KR102300752B1 - Method and Apparatus for Collision-Free Trajectory Optimization of Redundant Manipulator given an End-Effector Path - Google Patents

Abstract

A collision-free trajectory optimization method and apparatus of a redundant manipulator for accurately following a given end-effector path is presented. The collision-free trajectory optimization method of the redundant manipulator for accurately following a given end-effector path proposed in the present invention includes matching to minimize the pose error between the target and the current end-effector pose, conditions to ensure smoothness of the trajectory, Modeling the objective function with three characteristics of a quantitative measure of proximity to an obstacle to avoid collision, updating the trajectory iteratively to minimize the cost of the objective function with the three characteristics, and updating the three characteristics during the update Optimizing the trajectory using two-step gradient descent to reduce potential competition between In order to prevent this from happening, the desired trajectory is synthesized through an optimization process that incorporates the step of applying quantum annealing, which repeatedly randomizes the joint configuration of the initial trajectory, and the trajectory is updated by checking the collision of the trajectories applied with quantum annealing. includes steps.

Description

Method and Apparatus for Collision-Free Trajectory Optimization of Redundant Manipulator given an End-Effector Path

The present invention relates to a collision-free trajectory optimization method and apparatus of a redundant manipulator for accurately following a given end-effector path.

Remote control of various robots has been one of the major challenges in robotics, and is typically used when it is difficult or dangerous for humans to perform tasks. In this remote control scenario, the robot must precisely follow the work order, taking into account its surroundings and the constraints of the robot itself.

In the case of a redundant manipulator, a precisely specified set of joint configurations is required to precisely follow the end-effector path of Cartesian space. Traditionally, Inverse Kinematics (IK) has been used to determine the joint configuration given an end-effector pose. However, conventional IK cannot take into account the continuity of composition, collision avoidance, and kinematic specificity that occurs when following the end-effector path.

The previous approach solves this problem by using non-linear optimization taking these constraints into account. This approach also avoids self-collision using neural networks, but does not deal with collisions against external obstacles.

Inverse Kinematics (IK) has been extensively studied to find joint configurations in end-effector poses. For the redundant manipulator to which the target robot belongs, there can be multiple joint configurations in a single end-effector pose. For this problem, several techniques have been proposed to quickly find a solution. In particular, the task priority IK algorithm prioritizes solutions based on the objective function for each objective.

Most methods of synthesizing geometrically constrained trajectories for end-effector poses are based on Jacobian matrices instead of IK to find feasible solutions among various solution candidates. Unfortunately, Jacobian matrices are the first derivatives of multivariate vector-valued functions, and thus can stick to local minima or convergence failure due to joint angle limits, leading to false-negative failures.

Trac-IK uses a randomly selected joint configuration and sequential quadratic programming to pinpoint problems and improve success rates. Nevertheless, the solution does not guarantee the continuity of a series of joint configurations to create a feasible trajectory. In summary, the existing IK approaches have different advantages and disadvantages for synthesizing feasible trajectories along a given end-effect path.

To obtain a relaxed solution, many studies present optimization techniques with an objective function to synthesize feasible trajectories with matching end-effect poses. Luo and Hauser use geometric and temporal optimizations to dynamically generate possible trajectories from sketch inputs. Recently, Rakita proposed a real-time approach using weighted sum nonlinear optimization called RelaxedIK to solve the IK problem for a set of motion inputs. Since collision checking has a relatively large computational overhead, RelaxedIK uses neural networks for fast self-collision avoidance.

Based on RelaxedIK, two studies are proposed to synthesize trajectories with high accuracy offline. One of them is Stampede, which uses a dynamic programming algorithm to find the optimal trajectory on a discrete spatial graph built by samples of IK solutions. Other studies generate multiple candidate trajectories in a multi-start configuration and then select the optimal trajectory as a user guide, allowing for deviations in case of risk of self-collision or kinematic singularity.

Korean Patent Publication No. 10-1748632 (2017.06.13)

An object of the present invention is to provide a trajectory optimization method and apparatus for TORM (Trajectory Optimization of Redundant Manipulator) that precisely synthesizes a trajectory exactly following a given end-effector path and simultaneously achieves a smooth and collision-free manipulator.

In one aspect, the collision-free trajectory optimization method of the redundant manipulator for accurately following a given end-effector path proposed in the present invention provides matching and smoothness of the trajectory to minimize the pose error between the object and the current end-effector pose. Conditions to ensure, modeling the objective function with three characteristics of a quantitative measure of proximity to obstacles to avoid collisions, iteratively updating the trajectory to minimize the cost of the objective function with the three characteristics, and updating optimizing the trajectory using two-step gradient descent to reduce potential competition between the three features during , to synthesize the desired trajectory through an optimization process that incorporates the step of applying quantum annealing, which repeatedly randomizes the joint configuration of the initial trajectory to avoid falling into a local minimum, and an objective function, and check the collision of the trajectories applied with quantum annealing. to update the trajectory.

Updating the trajectory iteratively to minimize the cost of the objective function with three features, and optimizing the trajectory using two-step gradient descent to reduce potential competition between the three features during the update is a two-step gradient descent update the trajectory using quantitative measures of proximity to obstacles to avoid collisions, conditions for each odd iteration to ensure smoothness of the trajectory among the three properties of the objective function, and between the target and the current end-effector pose. The trajectory is updated iteratively using matching to minimize the pose error of

In order to select the optimal joint configuration of the end-effector pose, the step of selecting as the initial trajectory to minimize the objective function is to tessellate the path of the end-effector into a plurality of poses, and Find the joint configuration that minimizes the objective function in multiple poses of the simplified, simplified end-effector, and interconnect the selected joint configuration to calculate the initial trajectory through linear interpolation.

The step of applying quantum annealing, which repeatedly randomizes the joint configuration of the initial trajectory in order not to fall into a local minimum, prepares randomized parameters using quantum transitions, performs local optimization, and quantum transitions The lower cost is searched for by a random search controlled by Sequential Exploring (SE), which repeats quantum transformations and places more weight on the search part, is used.

In another aspect, the collision-free trajectory optimization apparatus of a redundant manipulator for accurately following a given end-effector path proposed in the present invention is a matching, trajectory to minimize the pose error between the target and the current end-effector pose. An objective function modeling unit that models the objective function with three characteristics: a condition to ensure smoothness, a quantitative measurement of proximity to an obstacle to avoid collision, and iteratively repeats the trajectory to minimize the cost of the objective function with three characteristics. , a trajectory optimizer that optimizes the trajectory using two-step gradient descent to reduce potential competition between the three features during the update, and minimizes the objective function to select the optimal joint configuration of the end-effector pose. The initial trajectory selector that selects the first trajectory as the initial trajectory, the quantum annealing unit that repeatedly randomizes the joint configuration of the initial trajectory in order not to fall into a local minimum, and an optimization process that integrates the objective function to select the desired trajectory and a trajectory updater for updating trajectories by checking collisions of trajectories to which the trajectories are synthesized and to which quantum annealing is applied.

According to embodiments of the present invention, the trajectory is optimized using two-step gradient descent to reduce potential competition between different features during update, and various configurations of the trajectory are used to further improve performance and avoid falling into local minima. We can apply quantum annealing to iteratively randomly randomize , and then update the trajectory. The proposed method and apparatus can strongly minimize pose errors in a gradual manner while satisfying various desirable characteristics.

1 is a flowchart illustrating a collision-free trajectory optimization method of a redundant manipulator for accurately following a given end-effector path according to an embodiment of the present invention.
2 is a diagram for explaining a process of calculating a joint configuration of a given end-effector pose according to an embodiment of the present invention.
3 is a view for explaining a process of simplifying a plurality of poses of the end-effector according to an embodiment of the present invention.
4 is a diagram for explaining a process of calculating an initial trajectory through linear interpolation according to an embodiment of the present invention.
5 is a view for explaining quantum annealing according to an embodiment of the present invention.
6 is a diagram illustrating a configuration of a collision-free trajectory optimization apparatus of a redundant manipulator for accurately following an end-effector path according to an embodiment of the present invention.
7 is a diagram illustrating an analysis result of an environment with obstacles and a proposed method according to an embodiment of the present invention.
8 is a diagram illustrating a comparison result between an obstacle-free environment and a state-of-the-art method according to an embodiment of the present invention.

The proposed method also tries to find a very accurate solution for the redundant manipulator while avoiding self-collision. In addition, collision avoidance with external obstacles is further considered. To synthesize accurate and feasible trajectories without collisions with the robot itself as well as obstacles, we propose trajectory optimization of TORM, which extends CHOMP, one of the most prominent optimization-based motion planning approaches to problems using redundant manipulators.

The optimization-based motion planning approach integrates efficient collision avoidance methods into optimization techniques to quickly find collision-free trajectories. Well-known techniques include the covariant gradient algorithm (CHOMP), stochastic optimization without gradient information (STOMP), and sequential convex optimization (Trajopt). Thanks to the high-quality trajectory, these techniques have been extended in other directions (eg, constrained motion planning).

The proposed method is based on CHOMP, but is extended by adding additional objective conditions to consider a given end-effect path. The main difference to the original CHOMP is that CHOMP basically finds a collision-free trajectory from the start to the target configuration, but the task of the present invention is to synthesize a feasible and accurate trajectory along a given end-effect path. Also, CHOMP based on gradient descent is a local optimization and thus can yield suboptimal trajectories. Therefore, the search space of the proposed method has many local minima by considering various objective conditions. In the present invention, quantum annealing, a randomization technique, is employed to avoid local minima. Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1 is a flowchart illustrating a collision-free trajectory optimization method of a redundant manipulator for accurately following a given end-effector path according to an embodiment of the present invention.

The proposed collision-free trajectory optimization method of redundant manipulators to accurately follow a given end-effector path includes matching to minimize pose errors between the target and the current end-effector pose, conditions to ensure smoothness of the trajectory, and avoidance of collisions. Modeling the objective function with three characteristics of the quantitative measure of proximity to the obstacle for risk (110), iteratively updating the trajectory to minimize the cost of the objective function with the three characteristics, and updating the three characteristics during the update optimizing the trajectory using two-step gradient descent to reduce potential competition between 120 , selecting an initial trajectory that minimizes the objective function to select the optimal joint configuration of the end-effector pose 130 . ), applying quantum annealing to iteratively randomize the joint configuration of the initial trajectory in order not to fall into the local minimum (140) and synthesizing the desired trajectory through an optimization process that integrates the objective function, and the trajectory to which quantum annealing is applied and a step 150 of updating the trajectory by checking the collision of .

2 is a diagram for explaining a process of calculating a joint configuration of a given end-effector pose according to an embodiment of the present invention.

를 찾는 것이다. 궤적

는 조인트 구성의 시퀀스이며, 엔드-이펙터 경로인

은 6차원 카테시안(Cartesian) 공간에 정의되어 있다. The goal is the trajectory of the redundant manipulator for a given end-effector path, X.

will be looking for trajectory

is the sequence of joint constructions, the end-effector path,

is defined in a six-dimensional Cartesian space.

의 경유지 매개변수화로 문제를 해결한다. x는 엔드-이펙터 포즈이다. 그런 다음 엔드-이펙터 포즈

의 조인트 구성을 계산한다. 그 결과, 궤적은

와 같다. 여기서 d는 매니퓰레이터의 자유도(DoF)이며, q0은 시작 구성이고 qn은 조인트 구성의 계산 궤적에 대한 목표 구성이다. 주요 표기법은 표 I에 요약되어 있다. A path that subdivides a given end-effector path

Solve the problem by parameterizing the waypoints of x is the end-effector pose. Then end-effector pose

Calculate the joint configuration of As a result, the trajectory is

same as where d is the degree of freedom (DoF) of the manipulator, q0 is the starting configuration and qn is the target configuration for the computational trajectory of the joint configuration. The main notations are summarized in Table I.

The target robot is a redundant manipulator with a multi-joint configuration taking an end-effector pose. If d > 6, it has infinitely many valid solutions. Among the many candidates, we find a suitable joint configuration to generate a smooth and accurate trajectory without collision for a given end-effector path.

To achieve the goal, we present the trajectory optimization of TORM, which adopts an optimization-based motion planning approach, especially CHOMP, to find a collision-free trajectory from the beginning to the target construction. We choose CHOMP as the default trajectory optimization method of our approach because CHOMP not only uses gradient descent to quickly optimize the trajectory, but also efficiently avoids collisions by integrating the objective function.

Hereinafter, a method of optimizing the objective function and a method of not falling into a local minimum or violating a constraint are described. To do this, first define an objective function with a new path according to the objective function. Then we update the target based on the two-step gradient descent, then we update the quantum annealing starting with the initial trajectory.

Referring back to FIG. 1 , in step 110 , matching to minimize pose error between the object and the current end-effector pose, conditions to ensure smoothness of the trajectory, and quantitative measurement of proximity to obstacles to avoid collisions Model the objective function with the three characteristics of .

We solve the problem by modeling the objective function with three properties: 1) matching end-effector poses, 2) smoothness, and 3) collision avoidance.

(1)

(One)

는 정규화 상수이다. Fpose는 대상과 현재 엔드-이펙터 포즈 사이의 포즈 오류를 최소화하기 위해 도입되며, 유클리디안 거리를 사용하여 정의된다.here

is the normalization constant. Fpose is introduced to minimize the pose error between the target and the current end-effector pose, and is defined using Euclidean distances.

(2)

(2)

where FK ( qi ) computes the end-effector from the joint configuration qi using forward kinematics (FK).

The definition given in CHOMP for the smooth condition Fsmooth and the obstacle condition Fobs is followed. Fsmooth measures dynamic quantities. That is, the sum of squares of the derivative is measured to ensure smoothness.

(3)

(3)

Fobs quantitatively measures proximity to obstacles to avoid collisions.

(4)

(4)

의 위치이고,

는 작업 공간 장애물 기하학에서 분석적으로 계산할 수 있는 부호화(signed) 거리 필드에서 계산한 장애물 코스트(cost)이다. 높은 수준에서 로봇 본체와 장애물 사이의 침투 깊이의 합계를 대략적으로 측정한다. where x ( ki,b ) is the partial FK, i.e. the body point in the working space of construction qi .

is the location of

is the obstacle cost calculated from the signed distance field that can be analytically calculated in the workspace obstacle geometry. At a high level, it roughly measures the sum of the penetration depths between the robot body and the obstacle.

In step 120, the trajectory is iteratively updated to minimize the cost of the objective function with three features, and the trajectory is optimized using two-step gradient descent to reduce potential competition between the three features during the update. .

Two-step gradient descent updates the trajectory using quantitative measures of proximity to obstacles to avoid collisions, the condition for each odd iteration to ensure smoothness of the trajectory among the three properties of the objective function, and the target and current end. -Iteratively updates the trajectory using matching to minimize pose errors between effector poses.

는 로봇을 장애물 밖으로 밀어내고, 매끄러움 조건의 기능 구배인

는 조인트 구성 사이의 연속성을 유지한다.The trajectory is iteratively updated to minimize the cost of the objective function with three characteristics. To minimize the cost, the update rule is based on the gradient descent technique employed in many optimization methods. Obstacle condition function incline

pushes the robot out of the obstacle and is the functional gradient of the smoothness condition.

maintains continuity between joint configurations.

와

는 모두 실현 가능한 궤적을 합성하는 역할을 하는 반면, 포즈 조건인

의 기능 경사는 엔드-이펙터 포즈

를 매칭하는 역할을 한다. 세 가지 기능 경사를 동시에 고려함으로써 궤적을 갱신할 수 있지만, 각 기능 경사 간의 충돌을 초래할 수 있다는 것을 알게 되었다.

Wow

are all responsible for synthesizing feasible trajectories, while the pose condition

The feature slope of the end-effector pose

plays a role in matching We found that although we could update the trajectory by considering the three functional gradients simultaneously, it could lead to conflicts between each functional gradient.

와

를 사용하여 궤적을 업데이트하고,

를 사용하여 궤적을 반복 업데이트한다.To alleviate this problem, we present Two-Stage Dradient Descent (TSGD), which consists of updating to make a feasible trajectory and updating the trajectory to more closely match X. TSGD indicates that each odd iteration

Wow

to update the trajectory,

to iteratively update the trajectory.

(5)

(5)

는 러닝 레이트(learning rate)이고, A는 매끄러움 조건의 동등하게 변형된 표현 Fsmooth =

로부터 나온 것이다. A^-1은 전체 궤적에 작은 영향을 미침으로써 매끄러움을 유지하고 최적화를 가속화시키는 작용을 한다. Fsmooth와 Fobs는 연속적인 조인트 구성 사이에 상관관계가 있으므로 A^-1을 이용하여 공변적 경사 강하로 궤적을 갱신하는 데 효과적이다. 반면 Fpose는 연속적인 조인트 구성을 고려하지 않으므로 A^-1을 사용하지 않는다.here

is the learning rate, and A is an equally modified expression of the smoothness condition Fsmooth =

it comes from A ^-1 acts to maintain smoothness and accelerate optimization by having a small effect on the overall trajectory. Since Fsmooth and Fobs have a correlation between successive joint configurations, it is effective to update the trajectory with covariant gradient descent using ^{A -1.} On the other hand, Fpose does not use ^{A -1} because it does not consider continuous joint construction.

와

를 정의하여 조인트 구성의 변경을 계산해야 한다.The problem is to avoid collisions and follow a given end-effect path in the Cartesian workspace, while solving the problem through sequential movement of the joint configuration in C-space. FPose and Fobs are computed in workspace using FK, but in C-space

Wow

should be defined to account for changes in the joint configuration.

는

로 나타낼 수 있기 때문에, 포즈 조건

의 기능 경사를 다음과 같이 도출할 수 있다.of formula (2)

Is

Since it can be expressed as , the pose condition

We can derive the functional gradient of

(6)

(6)

는 자코비안 매트릭스이다. 자코비안 기반 접근방식은 페일-네거티브(false-negative) 실패로 이어질 수 있다. 그러나, 제안하는 TSGD 방법이 반복적으로 기능 경사를 바꾸는 탐구적인 방법 덕분에 실제로 문제를 개선한다는 것을 발견했다.here

is the Jacobian matrix. A Jacobian-based approach can lead to false-negative failures. However, we found that the proposed TSGD method actually improves the problem thanks to the exploratory method of iteratively changing the functional gradient.

는 아래와 같이 도출될 수 있다.

can be derived as follows.

(7)

(7)

는 정규화 속도 벡터이며

는 곡률 벡터이다. Fsmooth는 이미 C-space에 표현되어 있기 때문에,

는 간단히

로 표현된다. where x _i,b is equal to x (q _i,b ), c _i,b equals c ( x _i,b ),

is the normalization rate vector

is the curvature vector. Since Fsmooth is already expressed in C-space,

is simply

is expressed as

Once a starting configuration q0 is given, iteratively updates from the next configuration q1 to the target configuration qn based on TSGD. However, the start configuration may not be given while the end-effect pose is given.

In step 130, an initial trajectory is selected that minimizes the objective function to select an optimal joint configuration of the end-effector pose.

The path of the end-effector is represented in a tessellated form in a plurality of poses, and the plurality of poses of the end-effector is simplified. Find the joint configuration that minimizes the objective function in multiple poses of the simplified end-effector, and connect the selected joint configuration to calculate the initial trajectory through linear interpolation.

3 is a view for explaining a process of simplifying a plurality of poses of the end-effector according to an embodiment of the present invention.

It is possible to optimize the trajectory according to the update rule, but it is not straightforward to obtain the initial trajectory for the task as only the end-effector path is provided. This section introduces a simple and heuristic method of constructing the initial trajectory, which is updated in quantum annealing.

The goal is to create a good initial trajectory, and it faces major challenges to consider including smoothness, obstacle avoidance, and following a given path. End-effector poses can have multiple or infinite joint configurations. So you can simply get the joint configuration using IK and linear interpolation at each end-effector pose, but some are not a good way to calculate the initial trajectory.

As a first step, given end-effector paths can be elaborately tessellated in many poses, and working with more poses can increase the complexity of generating a reasonably initial trajectory 310 . The effector pose is simplified to a simple pose S ∈ {s0, ..., sn} (320). Specifically, we choose the Ramer-Douglas-Peucker algorithm.

4 is a diagram for explaining a process of calculating an initial trajectory through linear interpolation according to an embodiment of the present invention.

Start with the first simplified pose, find a suitable joint configuration in the pose, and then connect one of the configurations to the other pose in the next pose. To choose the joint configuration, choose the one that minimizes the objective function. Finally, we connect the selected joint configurations to compute the initial trajectory via linear interpolation.

In step 140, quantum annealing is applied to iteratively randomize the joint configuration of the initial trajectory in order not to fall into a local minimum. Prepare randomization parameters using quantum conversion and perform local optimization. Quantum conversion searches for a lower cost by a random search controlled by a parameter, and the parameter controls the strength of the randomness according to the cost function. In this case, Sequential Exploring (SE) is used which places more weight on the search part by repeating the quantum transformation.

5 is a view for explaining quantum annealing according to an embodiment of the present invention.

While the initial trajectory is obtained, it is highly likely that the trajectory is less than optimal due to the local characteristics of the update method and the initial trajectory construction method. Moreover, since we incorporate the properties of three different constraints into the objective function, there can be many surrounding local minima in terms of the optimization search space.

To avoid falling into local minima, many proactive approaches employ some kind of global optimization, i.e. simulation annealing or probabilistic methods. In this study, rather than simulation annealing, quantum annealing (QA), which is a key feature of the present invention, is applied, which is more effective in deviating from many local minima around it.

에 의해 제어되는 랜덤 탐색에 의해 더 낮은 코스트를 검색한다. 매개변수

는 코스트 함수에 따라 랜덤성의 강도를 제어한다.QA is a kind of randomization algorithm that prepares randomization parameters using quantum conversion and performs local optimization. Quantum conversion is a parameter

A lower cost is searched for by a random search controlled by . parameter

controls the strength of randomness according to the cost function.

Adopting QA, the proposed algorithm iteratively performs two parts, which is described in Algorithm. A better trajectory of 1 (lines 4-7) and a trajectory update (lines 3).

Unlike the original QA, the quantum transformation according to the embodiment of the present invention is repeated b times to use a sequential search (SE) that places more weight on the search part. SE was chosen to reliably identify high-quality solutions through a randomized algorithm.

를 찾은 다음 2단계 경사 강하로 새로운 궤적

를 다시 다듬는다. 본 발명의 실시예에 따른 경우, 양자 전환은 목적 함수(Alg. 1의 5행)를 이용하여 랜덤으로 생성된 궤적을 추정함으로써 잠재적으로 좋은 해결책을 탐색한다. 궤적은 IK를 사용하여 단순화된 포즈로 얻은 랜덤 조인트 구성을 연결하여 계산한다.The search part uses quantum transitions to create new trajectories

, then a new trajectory with a two-step gradient descent

re-trim In the case of an embodiment of the present invention, quantum transformation searches for a potentially good solution by estimating a randomly generated trajectory using an objective function (line 5 of Alg. 1). The trajectory is calculated by concatenating random joint configurations obtained with simplified poses using IK.

의 코스트가 더 낮을 때, 그것을 현재의 궤적(Alg. 1의 7행)까지 사용한다. 단, 새로운 궤적

가 제약조건을 위반하는 경우에는 현재 궤적에 사용하지 않는다. 업데이트 부분은 2단계 경사 강하를 사용하여 궤적을 국소적으로 다듬는다. 이 과정은 특정 조건(예를 들어, 가동 시간 또는 코스트)을 충족할 때까지 계속된다. New trajectories found during exploration

When the cost of is lower, it is used up to the current trajectory (line 7 of Alg. 1). However, a new trajectory

In case of violates the constraint, it is not used for the current trajectory. The update part uses two-step gradient descent to locally refine the trajectory. This process continues until certain conditions (eg uptime or cost) are met.

In step 150, a desired trajectory is synthesized through an optimization process that integrates the objective function, and the trajectory is updated by checking the collision of the trajectory to which quantum annealing is applied.

Through an optimization process that integrates the objective function, the desired trajectory is synthesized by finding the low cost. The optimization process looks for a low-cost solution, but may violate some constraints. For example, even if the trajectory exactly follows a given end-effector pose, the trajectory can collide with an obstacle or magnetic collision. Therefore, whenever we find a better trajectory in the quantum annealing process, we check for collisions.

로 쓸 수 있는 Riemannian 메트릭 A^-1을 사용한다. 여기서 v는 조인트 값의 벡터이고 α는 스케일 상수이다. 이 과정은 위반이 없을 때까지 반복된다.In addition to collision checking, the manipulator has some constraints that generally satisfy the joint's lower and upper limits, velocity limits, and the kinematic singularity of the joint. For the lower and upper bounds of the joint, they are traditionally handled by performing an L1 projection that resets the offending joint value to the limit value. To maintain smoothness, we use the smooth projection used by CHOMP during the update process. a smooth projection

We use the Riemannian metric A ^{-1 , which can be written as} where v is the vector of joint values and α is the scale constant. This process is repeated until there are no violations.

동안 qi-1과 qi 사이의 조인트 속도를 계산하여 확인한다. 또 다른 제약조건은 로봇이 불안정한 지점인 키네마틱 특이점이며, 자코비안 매트릭스가 전체 순위를 잃을 때 발생할 수 있다. 키네마틱 특이점을 확인하기 위해, Relaxed-IK에서 사용하는 조작성 측정치를 사용한다. 높은 수준에서는 랜덤 샘플로 계산되는 특정 값보다 작은 조작성 측정을 피한다. 제안하는 방법은 실현 가능한 궤적을 구성하기 위한 제약조건을 확인함으로써 보장된 최저 코스트 궤적을 보상한다는 점에 주목하라.Other constraints, such as speed limits, are checked together while checking for collisions. The joint speed limit is set at a given time interval

Calculate and check the joint velocity between qi -1 and qi during Another constraint is the kinematic singularity, the point at which the robot is unstable, which can occur when the Jacobian matrix loses its overall rank. To identify kinematic singularities, we use the manipulative measures used by Relaxed-IK. At a high level, avoid measures of manipulability that are smaller than a certain value calculated from random samples. Note that the proposed method compensates for the guaranteed lowest cost trajectory by checking the constraints for constructing a feasible trajectory.

6 is a diagram illustrating a configuration of a collision-free trajectory optimization apparatus of a redundant manipulator for accurately following a given end-effector path according to an embodiment of the present invention.

The collision-free trajectory optimization apparatus 600 of the redundant manipulator for accurately following the proposed given end-effector path includes an objective function modeling unit 610 , a trajectory optimization unit 620 , an initial trajectory selection unit 630 , and a quantum annealing unit. 640 and a trajectory updater 650 . The objective function modeling unit 610 , the trajectory optimization unit 620 , the initial trajectory selection unit 630 , the quantum annealing unit 640 , and the trajectory update unit 650 perform steps 110 to 150 of FIG. 1 . can be configured for

The objective function modeling unit 610 has three characteristics: matching to minimize pose errors between the target and the current end-effector pose, conditions for ensuring smoothness of the trajectory, and quantitative measurement of proximity to obstacles to avoid collisions. to model the objective function.

The trajectory optimizer 620 iteratively updates the trajectory to minimize the cost of the objective function having three features, and optimizes the trajectory using two-step gradient descent to reduce potential competition between the three features during the update. do. The trajectory optimizer 620 uses a quantitative measurement of proximity to obstacles to avoid collisions, and the condition for ensuring smoothness of the trajectory among the three characteristics of the objective function for each odd repetition of the two-step gradient descent. update and iteratively update the trajectory using matching to minimize pose errors between the object and the current end-effector pose.

The initial trajectory selection unit 630 selects an initial trajectory that minimizes the objective function in order to select an optimal joint configuration of the end-effector pose. The initial trajectory selector 630 represents the path of the end-effector in a tessellated form in a plurality of poses, and simplifies the plurality of poses of the end-effector. Find the joint configuration that minimizes the objective function in multiple poses of the simplified end-effector, and connect the selected joint configuration to calculate the initial trajectory through linear interpolation.

The quantum annealing unit 640 applies quantum annealing that repeatedly randomizes the joint configuration of the initial trajectory in order not to fall into a local minimum. The quantum annealing unit 640 prepares randomization parameters using quantum conversion and performs local optimization. Quantum conversion searches for a lower cost by random search controlled by a parameter, and the parameter controls the strength of randomness according to a cost function. Sequential Exploring (SE), which repeats quantum transformations and places more weight on the search part, is used.

The trajectory updater 650 synthesizes a desired trajectory through an optimization process integrating the objective function, and updates the trajectory by checking collisions of the trajectories to which quantum annealing is applied.

7 is a diagram illustrating an analysis result of an environment with obstacles and a proposed method according to an embodiment of the present invention.

In order to evaluate the proposed method, the proposed method was removed one by one from the problem including external obstacles and tested. The proposed methods are two-step gradient descent (TSGD), quantum annealing (QA), and continuous search (SE). When all of the proposed methods were used, the best results were obtained.

8 is a diagram illustrating a comparison result between an obstacle-free environment and a state-of-the-art method according to an embodiment of the present invention.

For comparison with state-of-the-art methods, experiments were performed on their problems without external obstacles. RelaxedIK is a real-time method, but the posture error was large. Stampede finds the correct trajectory, but it takes a long time to find the original trajectory. The proposed method showed better performance than the latest method compared to the time by rapidly reducing the posture error gradually. The experimental results were measured based on the trajectory that was feasible with the average value of 20 times.

In this study, we present the trajectory optimization of TORM (Trajectory Optimization of Redundant Manipulator) for synthesizing the trajectory that accurately follows the smooth and collision-free trajectory of the robot itself and external obstacles.

The proposed method is based on CHOMP-inspired two-step gradient descent and integrates the aforementioned properties into the trajectory optimization process. Based on the descent of the objective function, the trajectory is iteratively updated through a two-step update method to create a feasible trajectory while accurately following the given end-effector path (Sec. III-B). Since this optimization process is based on local updates, it can stick to local minima. To avoid local minima, we adopt quantum annealing, an effective randomization technique, in our method to gradually identify better trajectories (Sec. III-D).

To see the merits of each component of the method, the reduced method is tested in two different scenarios involving external obstacles (Sec. IV-A). To compare the proposed method with the state-of-the-art method, we test three scenarios without obstacles, RelaxedIK and Stampede (Sec. IV-B). Overall, it can be observed that the proposed method strongly minimizes fairly fast pose errors in both obstacle and non-obstacle environments.

The device described above may be implemented as a hardware component, a software component, and/or a combination of the hardware component and the software component. For example, devices and components described in the embodiments may include, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable array (FPA), It may be implemented using one or more general purpose or special purpose computers, such as a programmable logic unit (PLU), microprocessor, or any other device capable of executing and responding to instructions. The processing device may execute an operating system (OS) and one or more software applications running on the operating system. The processing device may also access, store, manipulate, process, and generate data in response to execution of the software. For convenience of understanding, although one processing device is sometimes described as being used, one of ordinary skill in the art will recognize that the processing device includes a plurality of processing elements and/or a plurality of types of processing elements. It can be seen that can include For example, the processing device may include a plurality of processors or one processor and one controller. Other processing configurations are also possible, such as parallel processors.

The software may comprise a computer program, code, instructions, or a combination of one or more thereof, which configures a processing device to operate as desired or is independently or collectively processed You can command the device. The software and/or data may be any kind of machine, component, physical device, virtual equipment, computer storage medium or device, to be interpreted by or to provide instructions or data to the processing device. may be embodied in The software may be distributed over networked computer systems, and stored or executed in a distributed manner. Software and data may be stored in one or more computer-readable recording media.

The method according to the embodiment may be implemented in the form of program instructions that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, etc. alone or in combination. The program instructions recorded on the medium may be specially designed and configured for the embodiment, or may be known and available to those skilled in the art of computer software. Examples of the computer-readable recording medium include magnetic media such as hard disks, floppy disks and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic such as floppy disks. - includes magneto-optical media, and hardware devices specially configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine language codes such as those generated by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like.

As described above, although the embodiments have been described with reference to the limited embodiments and drawings, various modifications and variations are possible from the above description by those skilled in the art. For example, the described techniques are performed in a different order than the described method, and/or the described components of the system, structure, apparatus, circuit, etc. are combined or combined in a different form than the described method, or other components Or substituted or substituted by equivalents may achieve an appropriate result.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

Claims (10)

modeling the objective function with three characteristics: matching to minimize pose errors between the target and the current end-effector pose, conditions to ensure smoothness of the trajectory, and quantitative measurements of proximity to obstacles to avoid collisions;
iteratively updating the trajectory to minimize the cost of the objective function with three features, and optimizing the trajectory using two-step gradient descent to reduce potential competition between the three features during the update;
selecting an initial trajectory that minimizes the objective function to select an optimal joint configuration of the end-effector pose;
applying quantum annealing to iteratively randomize the joint configuration of the initial trajectory to avoid falling into a local minimum; and
A step of synthesizing a desired trajectory through an optimization process that integrates an objective function, and updating the trajectory by checking the collision of the trajectories to which quantum annealing is applied.
A trajectory optimization method comprising According to claim 1,
Iteratively updating the trajectory to minimize the cost of the objective function with three features, and optimizing the trajectory using two-step gradient descent to reduce potential competition between the three features during the update,
Two-step gradient descent updates the trajectory using quantitative measurements of proximity to obstacles to avoid collisions, the condition for each odd iteration to ensure smoothness of the trajectory among the three properties of the objective function, and the target and current end Iteratively updates the trajectory using matching to minimize pose errors between effector poses.
Trajectory optimization method. According to claim 1,
In order to select the optimal joint configuration of the end-effector pose, the step of selecting as the initial trajectory that minimizes the objective function is:
Represent the path of the end-effector in a tessellated form in multiple poses, simplify the multiple poses of the end-effector, find a joint configuration that minimizes the objective function in the multiple poses of the simplified end-effector, and perform linear interpolation. to interconnect the selected joint configurations for calculating the initial trajectory through
Trajectory optimization method. According to claim 1,
Applying quantum annealing to iteratively randomize the joint configuration of the initial trajectory in order not to fall into a local minimum,
Prepare randomization parameters using quantum transformation, perform local optimization, quantum transformation searches for lower cost by random search controlled by the parameter, and the parameter determines the strength of randomness according to the cost function to control
Trajectory optimization method. 5. The method of claim 4,
Using Sequential Exploring (SE), which repeats quantum transformations and places more weight on the search part,
Trajectory optimization method. An objective function that models the objective function with three characteristics: matching to minimize pose error between the target and the current end-effector pose, conditions to ensure smoothness of the trajectory, and quantitative measurement of proximity to obstacles to avoid collisions. modeling department;
a trajectory optimizer that iteratively updates the trajectory to minimize the cost of the objective function with three features, and optimizes the trajectory using two-step gradient descent to reduce potential competition between the three features during the update;
an initial trajectory selection unit that selects an initial trajectory that minimizes the objective function in order to select an optimal joint configuration of the end-effector pose;
a quantum annealing unit that applies quantum annealing to repeatedly randomize the joint configuration of the initial trajectory in order not to fall into a local minimum; and
A trajectory update unit that synthesizes a desired trajectory through an optimization process that integrates an objective function and updates the trajectory by checking collisions of trajectories to which quantum annealing is applied.
A trajectory optimization device comprising a. 7. The method of claim 6,
The trajectory optimization unit,
Two-step gradient descent updates the trajectory using quantitative measurements of proximity to obstacles to avoid collisions, the condition for each odd iteration to ensure smoothness of the trajectory among the three properties of the objective function, and the target and current end Iteratively updates the trajectory using matching to minimize pose errors between effector poses.
Trajectory Optimizer. 7. The method of claim 6,
The initial trajectory selection unit,
Represent the path of the end-effector in a tessellated form in multiple poses, simplify the multiple poses of the end-effector, find a joint configuration that minimizes the objective function in the multiple poses of the simplified end-effector, and perform linear interpolation. connecting the selected joint configurations to calculate the initial trajectory through
Trajectory Optimizer. 7. The method of claim 6,
Quantum annealing unit,
Prepare randomization parameters using quantum transformation, perform local optimization, quantum transformation searches for lower cost by random search controlled by the parameter, and the parameter determines the strength of randomness according to the cost function to control
Trajectory Optimizer. 10. The method of claim 9,
Using Sequential Exploring (SE), which repeats quantum transformations and places more weight on the search part,
Trajectory Optimizer.

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