Kinematically Constrained Workspace Control via Linear Optimization
Kinematically Constrained Workspace Control via Linear Optimization Zachary Kingston, Neil Dantam, and Lydia Kavraki Motivation Need efficient workspace control ● Honor limits of the manipulator ● Avoid large accelerations and singularities ●
Solution Introduces new workspace controller: Linearly Constrained 3 Cartesian Control (LC ) ● Enforces joint constraints ● Demonstrated on physical & simulated manipulators ●
Problem Formulation ● Given a workspace reference velocity X˙ r and the joint limits: q¨ max , q¨ min , q˙ max , q˙ min , q min , and q max ● Find q˙ u, the command joint velocity ● Objective function optimizes workspace acceleration ● Acceleration is used for feedback ● Dot product is used to maximize similarity ● Vectors modified to be non-negative based on sign of X¨ r
Joint Constraints
UR10 Simulation
Results LP vs. QP ● Previous methods use QP [2, 3, 4] ● Difference lies in objective function (L1 vs. L2 norm) ● Testing shows LP is effective ● QP is twice as slow as LP (Using CGAL)
Baxter Experiment
LC3 is implemented with lp_solve and BLAS ● Demonstrated on simulated UR10 and Baxter & a physical Baxter [1] ● Compared with Jacobian DLS (Damped Least-Squares) ● Runs at real-time control rates (>1 kHz) ●
Large Initial Spike
Bounded Velocity
Feedback Noise
[1] Yoshihiko Nakamura and Hideo Hanafusa. Inverse kinematic solutions with singularity robustness for robot manipulator control. Journal of Dynamic Systems, Measurement, and Control (108):163–171, 1986. [2] Adrien Escande, Nicolas Mansard, and Pierre-Brice Wieber. Hierarchical quadratic programming: Fast online humanoid-robot motion generation. The International Journal of Robotics Research, 33(7):1006–1028, June 2014. [3] Inhyeok Kim and Jun-Ho Oh. Inverse kinematic control of humanoids under joint constraints. International Journal of Advanced Robotic Systems, January 2013. [4] Maurice Fallon, Scott Kuindersma, Sisir Karumanchi, et al. An architecture for online affordance-based perception and whole-body planning. Journal of Field Robotics, 32(2):229–254, 2015.
Supported by NSF IIS 1317849 and funds by Rice University
My Website: zacharykingston.me
Lab Website: kavrakilab.org
Solution Introduces new workspace controller: Linearly Constrained 3 Cartesian Control (LC ) ● Enforces joint constraints ● Demonstrated on physical & simulated manipulators ●
Problem Formulation ● Given a workspace reference velocity X˙ r and the joint limits: q¨ max , q¨ min , q˙ max , q˙ min , q min , and q max ● Find q˙ u, the command joint velocity ● Objective function optimizes workspace acceleration ● Acceleration is used for feedback ● Dot product is used to maximize similarity ● Vectors modified to be non-negative based on sign of X¨ r
Joint Constraints
UR10 Simulation
Results LP vs. QP ● Previous methods use QP [2, 3, 4] ● Difference lies in objective function (L1 vs. L2 norm) ● Testing shows LP is effective ● QP is twice as slow as LP (Using CGAL)
Baxter Experiment
LC3 is implemented with lp_solve and BLAS ● Demonstrated on simulated UR10 and Baxter & a physical Baxter [1] ● Compared with Jacobian DLS (Damped Least-Squares) ● Runs at real-time control rates (>1 kHz) ●
Large Initial Spike
Bounded Velocity
Feedback Noise
[1] Yoshihiko Nakamura and Hideo Hanafusa. Inverse kinematic solutions with singularity robustness for robot manipulator control. Journal of Dynamic Systems, Measurement, and Control (108):163–171, 1986. [2] Adrien Escande, Nicolas Mansard, and Pierre-Brice Wieber. Hierarchical quadratic programming: Fast online humanoid-robot motion generation. The International Journal of Robotics Research, 33(7):1006–1028, June 2014. [3] Inhyeok Kim and Jun-Ho Oh. Inverse kinematic control of humanoids under joint constraints. International Journal of Advanced Robotic Systems, January 2013. [4] Maurice Fallon, Scott Kuindersma, Sisir Karumanchi, et al. An architecture for online affordance-based perception and whole-body planning. Journal of Field Robotics, 32(2):229–254, 2015.
Supported by NSF IIS 1317849 and funds by Rice University
My Website: zacharykingston.me
Lab Website: kavrakilab.org
