
generation of the entire grip sequence with a gait interpreter.
For Step (1), we have presented a high-efficiency global path planning method in [
27]. Further to our previous work, we present an optimal collision-free grip planning method to minimize the number of climbing steps in this paper.
The novelty of this paper is the first systematic presentation of an optimal collision-free grip planner for the biped climbing robots generating grip sequences in a complex truss environment. This grip planner not only handles well with the collision between the robot and the truss, but also guarantees the robot kinematics, the minimum number of climbing steps, the good manipulability of transition grips. It should be noted that this grip planner is able to solve the grip planning problem of more than 30 grips in a scene of 25 members within 0.65 s. Another novelty of this paper is the mathematical model for computing the operational regions for negotiating obstacle members.
The remainder of this paper is organized as follows. We briefly review the global path planning and its output, followed by introducing the idea of collision-free grip planning in
Section 2. We then create a mathematical model for computing the operational regions to negotiate obstacles in
Section 3. We construct a mathematical optimization model to determine the collision-free grips in the operational regions in
Section 4. A gait interpreter and its implementation are described in
Section 5. In
Section 6, we conduct simulations with Climbot to verify the proposed analysis and algorithms. Finally, we conclude our work in
Section 7.
5. Gait Interpreter
After determining the grips within each operational region, it is time to generate grips connecting the operational regions. That is to say, at this time, the grips are generated outside of operational regions. These remaining grips must be arranged in such a proper way that finally any pair of adjacent grips satisfies the robot kinematic constraints. A dedicated gait interpreter is proposed to implement this function in this section.
Algorithm 1 gives out the basic structure of the proposed gait interpreter. The outputs of the optimal collision-free grip planner are
, inclusive of
and
.
actually packages the parameters calculated in
Section 4.2.1, including the moving distance
, number of climbing steps
and corresponding
type. These parameters are important reference for the gait interpreter arranging the remaining grips. Therefore, the inputs to the gait interpreter are the truss environment and
. During processing, the gait interpreter takes the transition, the obstacle negotiation, or the movement between them as a unit. For each unit, the gait interpreter simply arranges grips by calling an appropriate sub-function, according to the corresponding
type. Sub-functions
InchwormGait,
HybGait and
SaFoGait are designed to generate grips and configurations for the movement between operational regions. While
PerformTransition and
NegotiateObstacle are designed to pack the transition and obstacle-negotiating grips into the grip sequence.
Algorithm 1: The gait interpreter |
|
Algorithm 2 is the implementation of the sub-function
InchwormGait.
InchwormGait takes charge of generating grips for the inchworm-like gait. According to
Section 4.2.1, one extra grip
should be inserted for connecting the operational regions. Based on
, the function
CalculateStepLength is called to calculate the proper step length
with respect to the gripping position
y. Then
can be obtained by an offset from the gripping position
y. After that, the adjacent grips of
y,
and
x will be sent for kinematic check. If
y and
or
and
x do not satisfy the kinematic constraints,
will be updated to the opposite direction on the member. Reflecting on the movement of the robot, it is moving forward or backward to adjust the gripping position. If the kinematic check is passed, the function G
enerateG
rip is then used to generate
of an inchworm-like gait. Otherwise, the robot cannot continue to climb along this route.
Algorithm 2: InchwormGait: generating grips for the inchworm-like gait |
|
Algorithm 3 is the implementation of the sub-function
HybGait, in charge of generating grips for the hybrid gait. To climb with the hybrid gait, two extra grips need to be inserted. According to
Section 4.2.1, every hybrid gait contains an inchworm-like gait. Therefore, one of these two grips will be solved firstly, then the function
InchwormGait is called to generate another. The direction
of inserting first grip is firstly initialized. Based on the distance between
y and
x, two different strategies are used by the algorithm. If this distance is in the range of
, an offset
is calculated with the function
CalculateOffset according to
and
. Then
can be solved easily. The other grip
can be obtained by calling the function
InchwormGait. If
is empty,
will be updated by changing to another side to insert the grip. Then
InchwormGait is called again. If this operation successes,
between
and
x are generated by the function
GenerateGrip. Otherwise, the robot cannot reach the destination via this route. If the moving distance is in
, two grips always can be inserted between
y and
x successfully since there is enough adjustment space.
In the case of
gait,
grips are distributed uniformly between the initial and finished gripping position. Verifications of kinematics and collision avoidance should be applied to each step.
Algorithm 3:HybGait: generating grips for the hybrid gait |
|
7. Conclusions and Future Work
Biped climbing robots have bright and broad application prospects in the field of performing high-rise truss-related routine tasks. To perform such a task, BiCRs must have the ability to plan their grips prior to climbing.
In this paper, we presented a novel optimal collision-free grip planner for BiCRs generating grip sequence in complex truss environments. The planner essentially consists of three components: (1) a mathematical model for computing the operational regions for surmounting obstacles; (2) a grip placement optimizer for determining the grips within operational regions; and (3) a gait interpreter for generating grips between adjacent operational regions. The idea behind this novel scheme is to use the priority to determine the grips at key places, i.e., operational regions for surmounting obstacles and that for performing transitions, then move to other places. Because normally there is less room to choose and adjust grips for these key places. Simulation results verified that the planner was able to plan approximately 30 grips within s, taking collision avoidance, grip manipulability and number of climbing steps into account. However, the current planner only considers the forward and backward movement on a member, which limits the applicable objects as BiCRs with, or less than, five degrees of freedom. In addition, the total time consumed in grip planning is related to the initial values for optimization.
In the near future, we will study the optimal climbing gait type and the collision-free motion for the robot shifting between adjacent grips. Extensive climbing experiments on various trusses will be conducted to further verify our planning algorithms.