This paper describes a collection of optimization algorithms for achieving dynamic planning, control, and state estimation for a bipedal robot designed to operate reliably in complex environments. To make challenging locomotion tasks tractable, we describe several novel applications of convex, mixed-integer, and sparse nonlinear optimization to problems ranging from footstep placement to whole-body planning and control. We also present a state estimator formulation that, when combined with our walking controller, permits highly precise execution of extended walking plans over non-flat terrain. We describe our complete system integration and experiments carried out on Atlas, a full-size hydraulic humanoid robot built by Boston Dynamics, Inc.

Optimization-based locomotion planning, estimation, and control design for the atlas humanoid robot

Feel lonely? What about reading books? Book is one of the greatest friends to accompany while in your lonely time. When you have no friends and activities somewhere and sometimes, reading book can be a great choice. This is not only for spending the time, it will increase the knowledge. Of course the b=benefits to take will relate to what kind of book that you are reading. And now, we will concern you to try reading modelling and control of robot manipulators as one of the reading material to finish quickly.

Modelling and Control of Robot Manipulators

The application of deep learning in robotics leads to very specific problems and research questions that are typically not addressed by the computer vision and machine learning communities. In this paper we discuss a number of robotics-specific learning, reasoning, and embodiment challenges for deep learning. We explain the need for better evaluation metrics, highlight the importance and unique challenges for deep robotic learning in simulation, and explore the spectrum between purely data-driven and model-driven approaches. We hope this paper provides a motivating overview of important research directions to overcome the current limitations, and helps to fulfill the promising potentials of deep learning in robotics.

https://journals.sagepub.com/doi/pdf/10.1177/0278364918770733

The limits and potentials of deep learning for robotics

To plan dynamic, whole-body motions for robots, one conventionally faces the choice between a complex, full-body dynamic model containing every link and actuator of the robot, or a highly simplified model of the robot as a point mass. In this paper we explore a powerful middle ground between these extremes. We exploit the fact that while the full dynamics of humanoid robots are complicated, their centroidal dynamics (the evolution of the angular momentum and the center of mass (COM) position) are much simpler. By treating the dynamics of the robot in centroidal form and directly optimizing the joint trajectories for the actuated degrees of freedom, we arrive at a method that enjoys simpler dynamics, while still having the expressiveness required to handle kinematic constraints such as collision avoidance or reaching to a target. We further require that the robot's COM and angular momentum as computed from the joint trajectories match those given by the centroidal dynamics. This ensures that the dynamics considered by our optimization are equivalent to the full dynamics of the robot, provided that the robot's actuators can supply sufficient torque. We demonstrate that this algorithm is capable of generating highly-dynamic motion plans with examples of a humanoid robot negotiating obstacle course elements and gait optimization for a quadrupedal robot. Additionally, we show that we can plan without pre-specifying the contact sequence by exploiting the complementarity conditions between contact forces and contact distance.

/pdf/whole-body-motion-planning-with-centroidal-dynamics-and-full-u337p82it7.pdf

Whole-body motion planning with centroidal dynamics and full kinematics

A wide variety of tactile (touch) sensors exist today for robotics and related applications. They make use of various transduction methods, smart materials and engineered structures, complex electronics, and sophisticated data processing. While highly useful in themselves, effective utilization of tactile sensors in robotics applications has been slow to come and largely remains elusive today. This paper surveys the state of the art and the research issues in this area, with the emphasis on effective utilization of tactile sensors in robotic systems. One specific with the use of tactile sensing in robotics is that the sensors have to be spread along the robot body, the way the human skin is-thus dictating varied 3-D spatio-temporal requirements, decentralized and distributed control, and handling of multiple simultaneous tactile contacts. Satisfying these requirements pose challenges to making tactile sensor modality a reality. Overcoming these challenges requires dealing with issues such as sensors placement, electronic/mechanical hardware, methods to access and acquire signals, automatic calibration techniques, and algorithms to process and interpret sensing data in real time. We survey this field from a system perspective, recognizing the fact that the system performance tends to depend on how its various components are put together. It is hoped that the survey will be of use to practitioners designing tactile sensing hardware (whole-body or large-patch sensor coverage), and to researchers working on cognitive robotics involving tactile sensing.

Directions Toward Effective Utilization of Tactile Skin: A Review

A control system for achieving high-speed torque for a joint of a robot includes a printed circuit board assembly (PCBA) having a collocated joint processor and high-speed communication bus The PCBA may also include a power inverter module (PIM) and local sensor conditioning electronics (SCE) for processing sensor data from one or more motor position sensors Torque control of a motor of the joint is provided via the PCBA as a high-speed torque loop Each joint processor may be embedded within or collocated with the robotic joint being controlled Collocation of the joint processor, PIM, and high-speed bus may increase noise immunity of the control system, and the localized processing of sensor data from the joint motor at the joint level may minimize bus cabling to and from each control node The joint processor may include a field programmable gate array (FPGA)

/pdf/integrated-high-speed-torque-control-system-for-a-robotic-3fqoflek8a.pdf

Integrated high-speed torque control system for a robotic joint

We propose a new method for simplifying semidefinite programs (SDP) inspired by symmetry reduction. Specifically, we show if an orthogonal projection map satisfies certain invariance conditions, restricting to its range yields an equivalent primal–dual pair over a lower-dimensional symmetric cone—namely, the cone-of-squares of a Jordan subalgebra of symmetric matrices. We present a simple algorithm for minimizing the rank of this projection and hence the dimension of this subalgebra. We also show that minimizing rank optimizes the direct-sum decomposition of the algebra into simple ideals, yielding an optimal “block-diagonalization” of the SDP. Finally, we give combinatorial versions of our algorithm that execute at reduced computational cost and illustrate effectiveness of an implementation on examples. Through the theory of Jordan algebras, the proposed method easily extends to linear and second-order-cone programming and, more generally, symmetric cone optimization.

/pdf/dimension-reduction-for-semidefinite-programs-via-jordan-4sdf2t3q6c.pdf

Dimension reduction for semidefinite programs via Jordan algebras

We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible solution (a frequent output of parsers) by solving a sequence of easier optimization problems and could be a useful pre-processing technique for SDP solvers. We demonstrate effectiveness of the method on SDPs arising in practice, and describe our publicly-available software implementation. We also show how to find maximum rank matrices in our PSD cone approximations (which helps us find maximal simplifications), and we give a post-processing procedure for dual solution recovery that generally applies to facial-reduction-based pre-processing techniques. Finally, we show how approximations can be chosen to preserve problem sparsity.

Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone

We explore region of attraction (ROA) estimation for polynomial systems via the numerical solution of polynomial equations. Computing an optimal, stable sub-level set of a Lyapunov function is first posed as a polynomial optimization problem. Solutions to this optimization problem are found by solving a polynomial system of equations using techniques from numerical algebraic geometry. This system describes KKT points and singular points not satisfying a regularity condition. Though this system has exponentially many solutions, the proposed method trivially parallelizes and is practical for problems of moderate dimension and degree. In suitably generic settings, the method can solve the underlying optimization problem to arbitrary precision, which could make it a useful tool for studying popular semidefinite programming based relaxations used in ROA analysis.

/pdf/a-numerical-algebraic-geometry-approach-to-regional-3ix9yp7uma.pdf

A numerical algebraic geometry approach to regional stability analysis of polynomial systems

Control Lyapunov functions (CLFs) and control barrier functions (CBFs) are widely used tools for synthesizing controllers subject to stability and safety constraints. Paired with online optimization, they provide stabilizing control actions that satisfy input constraints and avoid unsafe regions of state-space. Designing CLFs and CBFs with rigorous performance guarantees is computationally challenging. To certify existence of control actions, current techniques not only design a CLF/CBF, but also a nominal controller. This can make the synthesis task more expensive, and performance estimation more conservative. In this work, we characterize polynomial CLFs/CBFs using sum-of-squares conditions, which can be directly certified using convex optimization. This yields a CLF and CBF synthesis technique that does not rely on a nominal controller. We then present algorithms for iteratively enlarging estimates of the stabilizable and safe regions. We demonstrate our algorithms on a 2D toy system, a pendulum and a quadrotor.

Frank Noble Permenter

Papers

Integrated high-speed torque control system for a robotic joint

Dimension reduction for semidefinite programs via Jordan algebras

Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone

A numerical algebraic geometry approach to regional stability analysis of polynomial systems

Convex synthesis and verification of control-Lyapunov and barrier functions with input constraints