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arxiv: 1907.00388 · v1 · pith:HO6KQFEUnew · submitted 2019-06-30 · 💻 cs.RO · cs.SY· eess.SY

Reinforcement Learning for Robotic Time-optimal Path Tracking Using Prior Knowledge

Jiadong Xiao , Lin Li , Yanbiao Zou , Tie Zhang This is my paper

Pith reviewed 2026-05-25 12:30 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY
keywords reinforcement learningQ-learningtime-optimal path trackingrobotic manipulatorsactuator torque constraintsmotor characteristicspath planning
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The pith

An improved Q-learning algorithm finds time-optimal robot trajectories while respecting velocity-dependent actuator torque constraints.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a reinforcement learning method to solve time-optimal path tracking for industrial robots. Most prior work assumes fixed conservative torque limits, but real motors have limits that decrease with velocity according to a piecewise linear characteristic. The authors modify standard Q-learning by changing the action-value function and introducing rewards for actions that meet constraints along with penalties for those that violate them. This produces trajectories that are both as fast as possible and feasible under the dynamic limits. The approach matters because it lets robots exploit the full capability of their motors rather than moving more slowly to stay safe under simplified assumptions.

Core claim

After noting the limitations of basic Q-learning, an improved action-value function is introduced to raise the convergence rate; the resulting algorithm uses reward for constraint-satisfying actions and penalty for constraint-violating actions to obtain a time-optimal trajectory that satisfies the velocity-dependent actuator torque constraints.

What carries the argument

The improved action-value function in Q-learning, which encodes prior knowledge by assigning reward when actions satisfy the piecewise-linear torque-velocity constraints and penalty when they do not.

If this is right

  • Robots can follow the same geometric path in less time by using the velocity-dependent limits instead of conservative fixed bounds.
  • The reward-penalty scheme lets the learner discover feasible high-speed motions without explicit analytic solution of the constrained optimization problem.
  • Convergence occurs faster than with unmodified Q-learning because the action-value updates already incorporate constraint knowledge.
  • The method produces trajectories that remain within actuator capability at every point along the path.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same reward-penalty structure could be reused for other robotic tasks whose constraints also depend on state in a non-convex way.
  • Combining the discrete-action Q-learning with function approximation might allow scaling to higher-dimensional configuration spaces.
  • Comparing the learned times against a numerical nonlinear optimizer on the same piecewise-linear model would quantify how close the RL solution comes to true optimality.

Load-bearing premise

The actuator torque limits decrease with velocity in a piecewise linear manner, which both makes the optimization harder and is what the modified Q-learning is built to handle.

What would settle it

Run the algorithm on a robot whose measured torque-velocity curve deviates strongly from piecewise linear and check whether the output trajectory still respects the true limits or exceeds the known minimum travel time.

Figures

Figures reproduced from arXiv: 1907.00388 by Jiadong Xiao, Lin Li, Tie Zhang, Yanbiao Zou.

Figure 3
Figure 3. Figure 3: A typical prior knowledge in the phase plane 𝑠 − 𝑠̇ [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: 6-DOF GSK-RB03A1 robot [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Servo motor torque characteristics of joints 4, 5, and 6; (b) Servo motor torque characteristics of joint 3; (c) Servo motor torque characteristics of joints 1 and 2. (□A is the continuous operation area; □B is the acceleration/deceleration area) [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Task path in Cartesian space 6.2 Experiment results and analysis 6.2.1 Comparison experiment regarding path discretization To verify the effectiveness and necessity of the selective discrete method proposed in Section 4.1, the uniform discrete method that uniformly discretizes the task path into 527 points is chosen as the comparison method. To eliminate the influence of unrelated variables, the two discre… view at source ↗
Figure 11
Figure 11. Figure 11: Return obtained by IQL and IAVRL by exploiting the learning experience after a successful exploration, where (a) is the case of a 527×500 grid, (b) is the close-up view (zoomed-in view of the pink box in (a)) to show the detailed convergence of IAVRL, (c) is the case of a 527×1000 grid, (d) is the case of a 527×1500 grid and (e) is the case of a 527×2000 grid. 6.2.2 Comparison experiment regarding RL algo… view at source ↗
Figure 12
Figure 12. Figure 12: Return obtained by IQL with prior knowledge and IQL without prior knowledge through exploiting the learning [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Return obtained by IAVRL with prior knowledge and IAVRL without prior knowledge through exploiting the learning experience after a successful exploration, where (a) is the case of a 527×500 grid, (b) is the case of a 527×1000 grid, (c) is the case of a 527×1500 grid and (d) is the case of a 527×2000 grid [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Calculated torques of the optimal trajectory obtained by IAVRL with prior knowledge in a 527×2000 grid case, where (a) is the torques of joint 1, (b) is the torques of joint 2, (c) is the torques of joint 3, (c) is the torques of joint 4, (d) is the torques of joint 5 and (e) is the torques of joint 6. 7. Conclusion In this study, an improved Q-learning algorithm (IQL) and an improved action-value functio… view at source ↗
read the original abstract

Time-optimal path tracking, as a significant tool for industrial robots, has attracted the attention of numerous researchers. In most time-optimal path tracking problems, the actuator torque constraints are assumed to be conservative, which ignores the motor characteristic; i.e., the actuator torque constraints are velocity-dependent, and the relationship between torque and velocity is piecewise linear. However, considering that the motor characteristics increase the solving difficulty, in this study, an improved Q-learning algorithm for robotic time-optimal path tracking using prior knowledge is proposed. After considering the limitations of the Q-learning algorithm, an improved action-value function is proposed to improve the convergence rate. The proposed algorithms use the idea of reward and penalty, rewarding the actions that satisfy constraint conditions and penalizing the actions that break constraint conditions, to finally obtain a time-optimal trajectory that satisfies the constraint conditions. The effectiveness of the algorithms is verified by experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes an improved Q-learning algorithm for robotic time-optimal path tracking that accounts for velocity-dependent, piecewise-linear actuator torque constraints (rather than conservative constant bounds). After noting standard Q-learning limitations, it introduces a modified action-value function intended to accelerate convergence, combined with a reward/penalty scheme that rewards constraint-satisfying actions and penalizes violations, ultimately producing a feasible time-optimal trajectory; effectiveness is asserted via experimental verification.

Significance. If the modified update rule can be shown to preserve optimality while improving convergence under the stated torque model, the approach would offer a practical RL-based alternative to traditional time-optimal control methods that often rely on overly conservative torque limits, with potential applicability to industrial robot trajectory planning.

major comments (2)
  1. [Abstract] Abstract: the central claim that the improved action-value function accelerates convergence while still yielding a time-optimal trajectory under piecewise-linear velocity-dependent torque constraints is presented without any derivation, update-rule equation, or argument showing that the modification continues to satisfy the Bellman optimality equation or that the penalty term does not distort the pure time-minimization objective.
  2. [Abstract] Abstract: the experimental verification is asserted but no quantitative results, baseline comparisons, convergence plots, or constraint-satisfaction metrics are supplied, making it impossible to assess whether the claimed improvements actually support the optimality and feasibility assertions.
minor comments (1)
  1. [Abstract] The abstract refers to 'the proposed algorithms' (plural) but describes only a single improved Q-learning method; clarify the number and scope of algorithms.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on the abstract. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the improved action-value function accelerates convergence while still yielding a time-optimal trajectory under piecewise-linear velocity-dependent torque constraints is presented without any derivation, update-rule equation, or argument showing that the modification continues to satisfy the Bellman optimality equation or that the penalty term does not distort the pure time-minimization objective.

    Authors: The body of the manuscript (Section 3) derives the modified action-value function, which augments the standard Q-update with a prior-knowledge term derived from the piecewise-linear torque-velocity model; we argue that this term only re-weights feasible actions and therefore preserves the Bellman optimality equation on the feasible subset while accelerating convergence. The reward-penalty scheme is formulated so that the penalty is applied exclusively to infeasible transitions and does not alter the time-minimization objective for feasible trajectories. We agree, however, that the abstract should be self-contained and will revise it to include the explicit update-rule equation together with a one-sentence optimality argument. revision: yes

  2. Referee: [Abstract] Abstract: the experimental verification is asserted but no quantitative results, baseline comparisons, convergence plots, or constraint-satisfaction metrics are supplied, making it impossible to assess whether the claimed improvements actually support the optimality and feasibility assertions.

    Authors: The experiments section already contains quantitative comparisons against standard Q-learning, convergence curves, achieved trajectory times, and constraint-violation counts. We will revise the abstract to report the key numerical outcomes (e.g., convergence-speed improvement and final trajectory duration) so that the claims can be evaluated directly from the abstract. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental RL method with independent verification

full rationale

The paper proposes an improved Q-learning variant with a modified action-value function and reward/penalty scheme for time-optimal path tracking under velocity-dependent torque constraints. No derivation chain reduces any claimed result to fitted parameters, self-citations, or ansatzes by construction; the central contribution is presented as an algorithmic modification whose effectiveness is checked via experiments on the robot. The approach is self-contained against external benchmarks (standard Q-learning baselines and physical robot tests) with no load-bearing self-citation or renaming of known results. This is the normal honest case of an applied RL paper whose claims rest on empirical outcomes rather than algebraic reduction to inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that motor torque limits are velocity-dependent and piecewise linear; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Actuator torque constraints are velocity-dependent and the torque-velocity relationship is piecewise linear
    Explicitly stated in the abstract as the motor characteristic ignored by conservative assumptions and addressed by the proposed method.

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Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages

  1. [1]

    position

    Introduction The research on the time -optimal path tracking for robots began in 1970 s[1], which is a significant field of industrial robots. The research aims to maximize the performance of the servo motor, to make the robot work at the maximum velocity under the constraint conditions, reduce the execution time for the robotic tasks and improve the work...

    work page 1970

  2. [2]

    The method tha t using numerical integration to obtain time -optimal trajectory was first proposed in [3]

    Numerical integration [2-7]: The first group of the methods obtain the solution by numerical integration in a way which maximizes the path velocity. The method tha t using numerical integration to obtain time -optimal trajectory was first proposed in [3]. In [4], the manipulator dynamics were described using p arametric functions which represent geometric...

    work page

  3. [3]

    Convex optimization[8-12]: The second group of the methods uses convex optimization techniques to solve the minimum time optimization problems. In [8], a log-barrier-based solution method and a recursive formulation is used to enable online optimization, while in [9] the problem is formulated as a second -order cone program. In [10], based on the work of ...

    work page

  4. [4]

    Dynamic programming[13-16]: The third group of methods uses dynamic programming following the idea of Bellman[17]. The idea of using dynamic method to solve the time-optimal problem was first proposed in [13], where the dynamic programming method is used to find the positions, velocities, accelerations, and torques that minimize cost. In [14], three perfo...

    work page

  5. [5]

    The kinematic and dynamic constraints are sequentially analysed, and these constraints are also transformed from joint space into parameter space

    Constraint conditions and optimization objective This Section mainly analyses the dynamic model of a robot manipulator and transforms the dynamic model from joint space into parameter space. The kinematic and dynamic constraints are sequentially analysed, and these constraints are also transformed from joint space into parameter space . Finally, the optim...

    work page

  6. [6]

    Q-learning applies the concept of reward and penalty in exploring an unknown environment and searching for a policy that maximizes the reward

    Q-learning algorithm and its limitations Q-learning is a type of reinforcement learning (RL) algorithms developed by Watkins in 1988 [26]. Q-learning applies the concept of reward and penalty in exploring an unknown environment and searching for a policy that maximizes the reward. Figure 1 shows the typical agent -environment interaction in Q-learning. In...

    work page 1988

  7. [7]

    Approaches for setting the reinforcement learning states and improving convergence rate In order to counter the limitation as described above, some approaches for improving the Q-learning algorithm is suggested in this Section. Firstly, in order to avoid the increase of the exploration space and set the discrete reinforcement learning state, it is necessa...

    work page

  8. [8]

    Combined with the improved approaches in Section 4, the steps of the IQL algorithm are as follows: Step 1

    Reinforcement learning algorithms for robotic time-optimal path tracking 5.1 Improved Q-learning (IQL) algorithm for robotic time-optimal path tracking Considering the Q-learning algorithm and its limitations, as mentioned in Section 3, the Q-learning algorithm is improved to make it more suitable for solving the time-optimal path tracking problem. Combin...

    work page

  9. [9]

    Industrial robot for experiment The industrial robot used for experimental ver ification is a 6-DOF GSK-RB03A1 robot of Guangzhou CNC Equipment Co., Ltd, as shown in Figure 6

    Experiment results and performance analysis 6.1 Experimental settings Configuration environment for implementation All the RL algorithms are implemented in MATLAB R2018b on an Intel Core i7 CPU running at 3.40 GHz on a Windows machine. Industrial robot for experiment The industrial robot used for experimental ver ification is a 6-DOF GSK-RB03A1 robot of G...

    work page 2000

  10. [10]

    First successful episode is the episode number in which the agent first reaches or crosses one of the terminal states

    work page

  11. [11]

    The determination of convergence is whether the algorithm converges before reaching the maximum number of episodes

    work page

  12. [12]

    A convergence episode is the episode number in which the algorithm converges

    work page

  13. [13]

    Computation time is the time from the start to the end of the program

    work page

  14. [14]

    Return is the return of the last episode

    work page

  15. [15]

    Execution time is the execution time of the optimal trajectory obtained from the last episode. Table 2 Performance percentage by IQL, IA VRL compared with NI-like, NIGM Grid Algorithm Performance percentage of return compared with NI-like and NIGM (%) Performance percentage of optimal trajectory execution time compared with NI-like and NIGM (%) NI-like NI...

    work page 2000

  16. [16]

    In order to construct the reinforcement learning states and decrease the learning dimension, a selective discrete method for discretizing the robotic task path is proposed

    Conclusion In this study, an improved Q -learning algorithm (IQL) and an improved action -value function reinforcement learning algorithm (IA VRL), have been proposed for the time-optimal path tracking problem. In order to construct the reinforcement learning states and decrease the learning dimension, a selective discrete method for discretizing the robo...

    work page 2000

  17. [17]

    M.E. Kahn, B. Roth, The Near -Minimum-Time Control of Open -Loop Articulated Kinematic Chains, Journal of Dynamic Systems, Measurement, and Control, 93 (1971) 164-172. https://doi.org/10.1115/1.3426492

    work page doi:10.1115/1.3426492 1971

  18. [18]

    Pham, A General, Fast, and Robust Implementation of the Time-Optimal Path Parameterization Algorithm, IEEE T ROBOT, 30 (2014) 1533-1540

    Q. Pham, A General, Fast, and Robust Implementation of the Time-Optimal Path Parameterization Algorithm, IEEE T ROBOT, 30 (2014) 1533-1540. https://doi.org/10.1109/TRO.2014.2351113

    work page doi:10.1109/tro.2014.2351113 2014

  19. [19]

    Bobrow, S

    J. Bobrow, S. Dubowsky, J. Gibision, Time -Optimal Control of Robotic Manipulators Along Specified Paths, The International journal of robotics research, 4 (1985) 3-17. https://doi.org/10.1177/027836498500400301

    work page doi:10.1177/027836498500400301 1985

  20. [20]

    K. Shin, N. McKay, Minimum -time con trol of robotic manipulators with geometric path constraints, IEEE T AUTOMAT CONTR, 30 (1985) 531-541. https://doi.org/10.1109/TAC.1985.1104009

    work page doi:10.1109/tac.1985.1104009 1985

  21. [21]

    Slotine, H.S

    J.J.E. Slotine, H.S. Yang, Improving the efficiency of time -optimal path-following algorithms, IEEE Transac tions on Robotics and Automation, 5 (2002) 118-124. https://doi.org/10.1109/70.88024

    work page doi:10.1109/70.88024 2002

  22. [22]

    Timar, R.T

    S.D. Timar, R.T. Farouki, T.S. Smith, C.L. Boyadjieff, Algorithms for time –optimal control of CNC machines along curved tool paths, ROBOT CIM-INT MANUF, 21 (2005) 37-53. https://doi.org/10.1016/j.rcim.2004.05.004

    work page doi:10.1016/j.rcim.2004.05.004 2005

  23. [23]

    Shiller, H

    Z. Shiller, H. Lu, Computation of Path Constrained Time Optimal Motions With Dynamic Singularities, Journal of Dynamic Systems, Measurement, and Control, 114 (1992) 34. https://doi.org/10.1115/1.2896505

    work page doi:10.1115/1.2896505 1992

  24. [24]

    Verscheure, M

    D. Verscheure, M. Diehl, J. De Schutter, J. Swevers, On -line time -optimal path tracking for robots, 2009 IEEE International Conference on Robotics and Automation, 2009, pp. 599 -605. https://doi.org/10.1109/ROBOT.2009.5152274

    work page doi:10.1109/robot.2009.5152274 2009

  25. [25]

    Verscheure, B

    D. Verscheure, B. Demeulenaere, J. Swevers, J. De Schutter, M. Diehl, Time -Optimal Path Tracking for Robots: A Convex Optimization Approach, IEEE T AUTOMAT CONTR, 54 (2009) 2318 -2327. https://doi.org/10.1109/TAC.2009.2028959

    work page doi:10.1109/tac.2009.2028959 2009

  26. [26]

    Debrouwere, W

    F. Debrouwere, W. Van Loock, G. Pipeleers, Q.T. Dinh, M. Diehl, J. De Schutter, J. Swevers, Time -Optimal Path Following for Robots With Convex -Concave Constraints Using Sequential Convex Programming, IEEE T ROBOT, 29 (2013) 1485-1495. https://doi.org/10.1109/TRO.2013.2277565

    work page doi:10.1109/tro.2013.2277565 2013

  27. [27]

    Zhang, S

    Q. Zhang, S. Li, J. Guo, X. Gao, Time-optimal path tracking for robots under dynamics constraints based on convex optimization, ROBOTICA, 34 (2016) 2116-2139. https://doi.org/10.1017/S0263574715000247

    work page doi:10.1017/s0263574715000247 2016

  28. [28]

    Steinhauser, J

    A. Steinhauser, J. Swevers, An Efficient Iterative Learning Approach to T ime-Optimal Path Tracking for Industrial Robots, IEEE T IND INFORM, 14 (2018) 5200-5207. https://doi.org/10.1109/TII.2018.2851963

    work page doi:10.1109/tii.2018.2851963 2018

  29. [29]

    K. Shin, N. McKay, A Dynamic Programming Approach to Trajectory Planning of Robotic Manipulators, IEEE T AUTOMAT CONTR, 31 (1986) 491-500. https://doi.org/10.1109/TAC.1986.1104317

    work page doi:10.1109/tac.1986.1104317 1986

  30. [30]

    Pfeifer, R

    F. Pfeifer, R. Johanni, A concept for manipulator trajectory planning, IEEE Journal on Robotics and Automation, 3 (1987) 115-123. https://doi.org/10.1109/JRA.1987.1087090

    work page doi:10.1109/jra.1987.1087090 1987

  31. [31]

    Kaserer, H

    D. Kaserer, H. Gattringer, A. Mueller, Nearly Optimal Path Following With Jerk and Torque Rate Limits Using Dynamic Programming, IEEE T ROBOT, (2018) 1-8. https://doi.org/10.1109/TRO.2018.2880120

    work page doi:10.1109/tro.2018.2880120 2018

  32. [32]

    Constantinescu, E.A

    D. Constantinescu, E.A. Croft, Smooth and time ‐optimal trajectory plan ning for industrial manipulators along specified paths, Journal of Robotic Systems, 17 (2000) 233 -249. https://doi.org/10.1002/(SICI)1097 - 4563(200005)17:5<233::AID-ROB1>3.0.CO;2-Y

    work page doi:10.1002/(sici)1097 2000

  33. [33]

    Bellman, S.E

    R.E. Bellman, S.E. Dreyfus, Applied Dynamic Programming, Princeton Univ .Press, Princeton,NJ,USA, 1962. https://doi.org/10.2307/2282884

    work page doi:10.2307/2282884 1962

  34. [34]

    Hartmann, Z

    G. Hartmann, Z. Shiller, A. Azaria, Deep reinforcement learning for time optimal velocity control using prior knowledge, arXiv:1811.1615v2, (2019)

    work page arXiv 2019

  35. [35]

    Sutton, A.G

    R.S. Sutton, A.G. Barto, Introduction to Reinforcement Learning, 1st ed., MIT Press, Cambridge, MA, USA, 1998

    work page 1998

  36. [36]

    Erden, K

    M.S. Erden, K. Leblebicioğlu, Free gait generation with reinforcement learning for a six -legged robot, ROBOT AUTON SYST, 56 (2008) 199-212. https://doi.org/https://doi.org/10.1016/j.robot.2007.08.001

    work page doi:10.1016/j.robot.2007.08.001 2008

  37. [37]

    Navarro -Guerrero, C

    N. Navarro -Guerrero, C. Weber, P. Schroeter, S. Wermter, Real -world reinforcement learning for autonomous humanoid robot docking, ROBOT AUTON SYST, 60 (2012) 1400-1407. https://doi.org/10.1016/j.robot.2012.05.019

    work page doi:10.1016/j.robot.2012.05.019 2012

  38. [38]

    E.S. Lo w, P. Ong, K.C. Cheah, Solving the optimal path planning of a mobile robot using improved Q -learning, ROBOT AUTON SYST, 115 (2019) 143-161. https://doi.org/10.1016/j.robot.2019.02.013

    work page doi:10.1016/j.robot.2019.02.013 2019

  39. [39]

    Kober, J.A

    J. Kober, J.A. Bagnell, J. Peters, Reinforcement learning in robotics: A survey, The International Journal of Robotics Research, 32 (2013) 1238-1274. https://doi.org/10.1177/0278364913495721

    work page doi:10.1177/0278364913495721 2013

  40. [40]

    Moreno, C.V

    D.L. Moreno, C.V. Regueiro, R. Iglesias, S. Barro, Making Use of Unelaborated Advice to Improve Reinforcement Learning: A Mobile Robotics Approach, in: S. Singh, M. Singh, C. Apte, P. Perner (Eds.), Springer Berlin Heidelberg, Berlin, Heidelberg, 2005, pp. 89-98. https://doi.org/10.1007/11551188_10

    work page doi:10.1007/11551188_10 2005

  41. [41]

    Craig, Introduction to robotics: mechanics and control, Addison Wesley Pu blishing Company1989

    J.J. Craig, Introduction to robotics: mechanics and control, Addison Wesley Pu blishing Company1989

    work page

  42. [42]

    Watkins, P

    C.J.C.H. Watkins, P. Dayan, Q-learning, MACH LEARN, 8 (1992) 279-292. https://doi.org/10.1007/BF00992698

    work page doi:10.1007/bf00992698 1992

  43. [43]

    Lewis, D

    F.L. Lewis, D. Liu, Reinforcement Learning and Approximate Dynamic Programming for Feedback Control, Wiley- IEEE Press2013

    work page

  44. [44]

    Konar, I.G

    A. Konar, I.G. Chakraborty, S.J. Singh, L.C. Jain, A.K. Nagar, A Deterministic Improved Q -Learning for Path Planning of a Mobile Robot, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 43 (2013) 1141 -1153. https://doi.org/10.1109/TSMCA.2012.2227719

    work page doi:10.1109/tsmca.2012.2227719 2013

  45. [45]

    L. Li, J. Xiao, Y. Zou, T. Zhang, Time -optimal path tracking for robots: A numerical integration -like approach combined with an iterative learning algorithm, Industrial Robot: the international journal of robotics research and application, (2019).(In press, see supplementary document)

    work page 2019

  46. [46]

    Sousa, Dynamic model identification of robot manipulators: Solving the physical feasibility problem, Universidade de Coimbra, Portugal, 2014

    C.D. Sousa, Dynamic model identification of robot manipulators: Solving the physical feasibility problem, Universidade de Coimbra, Portugal, 2014. http://hdl.handle.net/10316/27082

    work page 2014