ArticlePDF Available

Motion Planning of Robot Manipulators for a Smoother Path Using a Twin Delayed Deep Deterministic Policy Gradient with Hindsight Experience Replay


Abstract and Figures

In order to enhance performance of robot systems in the manufacturing industry, it is essential to develop motion and task planning algorithms. Especially, it is important for the motion plan to be generated automatically in order to deal with various working environments. Although PRM (Probabilistic Roadmap) provides feasible paths when the starting and goal positions of a robot manipulator are given, the path might not be smooth enough, which can lead to inefficient performance of the robot system. This paper proposes a motion planning algorithm for robot manipulators using a twin delayed deep deterministic policy gradient (TD3) which is a reinforcement learning algorithm tailored to MDP with continuous action. Besides, hindsight experience replay (HER) is employed in the TD3 to enhance sample efficiency. Since path planning for a robot manipulator is an MDP (Markov Decision Process) with sparse reward and HER can deal with such a problem, this paper proposes a motion planning algorithm using TD3 with HER. The proposed algorithm is applied to 2-DOF and 3-DOF manipulators and it is shown that the designed paths are smoother and shorter than those designed by PRM.
Content may be subject to copyright.
Motion Planning of Robot Manipulators for
a Smoother Path Using a Twin Delayed Deep
Deterministic Policy Gradient with Hindsight
Experience Replay
MyeongSeop Kim 1,† , Dong-Ki Han 1,† , Jae-Han Park 2and Jung-Su Kim 1,*
Department of Electrical and Information Engineering, Seoul National University of Science and Technology,
Seoul 01811, Korea; (M.K.); (D.-K.H.)
2Robotics R&D Group, Korea Institute of Industrial Technology (KITECH), Ansan 15588,
*Correspondence:; Tel.: +82-2-970-6547
These authors contributed equally to this work.
Received: 2 December 2019; Accepted: 7 January 2020; Published: 13 January 2020
In order to enhance performance of robot systems in the manufacturing industry, it is
essential to develop motion and task planning algorithms. Especially, it is important for the
motion plan to be generated automatically in order to deal with various working environments.
Although PRM
(Probabilistic Roadmap) provides feasible paths when the starting and goal positions
a robot
manipulator are given, the path might not be smooth enough, which can lead to inefficient
performance of the robot system. This paper proposes a motion planning algorithm for robot
manipulators using a twin delayed deep deterministic policy gradient (TD3) which is a reinforcement
learning algorithm tailored to MDP with continuous action. Besides, hindsight experience replay
(HER) is employed in the TD3 to enhance sample efficiency. Since path planning for a robot
manipulator is an MDP (Markov Decision Process) with sparse reward and HER can deal with such
a problem, this paper proposes a motion planning algorithm using TD3 with HER. The proposed
algorithm is applied to 2-DOF and 3-DOF manipulators and it is shown that the designed paths are
smoother and shorter than those designed by PRM.
motion planning; Probabilistic Roadmap (PRM); Reinforcement learning; policy gradient;
Hindsight Experience Replay (HER)
1. Introduction
In the Industry 4.0 era, robots and related technologies are fundamental elements of assembley
systems in manufacturing; for instance, efficient robot manipulators for various tasks in assembly lines,
control of robots with high accuracy, and optimization methods for task scheduling [1,2].
When a task is given from a high level task scheduler, the manipulator has to move its end-effector
from the starting point to the goal point without collision with any obstacles or other robots. For this,
motion planning algorithms let robot manipulators know how to change their joint angles in order
for the end-effector to reach the goal point without collision. Currently, in practice, human experts
teach robot manipulators how to move in order to conduct various predefined tasks. Namely, a robot
manipulator learns from human experts how to change its joint angles for a given task. However,
when the tasks or the working environments change, such manual teaching (a robot manipulator’s
learning) procedure has to be done again. The other downside of the current approach is optimality or
efficiency. In other words, it is not clear if the robot manipulator moves optimally even though the
Appl. Sci. 2020,10, 575; doi:10.3390/app10020575
Appl. Sci. 2020,10, 575 2 of 15
robot manipulator can perform a given task successfully when a robot manipulator learns from human
Therefore, it is
important to teach the robot manipulators an optimal path automatically
when a task is given.
Using policy
search-based reinforcement learning, this paper presents a motion
planning algorithm for robot manipulators, which makes it possible for the robot manipulator to
generate an optimal path automatically; it is a smoother path compared with existing results [35].
For robot path planning, sampling-based algorithms find feasible paths for the robot manipulator
using a graph consisting of randomly sampled nodes and connected edges in the given configuration
space [
]. PRM (Probabilistic Roadmaps) and RRT (Rapid Exploring Random Trees) are two
representatives of sampling-based planning algorithms. PRM consists of two phases. The learning
phase samples nodes randomly from collision-free space in the configuration space and makes edges
with direction by connecting the sampled nodes. Then, it constructs a graph using the nodes and edges.
The query phase finds the optimal path connecting the starting node and goal node in the graph [
Note that the resulting path by PRM is made by connecting the sampled nodes in the configuration
space; usually, it is not smooth and might be longer than the optimal path. RRT samples nodes from
the neighbor of the starting point in the configuration space, constructs a tree by finding a feasible path
from the starting node, and expands the graph until the goal point is reached. It works for various
environments and can generate a path quickly, but its optimality is not guaranteed in general [
More recently, Fast Marching Methods (FMMs) using level sets have been proposed for path planning.
The FMMs
are mainly about efficiently solving the Eikonal equation whose solution provides the
optimal path. It is shown that FMMs lead to an asymptotically optimal path and faster convergence
than PRM and RRT [
]. Since FMMs, PRM, and RTT are sampling-based approaches, they need a high
number of sampling points for high dimensional configuration space in order to obtain a smoother
path, which means that they are computationally demanding in calculating the optimal path for given
arbitrary starting and ending points. Also, they can suffer from memory deficiency in high dimensional
space. However, in the proposed method, when a TD3 agent is trained, the optimal path can easily be
computed (i.e., trained neural network computation).
Reinforcement learning is a deep learning approach which finds an optimal policy for an MDP
(Markov Decision Process). The agent applies an action according to the policy to the environment
and then the agent gets the next state and reward from the environment. The agent finds the optimal
policy such that the sum of reward over the horizon is maximized [
]. In reinforcement learning,
there are two typical approaches to find the optimal policy. Value-based approaches estimate the
optimal (action) state value function and derive the corresponding policy from the estimate of the
value function [
]. On the other hand, policy gradient approaches search the optimal policy
directly from the set of state and reward data. It is known that policy gradient approaches show much
better performance in general [
]. Recently, deep learning-based control and operation of robot
manipulators have drawn much attention. In [
], robot path planning methods are proposed using
a deep
-network algorithm with emphasis on learning efficiency. For path training, a stereo image is
used to train DDPG (Deep Deterministic Policy Gradient) in [31]. In [32], a real robot is trained using
reinforcement learning for its path planning.
This paper presents a policy gradient-based path planning algorithm. To this end, RAMDP (Robot
Arm Markov Decision Process) is defined first. In RAMDP, the state is the joint angle of the robot
manipulator and the action is the variation of the joint angle. Then, DDPG (Deep Deterministic Policy
Gradient) with HER (Hindsight Experience Replay) is employed for the purpose of searching the
optimal policy [
]. DDPG is applied since the action in RAMDP is a continuous value and DDPG
is devised for MDP with a continuous action. The twin delayed DDPG enhances performance of
DDPG so that it shows good convergent property and avoids overestimation. In fact, HER is quite
fit to robot path planning since RAMDP is an MDP with sparse reward. Sparse reward means that
when an MDP has a finite length of an episode with a specific goal state and the episodes end at
non-goal states (say, a failed episode) due to any reasons frequently, the agent can not get much
reward. Since all reinforcement learning finds the optimal policy by maximizing the sum of reward,
Appl. Sci. 2020,10, 575 3 of 15
sparse reward is critical in reinforcement learning. However, as the episodes are saved in the memory,
HER modifies the last state in a failed episode as a new goal. Then, the failed episode becomes
a normal
episode which ends at the goal state. Hence, HER enhances the sample efficiency and fits to the robot
path planning.
It is
shown that such a procedure is quite helpful in a motion planning algorithm.
In the proposed algorithm, when the state is computed after applying the action, the collision with
obstacle or reaching the goal are checked. It turns out that many states end at non-goal states in the
middle of learning. This is why conventional reinforcement learnings do not work well for robot
path planning. However, using HER, those episodes can be changed to a normal episode which
ends at goal states. Hence, the contribution of the paper is to present a path planning algorithm
using DDPG with HER. The proposed method is applied to a 2-DOF and 3-DOF robot manipulators
using simulation; experimental results are also shown for a 3-DOF manipulator. In both cases, it is
quantitatively demonstrated that the resulting paths are shorter than those by PRM.
2. Preliminaries and Problem Setup
2.1. Configuration Space and Sampling-Based Path Planning
In sampling-based path planning, configuration space
(also called joint space for robot
manipulators) represents the space of possible joint angles and is a subset of
-dimensional Euclidean
denotes the number of the joints of the manipulator. The values of the joint angles
of a robot manipulator are denoted as a point in
]. The configuration space consists of two
subsets: the collision-free space
in which the robot manipulator collides with other
obstacles or itself. For motion planning, a discrete representation of the continuous
is generated
by random sampling. Then a connected graph (roadmap) is obtained. The nodes in the graph denote
admissible configuration of the robot manipulators, and the edges connecting any two nodes mean
feasible paths (trajectory) between the corresponding configurations. Finally, when the starting and
goal configurations
are given, any graph search algorithm is employed to find the shortest
path connecting
. There exists a shortest path between
since they are two nodes
on the connected graph.
2.2. Reinforcement Learning
Reinforcement learning is an optimization-based method to solve an MDP (Markov Decision
Process) [
]. An MDP is comprised of
is a set of the state and
a set
of the action. Besides,
consists of
which is the transition probability that the current
with the action
becomes the next state
stands for the reward function
0, 1
is the discount factor. The agent’s policy
implies the distribution of the action
for the given state
. In reinforcement learning, the agent takes action
according to the policy
at time
and state
, and the environment returns the next state
and reward
by the
and reward function
. By repeating this, the agent updates its policy so as to maximize
its expected return
. The resulting optimal policy is denoted by
. In order to find
the optimal policy, value-based methods like DQN (Deep Q-Network) estimate the optimal value
function (
i.e., estimate the
maximum return) and find the corresponding policy [
]. On the other hand,
policy gradient
methods compute the optimal policy directly from samples. For instance, REINFORCE,
actor-critic method, DPG (Deterministic Policy Gradient), DDPG (Deep DPG), A3C (Asynchronous
Advantage Actor-Critic), TRPO (Trust Region Policy Optimization) are representative methods of policy
gradient methods [
]. Training performance of reinforcement learning is heavily dependent on
samples which are several sets of the state, action, and next state.
Hence, in addition
to the various
reinforcement learning algorithms, many research efforts have been directed to study on how to use
episodes efficiently for the purpose of better agent learning, for example,
replay memory [19]
HER (Hindsight Experience Replay) [
]. In this paper, for the sake of designing
a motion
Appl. Sci. 2020,10, 575 4 of 15
algorithm, a policy gradient called TD3 (twin delayed Deep Deterministic Policy Gradient) is used for
path planning.
3. TD3 Based Motion Planning for Smoother Paths
3.1. RAMDP (Robot Arm Markov Decision Process) for Path Planning
In order to develop a reinforcement learning (RL) based path planning, the robot arm MDP
(RAMDP) needs to be defined properly first [
]. The state
of the RAMDP is the angle value
of each joint of the manipulator where the joint angle belongs to the configuration space
Hence, for collision-free
operation of a robot manipulator, in the motion planning, the state
to only
Qfree Rn
is the number of the joint in the manipulator. In the RAMDP, the action is
joint angle variation. Unlike MDP with discrete state and action such as frozen-lake ([
]), the RAMDP
under consideration has continuous state (i.e., joint angle) and continuous action (i.e., joint angle
variation). Due to this, DDPG or its variants are fit to find the optimal policy for the agent in the
RAMDP. In this paper, TD3 (twin delayed DDPG) is employed to find an optimal policy for the
continuous action with deterministic policy
in the RAMDP. Figure 1describes how to generate the
sample (
) in the RAMDP. Suppose that arbitrary initial state (
) and goal state (
are given, and that the maximum length of the episode is
. At state
, if the action
is applied
to the RAMDP,
is produced from the RAMDP. Then, according to the reward function in
the next state
are determined. In view of
, if
does not belong to
, then the
next state is set as the current state. Furthermore, if the next state is the goal point, then the reward
is 0, and otherwise the reward is
1. Then, the whole procedure is repeated until the episode ends.
Note that this reward function leads to as short as possible path since TD3 tries to maximize the sum
of reward and a longer path implies more 1 reward.
qt+1, if ˆ
qt, if ˆ
0, if qt+1== qgoal
1, if qt+1Qcollide
1, if qt+1Qfree
Figure 1. Robot Arm Markov Decision Process (RAMDP).
There are two possibilities for the episode to end: (1) the next state becomes the goal
state, i.e.,
e= [(q0
· · ·
, and (2) the length of the episode is
, i.e.,
· · ·
. For both cases, every sample in the form of
) is saved in the memory. Note that when
, the next state
is set to the
current state
in order to avoid collision. In the worst case, if this happens repeatedly, the agent is
Appl. Sci. 2020,10, 575 5 of 15
trained such that the corresponding episode does not occur. Based on these samples in the memory,
the optimal policy is determined in accordance with TD3, which is explained in the next subsection.
3.2. TD3 (Twin Delayed Deep Deterministic Policy Gradient)
In this section, TD3 is introduced [
], which is used to search the optimal policy in the proposed
algorithm [
]. To this end, it is assumed that a sufficient number of samples (
are stored in the memory.
Figure 2describes the structure of TD3. The basic structure of TD3 is the actor-critic network.
However, unlike the actor critic network, there are two critic deep neural networks (DNN), one actor
DNN, and three target DNNs for each critic and actor DNNs. Hence, there are 6 DNNs (2 critic DNNs
and their target DNNs, 1 actor DNN, and its target DNN) in TD3. As seen in Figure 3, the critic DNNs
generate an optimal estimate
of the state-action value function. The input of the critic DNN
is a mini-batch from the memory and its output is
1, 2. The mini-batch is a finite set of
samples (
) from the memory. In TD3, it is important that the two critic DNNs are used in
order to remove overestimation bias in
function approximation. The overestimation bias can
take place when bad states due to accumulated noises are overestimated. In order to cope with this,
TD3 chooses the smaller
value out of two critic DNN outputs critic DNN as the target value.
In Figure 3,
are the parameters of the two critic DNNs, and
those of corresponding
target DNNs. In order to train the critic DNN, as the cost function, the following quadratic function of
temporal difference error δ:=Qθ(q,a)ytarget is minimized,
Jδ(θ):=1/2(Qθ(q,a)ytarget)2, (2)
where Qθ(s,a)stands for the parameterized state-action value function Qwith parameter θ,
ytarget =r+γmin
i=1,2 Qθ0
is the target value of the function
, and the target action (i.e., the action used in the critic target
DNN) is defined as,
a=µφ(q) + ¯
e, (4)
where noise
follows a clipped normal distribution
0. This implies that
a random variable with N(0, σ)and belongs to the interval [c,c].
Figure 2. Structure of TD3 (Twin Delayed Deep Deterministic Policy Gradient) with RAMDP.
Appl. Sci. 2020,10, 575 6 of 15
Figure 3. Details of critic and actor deep neural network for RAMDP.
The inputs of the actor DNN are both
from the critic DNN and the mini-batch from the
memory, and the output is the action. Precisely, the action is given by
at=µφ(qt) + e
is the
parameter of the actor DNN,
is the output from the actor DNN, and a deterministic and continuous
value. Noise
follows the normal distribution
, and is added for exploration. In order to tune
the parameter φ, the following cost function is minimized.
Jµ(φ) =
dµ(q)Qθ(q,µφ(q) + e),(5)
denotes the distribution of the state. Note that the gradient
Qθ(q,a)) is used to update the parameter φ. This is why the method is called the policy gradient.
Between the two outputs from the two critic target DNN, the common target value in
is used
to update the two critic DNNs. Also, TD3 updates the actor DNN and all three target DNNs every
steps periodically in order to avoid too fast convergence. Note that the policy
is updated
proportionally to only
]. The parameters for the critic target DNN and the actor target
DNN are updated according to
θ0τθ + (
at every
steps, which not only maintain small
temporal difference error, but also make the parameters in the target DNN updated slowly.
3.3. Hindsight Experience Replay
Since the agent in reinforcement learning is trained from samples, it is utmost important to have
helpful samples which mean that the action state pair improve the action value function. On the other
hand, many unhelpful samples are generated in RAMDP since many episodes end without reaching
the goal. In other words, RAMDP is an MDP with sparse reward. For the purpose of enhancing
sample efficiency, HER (Hindsight Experience Replay) is employed in this paper. For the episode
e= [(q0
· · ·
in the memory where
is not the goal state, HER resets
. This means that even though the episode does not end the goal state, the episode becomes a ended
state at the goal after modification by HER. Then, the failed episodes can be use to train the agent since
the modified episodes are a goal achieved episodes. Algorithm 1 summarizes the proposed algorithm
introduced in this section.
Appl. Sci. 2020,10, 575 7 of 15
Algorithm 1
Training procedure for motion planning by TD3 with HER. The red part is for a robot
manipulator, and the blue part is for HER.
1: Initialize critic networks Qθ1,Qθ2, and actor network πφwith θ1,θ2,φ
2: Initialize target networks θ0
3: Initialize replay buffer R
4: for e=1to Mdo
5: Initialize local buffer L.memory for HER
6: for t=0to T1do
7: Randomly choose goal point qgoal Qfree
8: Select action with noise:
9: atµφ(qt||qgoal ) + e,e N (0, σ).|| denotes concatenation
10: qt+1=qt+αat
12: if qt+α(µφ(qt||qgoal ) + e)/Q then
13: qt+1qt
14: else if qt+1Qcollide then
15: qt+1qt
16: else if |qt+1qgoal| 0.2 αthen
17: Terminal by goal arrival
18: end if
20: rt:=r(qt,at,qgoal)
21: Store the transition (qt||qgoal,at,rt,qt+1||qgoal )in R,L
23: Sample mini-batch of ntransitions (qj||qgoal ,aj,rj,qj+1||qgoal)from R
24: ˜
ajµφ0(qj+1||qgoal ) + e,eclip(N(0, σ),c,c)
25: yjrj+γmini=1,2Qθ0
26: Update critics θiwith temporal difference error:
27: θiJ(θi) = 1
29: if tmod dthen .delayed update with d
30: Update actor φby the deterministic policy gradient:
31: φJ(φ) = 1
j=1φQθ1(qj,µφ(qj||qgoal ))
32: Update target networks:
33: θ0
iτθi+ (1τ)θ0
34: φ0τφ + (1τ)φ0
35: end if
36: end for
37: if qT6=qgoal then
38: Set additional goal q0
goal qT
39: for t=0to T1do
40: Sample a transition (qt||qgoal ,at,rt,qt+1||qgoal)from L
41: r0
42: Store the transition (qt||q0
goal)in R
43: end for
44: end if
45: end for
Appl. Sci. 2020,10, 575 8 of 15
4. Case Study for 2-DOF and 3-DOF Manipulators
In order to show the effectiveness of the proposed method, it is applied to robot manipulators.
Table 1shows the information of the used 2-DOF and 3-DOF and manipulators.
Table 1. Parameters of 2-DOF and 3-DOF manipulators.
DOF Joint Max (degree) Joint Min (degree) Action Step Size (α)Goal Boundary
2 (140, 45, 150) (140, 180, 45) 0.1381 0.2
3 (60, 60) (0, 0) 3.0 1.0
For easy visualization, the proposed algorithm is applied to the 2-DOF manipulator first. Table 2
summarizes the tuning parameters for the designed TD3 with HER.
Table 2. Tuning parameters for the designed TD3 with HER.
Network Name Learning Rate Optimizer Update Delay DNN Size
Actor 0.001 adam 2 6 ×400 ×300 ×3
Critic 0.001 adam 0 6 ×400 ×300 ×1
Actor target 0.005 - 2 6 ×400 ×300 ×3
Critic target 0.005 - 2 6 ×400 ×300 ×1
In order to train TD3 with HER for the 2-DOF manipulator, 8100 episodes are used. Figure 4
describes the success ratio of each episode with HER when the network is training. In other words,
when the network is learning with arbitrary starting and goal points, sometimes the episodes end at
the given goal point but sometimes the episodes end before reaching the given goal point.
In Figure 4
the green lines denote the success ratio of every 10 episodes and the thick lines stand for the
moving average of the gray lines. Figure 5shows the reward as the number of the episode increases,
i.e., the training
is proceeding. The reward converges as the number of the episode increases. In view
of the results in Figures 4and 5, we can see that learning is over successfully.
For the purpose of testing the trained TD3, it is verified if the optimal paths are generated when
random starting and goal points are given to the trained TD3. For testing, only the actor DNN without
its target DNN is used with the input being a starting and goal point repeatedly. The input to the
trained actor DNN is
, the output is
, and then this is repeated with
depicted in Figure 6.
Figure 4. 2-DOF manipulator: success ration of reaching the goal point with HER.
Appl. Sci. 2020,10, 575 9 of 15
Figure 5. 2-DOF manipulator: reward from learning.
Figure 6. Path generation using the trained actor DNN.
When this is applied to the 2-DOF manipulator, the resulting paths are shown in Figure 7.
In Figure 7
, the green areas represent obstacles in the configuration space, and the rhombus denote the
starting point and the circles means the goal point. For comparison, PRM is also applied to generate the
paths with the same starting and goal points. As shown in Figure 7, the proposed method generates
smoother paths in general. This is confirmed from many other testing data as well. In Figure 7,
the red lines are the resulting paths by PRM and the blue lines by the proposed method. In average,
the resulting path by the proposed method is shortened by 3.45% compared with the path by PRM.
In order to test the proposed method for a real robot manipulator, the 3-DOF open manipulator.
For details, see is considered.
For easy understanding, Figure 8shows the workspaces in Matlab and Gazebo in ROS (Robot Operating
System) respectively, and configuration space of the open manipulator with four arbitrary obstacles.
The tuning parameters for the TD3 with HER are also shown in Table 2.
Appl. Sci. 2020,10, 575 10 of 15
Figure 7. DDPG based path generation for arbitrary starting and goal points in C-space.
(a) Workspace in Matlab
) Workspace in Gazebo (in ROS)
(c) Configuration space
Figure 8.
Workspace and configuration space. (
) Workspace in Matlab; (
) Workspace in Gazebo
(in ROS); (c) Configuration space.
For training, 140000 episodes are used. In view of the converged reward and success ratio in
Figures 9and 10, we can see that the learning is also over successfully. With this result, random starting
and goal points are given to the trained network in order to obtain a feasible path between them.
Figure 11 shows several examples of generated paths by the trained actor DNN when arbitrary starting
points and goal points are given. The red lines are resulting paths by PRM and the blue lines by the
proposed method. As seen in the figure, the proposed method results in smoother and shorter paths
in general. For the sake of between comparison, 100 arbitrary starting and gold points are used to
generate paths using PRM and the proposed method. Figure 12 shows the lengths of the resulting
100 paths
. In light of Figure 12, it is obvious that the proposed method generates smoother and shorter
paths in general. Note that, in average, the resulting path by the proposed method is shortened by
2.69% compared with the path by PRM.
When the proposed method is also implemented to the open manipulator, the same experimental
result as the simulation was obtained. The experimental result is presented in the
Appl. Sci. 2020,10, 575 11 of 15
Figure 9. 3-DOF manipulator: success ration of reaching the goal point with HER.
Figure 10. 3-DOF manipulator: reward from learning.
Figure 11. Cont.
Appl. Sci. 2020,10, 575 12 of 15
Figure 11. Path generation using DDPG with HER.
Figure 12. Comparison of paths by PRM and the proposed method.
5. Conclusions
For the purpose of enhancing efficiency in manufacturing industry, it is important to improve
performance of robot path planning and tasking scheduling. This paper presents a reinforcement
learning-based motion planning method of robot manipulators with focus on smoother and
shorter path generation, which means better operation efficiency. To this end, motion planning
problem is reformulated as a MDP (Markov Decision Process), called RAMDP (Robot Arm MDP).
Then, TD3 (twin delayed deep deterministic policy gradient, twin delayed DDPG) with HER (Hindsight
Experience Replay) is designed. DDPG is used since the action in RAMDP is a continuous value and
a policy
gradient tailored to an MDP with
a continuous action
. Moreover, since many failed
episodes are generated in the RAMDP meaning that the episode ends at non-goal state due to mainly
collision, HER is employed in order to enhance sample efficiency.
Future research topic includes how to solve motion planning problem for multi-robot arms whose
common working space is non-empty. To solve this problem, configuration space augmentation might
be a candidate solution. Since the augmented configuration space becomes high dimensional, it would
be interesting to compare performance of the proposed reinforcement learning-based approach by that
of sampling-based approaches such as FMMs, PRM, and RTT. Moreover, reinforcement learning-based
motion planning for dynamic environment is also a challenge problem.
Author Contributions:
M.K. and D.-K.H. surveyed the backgrounds of this research,
designed the
data, designed the deep learning network, and performed the simulations and experiments to show the benefits
of the proposed method. J.-S.K. and J.-H.P. supervised and supported this study. All authors have read and agreed
to the published version of the manuscript.
Appl. Sci. 2020,10, 575 13 of 15
Funding: This research received no external funding.
This work was supported by the Technology Innovation Program (or Industrial Strategic
Technology Development Program) (10080636, Development of AI-based CPS technology for Industrial robot
applications) funded By the Ministry of Trade, Industry & Energy(MOTIE, Korea), and by the Human Resources
Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the
Ministry of Trade, Industry & Energy of the Korea government (No. 20154030200720).
Conflicts of Interest: The authors declare no conflict of interest.
The following abbreviations are used in this manuscript:
MDP Markov Decision Process
RAMDP Robot Arm Markov Decision Process
DOF Degrees Of Freedom
PRM Probabilistic Roadmaps
RRT Rapid Exploring Random Trees
FMMs Fast Marching Methods
DNN Deep Neural Networks
DQN Deep Q-Network
(A3C) Asynchronous Advantage Actor-Critic
(TRPO) Trust Region Policy Optimization
(DPG) Deterministic Policy Gradient
DDPG Deep Deterministic Policy Gradient
TD3 Twin Delayed Deep Deterministic Policy Gradient
HER Hindsight Experience Replay
(ROS) Robot Operating System
1. Laumond, J.P. Robot Motion Planning and Control; Springer: Berlin, Germany, 1998; Volume 229.
Choset, H.M.; Hutchinson, S.; Lynch, K.M.; Kantor, G.; Burgard, W.; Kavraki, L.E.; Thrun, S. Principles of
Robot Motion: Theory, Algorithms, and Implementation; MIT Press: Cambridge, MA, USA, 2005.
Cao, B.; Doods, G.; Irwin, G.W. Time-optimal and smooth constrained path planning for robot manipulators.
In Proceedings of the 1994 IEEE International Conference on Robotics and Automation, San Diego, CA, USA,
8–13 May 1994; pp. 1853–1858.
Kanayama, Y.J.; Hartman, B.I. Smooth local-path planning for autonomous vehicles1. Int. J. Robot. Res.
16, 263–284. [CrossRef]
Rufli, M.; Ferguson, D.; Siegwart, R. Smooth path planning in constrained environments. In Proceedings
of the 2009 IEEE International Conference on Robotics and Automation, Kobe, Japan, 12–17 May 2009;
pp. 3780–3785.
Karaman, S.; Frazzoli, E. Sampling-based algorithms for optimal motion planning. Int. J. Robot. Res.
30, 846–894. [CrossRef]
Spong, M.W.; Hutchinson, S.A.; Vidyasagar, M. Robot modeling and control. IEEE Control Syst.
26, 113–115.
Kavraki, L.E.; Kolountzakis, M.N.; Latombe, J.C. Analysis of probabilistic roadmaps for path planning.
IEEE Trans. Robot. Autom. 1998,14, 166–171. [CrossRef]
Kavraki, L.E.; Svestka, P.; Latombe, J.C.; Overmars, M.H. Probabilistic roadmaps for path planning in
high-dimensional configuration spaces. IEEE Trans. Robot. Autom. 1996,12, 566–580. [CrossRef]
Kavraki, L.E. Random Networks in Configuration Space for Fast Path Planning. Ph.D. Thesis,
Stanford University, Stanford, CA, USA, 1995.
Kavraki, L.E.; Latombe, J.C.; Motwani, R.; Raghavan, P. Randomized query processing in robot path planning.
J. Comput. Syst. Sci. 1998,57, 50–60. [CrossRef]
Bohlin, R.; Kavraki, L.E. A Randomized Approach to Robot Path Planning Based on Lazy Evaluation.
Comb. Optim. 2001,9, 221–249.
Appl. Sci. 2020,10, 575 14 of 15
Hsu, D.; Latombe, J.C.; Kurniawati, H. On the probabilistic foundations of probabilistic roadmap planning.
Int. J. Robot. Res. 2006,25, 627–643. [CrossRef]
Kuffner, J.J.; LaValle, S.M. RRT-connect: An efficient approach to single-query path planning.
In Proceedings
of the 2000 IEEE International Conference on Robotics and Automation, San Francisco, CA, USA,
24–28 April 2000; Volume 2, pp. 995–1001.
Lavalle, S.; Kuffner, J. Rapidly-exploring random trees: Progress and prospects. In Algorithmic and
Computational Robotics: New Directions; CRC Press: Boca Ratol, FL, USA, 2000; pp. 293–308.
Janson, L.; Schmerling, E.; Clark, A.; Pavone, M. Fast marching tree: A fast marching sampling-based method
for optimal motion planning in many dimensions. Int. J. Robot. Res.
,34, 883–921. [CrossRef] [PubMed]
17. Sutton, R.S.; Barto, A.G. Reinforcement Learning: An Introduction; MIT Press: Cambridge, MA, USA, 2011.
Puterman, M.L. Markov Decision Processes: Discrete Stochastic Dynamic Programming, 1st ed.; John Wiley &
Sons, Inc.: New York, NY, USA, 1994.
Mnih, V.; Kavukcuoglu, K.; Silver, D.; Rusu, A.; Veness, J.; Bellemare, M.; Graves, A.; Riedmiller, M.;
Fidjeland, A.
; Ostrovski, G.; et al. Human-level control through deep reinforcement learning. Nature
518, 529–533. [CrossRef] [PubMed]
Langford, J. Efficient Exploration in Reinforcement Learning. In Encyclopedia of Machine Learning and Data
Mining; Sammut, C., Webb, G.I., Eds.; Springer US: Boston, MA, USA, 2017; pp. 389–392.
Tokic, M. Adaptive
-greedy exploration in reinforcement learning based on value differences. In Annual
Conference on Artificial Intelligence; Springer: Berlin, Germany, 2010; pp. 203–210.
Lillicrap, T.P.; Hunt, J.J.; Pritzel, A.; Heess, N.M.O.; Erez, T.; Tassa, Y.; Silver, D.; Wierstra, D.
Continuous control with deep reinforcement learning. arXiv 2015, arXiv:1509.02971.
Hasselt, H.v.; Guez, A.; Silver, D. Deep Reinforcement Learning with Double Q-Learning. In Proceedings
of the Thirtieth AAAI Conference on Artificial Intelligence, Phoenix, AZ, USA, 12–17 February 2016;
pp. 2094–2100.
Fujimoto, S.; van Hoof, H.; Meger, D. Addressing function approximation error in actor-critic methods. arXiv
2018, arXiv:1802.09477.
Hessel, M.; Modayil, J.; Van Hasselt, H.; Schaul, T.; Ostrovski, G.; Dabney, W.; Horgan, D.; Piot, B.;
Azar, M.
Silver, D. Rainbow: Combining improvements in deep reinforcement learning. In Proceedings of the
Thirty-Second AAAI Conference on Artificial Intelligence, New Orleans, LA, USA, 2–7 February 2018.
Mnih, V.; Badia, A.P.; Mirza, M.; Graves, A.; Lillicrap, T.; Harley, T.; Silver, D.; Kavukcuoglu, K.
Asynchronous methods
for deep reinforcement learning. In Proceedings of the International Conference on
Machine Learning, New York, NY, USA, 20–22 June 2016; pp. 1928–1937.
27. Degris, T.; Pilarski, P.M.; Sutton, R.S. Model-free reinforcement learning with continuous action in practice.
In Proceedings of the 2012 American Control Conference (ACC), Montreal, QC, Canada, 27–29 June 2012;
pp. 2177–2182.
28. Degris, T.; White, M.; Sutton, R.S. Off-policy actor-critic. arXiv 2012, arXiv:1205.4839.
Bae, H.; Kim, G.; Kim, J.; Qian, D.; Lee, S. Multi-Robot Path Planning Method Using Reinforcement Learning.
Appl. Sci. 2019,9, 3057. [CrossRef]
Lv, L.; Zhang, S.; Ding, D.; Wang, Y. Path Planning via an Improved DQN-Based Learning Policy. IEEE Access
2019,7, 67319–67330. [CrossRef]
Paul, S.; Vig, L. Deterministic policy gradient based robotic path planning with continuous action spaces.
In Proceedings
of the IEEE International Conference on Computer Vision, Venice, Italy, 22–29 October 2017;
pp. 725–733.
Gu, S.; Holly, E.; Lillicrap, T.; Levine, S. Deep reinforcement learning for robotic manipulation with
asynchronous off-policy updates. In Proceedings of the 2017 IEEE International Conference on Robotics and
Automation (ICRA), Singapore, 29 May–3 June 2017; pp. 3389–3396.
Andrychowicz, M.; Wolski, F.; Ray, A.; Schneider, J.; Fong, R.; Welinder, P.; McGrew, B.; Tobin, J.; Abbeel, O.P.;
Zaremba, W. Hindsight experience replay. In Proceedings of the Advances in Neural Information Processing
Systems, Long Beach, CA, USA, 4–9 December 2017; pp. 5048–5058.
Lozano-Pérez, T. Spatial Planning: A Configuration Space Approach. In Autonomous Robot Vehicles; Cox, I.J.;
Wilfong, G.T., Eds.; Springer New York: New York, NY, USA, 1990; pp. 259–271.
Appl. Sci. 2020,10, 575 15 of 15
Silver, D.; Lever, G.; Heess, N.; Degris, T.; Wierstra, D.; Riedmiller, M. Deterministic Policy Gradient
Algorithms. In Proceedings of the 31st International Conference on International Conference on Machine
Learning, Bejing, China, 22–24 June 2014; pp. I-387–I-395.
36. Sutton, R.S.; Mcallester, D.; Singh, S.; Mansour, Y. Policy gradient methods for reinforcement learning with
function approximation. In Advances in Neural Information Processing Systems 12; MIT Press: Cambridge, MA,
USA, 2000; pp. 1057–1063.
2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (
... Soft actor-critic (SAC) is used for the same task in [12][13][14] with the ability to obtain smooth actions within a specified range. Deep deterministic policy gradient (DDPG) and its extension twin delayed deep deterministic policy gradient (TD3) have been successfully applied to navigation tasks with smooth navigation controls [15][16][17][18]. Here, state representations are given to a neural network that consists of two parallel structures: the actor and the critic. ...
Full-text available
For mobile cleaning robot navigation, it is crucial to not only base the motion decisions on the ego agent’s capabilities but also to take into account other agents in the shared environment. Therefore, in this paper, we propose a deep reinforcement learning (DRL)-based approach for learning motion policy conditioned not only on ego observations of the environment, but also on incoming information about other agents. First, we extend a replay buffer to collect state observations on all agents at the scene and create a simulation setting from which to gather the training samples for DRL policy. Next, we express the incoming agent information in each agent’s frame of reference, thus making it translation and rotation invariant. We propose a neural network architecture with edge embedding layers that allows for the extraction of incoming information from a dynamic range of agents. This allows for generalization of the proposed approach to various settings with a variable number of agents at the scene. Through simulation results, we show that the introduction of edge layers improves the navigation policies in shared environments and performs better than other state-of-the-art DRL motion policy methods.
... In addition, since the system-dynamics model is not considered in the path-tracking experiment based on deep reinforcement learning, in order to verify the advantage of the method based on deep reinforcement learning without the need for the dynamic model, this paper further explores the influence of the change in dynamic characteristics in the experimental results. To this end, we changed the quality of the end effector, the trained model was tested, and the experimental results are shown in Tables 3 and 4. The degree of smoothness [30,31] in the trajectory of the manipulator's end effector has an impact on the overall working effect in both scientific trials and real-world production. A crucial reference point is the energy that the manipulator generates while it operates [32]. ...
Full-text available
The continuous path of a manipulator is often discretized into a series of independent action poses during path tracking, and the inverse kinematic solution of the manipulator’s poses is computationally challenging and yields inconsistent results. This research suggests a manipulator-route-tracking method employing deep-reinforcement-learning techniques to deal with this problem. The method of this paper takes an end-to-end-learning approach for closed-loop control and eliminates the process of obtaining the inverse answer by converting the path-tracking task into a sequence-decision issue. This paper first explores the feasibility of deep reinforcement learning in tracking the path of the manipulator. After verifying the feasibility, the path tracking of the multi-degree-of-freedom (multi-DOF) manipulator was performed by combining the maximum-entropy deep-reinforcement-learning algorithm. The experimental findings demonstrate that the approach performs well in manipulator-path tracking, avoids the need for an inverse kinematic solution and a dynamics model, and is capable of performing manipulator-tracking control in continuous space. As a result, this paper proposes that the method presented is of great significance for research on manipulator-path tracking.
... Similarly, Yang and He (2020) proposed a decentralized event-triggered control (ETC) strategy based on Adaptive Critic Learning (ACL) and using experience replay, and Zhou et al (2022) proposed an attention-based actor-critic algorithm with Prioritized Experience Replay (PER) to improve the convergence time on robotic motion planning problems, changing the LSTM-based advantage actor-critic algorithm by using an encoder attention weight and initializing the networks using PER. Kim et al (2020) proposed a motion planning algorithm for robot manipulators using a twin delayed deep deterministic policy gradient, which applies hindsight experience replay. Prianto et al (2020) approached the path planning for multi-arm manipulators by proposing a method based on the Soft Actor-Critic (SAC) algorithm with hindsight experience replay to improve exploration in high-dimensional problems. ...
Full-text available
From the first theoretical propositions in the ’50s, inspired by the neuroscience and psychology studies about the learning processes in human beings and animals, to its application in real-world problems on learning to action, Reinforcement Learning (RL) is still being a fascinating, rich, and complex class of machine learning algorithms. In particular, we will start reviewing its fundamental principles and develop a discussion about how a technique called Experience Replay (ER) has been of fundamental importance in making a variety of methods in most of the relevant problems and different domains more data efficient, using agent experiences to improve its performance. We present some of the more relevant methods in the literature, which base most recent research on improving RL with ER. Finally, we bring from the recent literature some of the main trends, challenges, and advances focused on reviewing and discussing ER formal basement and how to improve its proposition to make it even more efficient in different methods and domains.
... This study solves the problem of Pick-and-Place using a reinforcement learning algorithm. First, to use reinforcement learning, a Markov decision process (MDP) for the problem which is handled should be defined [31]. MDP is a mathematical framework modeling the decision-making problems for stochastic events and actions taken by an agent. ...
Full-text available
This paper proposes a task decomposition and dedicated reward-system-based reinforcement learning algorithm for the Pick-and-Place task, which is one of the high-level tasks of robot manipulators. The proposed method decomposes the Pick-and-Place task into three subtasks: two reaching tasks and one grasping task. One of the two reaching tasks is approaching the object, and the other is reaching the place position. These two reaching tasks are carried out using each optimal policy of the agents which are trained using Soft Actor-Critic (SAC). Different from the two reaching tasks, the grasping is implemented via simple logic which is easily designable but may result in improper gripping. To assist the grasping task properly, a dedicated reward system for approaching the object is designed through using individual axis-based weights. To verify the validity of the proposed method, wecarry out various experiments in the MuJoCo physics engine with the Robosuite framework. According to the simulation results of four trials, the robot manipulator picked up and released the object in the goal position with an average success rate of 93.2%.
Full-text available
This paper proposes a noble multi-robot path planning algorithm using Deep q learning combined with CNN (Convolution Neural Network) algorithm. In conventional path planning algorithms, robots need to search a comparatively wide area for navigation and move in a predesigned formation under a given environment. Each robot in the multi-robot system is inherently required to navigate independently with collaborating with other robots for efficient performance. In addition, the robot collaboration scheme is highly depends on the conditions of each robot, such as its position and velocity. However, the conventional method does not actively cope with variable situations since each robot has difficulty to recognize the moving robot around it as an obstacle or a cooperative robot. To compensate for these shortcomings, we apply Deep q learning to strengthen the learning algorithm combined with CNN algorithm, which is needed to analyze the situation efficiently. CNN analyzes the exact situation using image information on its environment and the robot navigates based on the situation analyzed through Deep q learning. The simulation results using the proposed algorithm shows the flexible and efficient movement of the robots comparing with conventional methods under various environments.
Full-text available
The path planning technology is an important part of navigation, which is the core of robotics research. Reinforcement learning is a fashionable algorithm that learns from experience by mimicking the process of human learning skills. When learning new skills, the comprehensive and diverse experience help to refine the grasp of new skills which are called as the depth and the breadth of experience. According to the path planning, this paper proposes an improved learning policy based on the different demand of the experience’s depth and breadth in different learning stages, where the deep Q-networks calculated Q-value adopts the dense network framework. In the initial stage of learning, an experience value evaluation network is created to increase the proportion of deep experience to understand the environmental rules more quickly. When the path wandering phenomenon happens, the exploration of wandering point and other points are taken into account to improve the breadth of the experience pool by using parallel exploration structure. In addition, the network structure is improved by referring to the dense connection method, so the learning and expressive abilities of the network are improved to some extent. Finally, the experimental results show that our model has certain improvement in convergence speed, planning success rate and path accuracy. Under the same experimental conditions, the method of this paper is compared with the conventional intensive learning method via deep Q-networks. The results show that the indicators of this method are significantly higher.
Full-text available
We adapt the ideas underlying the success of Deep Q-Learning to the continuous action domain. We present an actor-critic, model-free algorithm based on the deterministic policy gradient that can operate over continuous action spaces. Using the same learning algorithm, network architecture and hyper-parameters, our algorithm robustly solves more than 20 simulated physics tasks, including classic problems such as cartpole swing-up, dexterous manipulation, legged locomotion and car driving. Our algorithm is able to find policies whose performance is competitive with those found by a planning algorithm with full access to the dynamics of the domain and its derivatives. We further demonstrate that for many of the tasks the algorithm can learn policies end-to-end: directly from raw pixel inputs.
In value-based reinforcement learning methods such as deep Q-learning, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. We show that this problem persists in an actor-critic setting and propose novel mechanisms to minimize its effects on both the actor and critic. Our algorithm takes the minimum value between a pair of critics to restrict overestimation and delays policy updates to reduce per-update error. We evaluate our method on the suite of OpenAI gym tasks, outperforming the state of the art in every environment tested.
In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a ‘lazy’ dynamic programming recursion on a predetermined number of probabilistically drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As such, this algorithm combines features of both single-query algorithms (chiefly RRT) and multiple-query algorithms (chiefly PRM), and is reminiscent of the Fast Marching Method for the solution of Eikonal equations. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence rate bounds—the first in the field of optimal sampling-based motion planning. Specifically, for a certain selection of tuning parameters and configuration spaces, we obtain a convergence rate bound of order O(n −1/d+ρ), where n is the number of sampled points, d is the dimension of the configuration space, and ρ is an arbitrarily small constant. We go on to demonstrate asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius. Numerical experiments over a range of dimensions and obstacle configurations confirm our theoretical and heuristic arguments by showing that FMT*, for a given execution time, returns substantially better solutions than either PRM* or RRT*, especially in high-dimensional configuration spaces and in scenarios where collision-checking is expensive.
Why is probabilistic roadmap (PRM) planning probabilistic? How does the probability measure used for sampling a robot’s configuration space affect the performance of a PRM planner? These questions have received little attention to date. This paper tries to fill this gap and identify promising directions to improve future planners. It introduces the probabilistic foundations of PRM planning and examines previous work in this context. It shows that the success of PRM planning depends mainly and critically on favorable “visibility” properties of a robot’s configuration space. A promising direction for speeding up PRM planners is to infer partial knowledge of such properties from both workspace geometry and information gathered during roadmap construction, and to use this knowledge to adapt the probability measure for sampling. This paper also shows that the choice of the sampling source—pseudo-random or deterministic—has small impact on a PRM planner’s performance, compared with that of the sampling measure. These conclusions are supported by both theoretical and empirical results.
The theory of reinforcement learning provides a normative account, deeply rooted in psychological and neuroscientific perspectives on animal behaviour, of how agents may optimize their control of an environment. To use reinforcement learning successfully in situations approaching real-world complexity, however, agents are confronted with a difficult task: they must derive efficient representations of the environment from high-dimensional sensory inputs, and use these to generalize past experience to new situations. Remarkably, humans and other animals seem to solve this problem through a harmonious combination of reinforcement learning and hierarchical sensory processing systems, the former evidenced by a wealth of neural data revealing notable parallels between the phasic signals emitted by dopaminergic neurons and temporal difference reinforcement learning algorithms. While reinforcement learning agents have achieved some successes in a variety of domains, their applicability has previously been limited to domains in which useful features can be handcrafted, or to domains with fully observed, low-dimensional state spaces. Here we use recent advances in training deep neural networks to develop a novel artificial agent, termed a deep Q-network, that can learn successful policies directly from high-dimensional sensory inputs using end-to-end reinforcement learning. We tested this agent on the challenging domain of classic Atari 2600 games. We demonstrate that the deep Q-network agent, receiving only the pixels and the game score as inputs, was able to surpass the performance of all previous algorithms and achieve a level comparable to that of a professional human games tester across a set of 49 games, using the same algorithm, network architecture and hyperparameters. This work bridges the divide between high-dimensional sensory inputs and actions, resulting in the first artificial agent that is capable of learning to excel at a diverse array of challenging tasks.